Body Size: The Structure and Function of Aquatic Ecosystems

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Body Size: The Structure and Function of Aquatic Ecosystems Ecologists have long struggled to predict features of ecological systems, such as the numbers and diversity of organisms. The wide range of body sizes in ecological communities, from tiny microbes to large animals and plants, is emerging as the key to prediction. Based on the relationship of body size with key biological rates and with the physical world experienced by aquatic organisms, we may be able to understand patterns of abundance and diversity, biogeography, interactions in food webs and the impact of fishing, adding up to a potential ‘periodic table’ for ecology. Remarkable progress on the unravelling, describing and modelling of aquatic food webs, revealing the fundamental role of body size, makes a book emphasizing marine and freshwater ecosystems particularly apt. Here, the importance of body size is examined at a range of scales, yielding broad perspectives that will be of interest to professional ecologists, from students to senior researchers. A L A N G . H I L D R E W is Professor of Ecology in the School of Biological and Chemical Sciences at Queen Mary, University of London. D A V I D G . R A F F A E L L I is Professor of Environmental Science at the University of York. R O N N I E D M O N D S - B R O W N is a Senior Lecturer in Environmental Sciences at the University of Hertfordshire.

Body Size The Structure and Function of Aquatic Ecosystems Edited by ALAN G. HILDREW School of Biological and Chemical Sciences, Queen Mary, University of London, UK

DAVID G. RAFFAELLI Environment Department, University of York, UK

RONNI EDMONDS-BROWN Division of Geography and Environmental Sciences, University of Hertfordshire, UK

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521861724 © British Ecological Society 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2007 eBook (EBL) ISBN-13 978-0-511-29508-9 ISBN-10 0-511-29508-1 eBook (EBL) ISBN-13 ISBN-10

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ISBN-13 ISBN-10

paperback 978-0-521-67967-1 paperback 0-521-67967-2

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Contents

List of contributors Preface

page vii ix

1 The metabolic theory of ecology and the role of body size in marine and freshwater ecosystems

James H. Brown, Andrew P. Allen and James F. Gillooly

1

2 Body size and suspension feeding

Stuart Humphries

16

3 Life histories and body size 4

5

6

7 8

9 10

David Atkinson and Andrew G. Hirst Relationship between biomass turnover and body size for stream communities Alexander D. Huryn and Arthur C. Benke Body size in streams: macroinvertebrate community size composition along natural and human-induced environmental gradients Colin R. Townsend and Ross M. Thompson Body size and predatory interactions in freshwaters: scaling from individuals to communities Guy Woodward and Philip Warren Body size and trophic cascades in lakes J. Iwan Jones and Erik Jeppesen Body size and scale invariance: multifractals in invertebrate communities Peter E. Schmid and Jenny M. Schmid-Araya Body size and biogeography B. J. Finlay and G. F. Esteban By wind, wings or water: body size, dispersal and range size in aquatic invertebrates Simon D. Rundle, David T. Bilton and Andrew Foggo

33

55

77

98 118

140 167

186

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CONTENTS

11 Body size and diversity in marine systems 12

13 14 15

16 17

Richard M. Warwick Interplay between individual growth and population feedbacks shapes body-size distributions Lennart Persson and Andre´ M. De Roos The consequences of body size in model microbial ecosystems Owen L. Petchey, Zachary T. Long and Peter J. Morin Body size, exploitation and conservation of marine organisms Simon Jennings and John D. Reynolds How body size mediates the role of animals in nutrient cycling in aquatic ecosystems Robert O. Hall, Jr., Benjamin J. Koch, Michael C. Marshall, Brad W. Taylor and Lusha M. Tronstad Body sizes in food chains of animal predators and parasites Joel E. Cohen Body size in aquatic ecology: important, but not the whole story Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown

Index

210

225 245 266

286 306 326 335

Contributors

Andrew P. Allen National Center for Ecological Analysis and Synthesis, Santa Barbara, CA 93101, USA. David Atkinson Population and Evolutionary Biology Research Group, School of Biological Sciences, The University of Liverpool, Biosciences Building, Crown Street, Liverpool L69 7ZB, UK. Arthur C. Benke Aquatic Biology Program, Box 870206, Department of Biological Sciences, University of Alabama, Tuscaloosa, AL 35487-0206, USA. David T. Bilton Marine Biology and Ecology Research Centre, University of Plymouth, Plymouth PL4 8AA, UK. James H. Brown Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA. Joel E. Cohen Laboratory of Populations, Rockefeller and Columbia Universities, 1230 York Avenue, Box 20, New York, NY 10021-6399, USA. Andre´ M. De Roos Institute of Biodiversity and Ecosystems, University of Amsterdam, P.O.B. 94084, NL-1090 GB Amsterdam, the Netherlands. Ronni Edmonds-Brown Division of Geography and Environmental Sciences, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK.

G. F. Esteban School of Biological and Chemical Sciences, Queen Mary, University of London, East Stoke, Wareham Dorset BH20 6BB, UK. B. J. Finlay School of Biological and Chemical Sciences, Queen Mary, University of London, East Stoke, Wareham Dorset BH20 6BB, UK. Andrew Foggo Marine Biology and Ecology Research Centre, University of Plymouth, Plymouth PL4 8AA, UK. James F. Gillooly Department of Zoology, University of Florida, Gainesville, FL 32607, USA. Robert O. Hall, Jr. Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Alan G. Hildrew School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK. Andrew G. Hirst British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK. Stuart Humphries Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK. Alexander D. Huryn Aquatic Biology Program, Box 870206, Department of

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LIST OF CONTRIBUTORS

Biological Sciences, University of Alabama, Tuscaloosa, AL 35487-0206, USA. Simon Jennings Centre for Environment, Fisheries and Aquaculture Science (CEFAS), Lowestoft Laboratory, NR33 0HT, UK. Erik Jeppesen Department of Freshwater Ecology, National Environmental Research Institute, Denmark and Department of Plant Biology, University of Aarhus, Ole Worms Alle´, Aarhus, Denmark. J. Iwan Jones Centre for Ecology and Hydrology Dorset, Dorchester DT2 8ZD, UK. Benjamin J. Koch Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Zachary T. Long Institute of Marine Sciences, University of North Carolina at Chapel Hill, 3431 Arendell Street, Morehead City, NC 28557 and Virginia Institute of Marine Science, The College of William and Mary, Gloucester Point, VA 23062. Michael C. Marshall Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Peter J. Morin Department of Ecology, Evolution & Natural Resources, 14 College Farm Rd., Cook College, Rutgers University, New Brunswick, NJ 08901, USA. Lennart Persson Department of Ecology and Environmental Science, Umea8 University, S-901 87 Umea8 , Sweden. Owen L. Petchey Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 1SA, UK. David G. Raffaelli Environment Department, University of York, Heslington, York Y010 SDD, UK.

John D. Reynolds Department of Biological Sciences, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada. Simon D. Rundle Marine Biology and Ecology Research Centre, University of Plymouth, Plymouth PL4 8AA, UK. Peter E. Schmid School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK and Institute of Freshwater Ecology, University of Vienna, 1090 Wien, Althanstrasse 14, Austria. Jenny M. Schmid-Araya School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK. Brad W. Taylor Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Ross M. Thompson School of Biological Sciences, Building 18, Monash University, Victoria 3800, Australia. Colin R. Townsend Department of Zoology, University of Otago, 340 Great King Street, Dunedin 9054, New Zealand. Lusha M. Tronstad Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Philip Warren Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK. Richard M. Warwick Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth, PL1 3DH, UK. Guy Woodward School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK.

Preface

More than ten years ago, two of us (AGH and DGR) were lucky enough to edit a previous symposium of the British Ecological Society (BES) – Aquatic Ecology: Scale, Pattern and Process (Giller, Hildrew & Raffaelli, 1994). In the Introduction to that volume, we pointed out that the BES had not devoted a single previous symposium to aquatic ecosystems. Evidently we did not change the culture, since the Body Size symposium held at the University of Hertfordshire in September 2005 was only the second! Aquatic Ecology: Scale, Pattern and Process had two objectives: (i) to explore how the scale of approach affected the patterns that were detected and the processes that appeared to be important, and (ii) to compare freshwater and marine ecosystems. In Body Size: The Structure and Function of Aquatic Ecosystems, both those questions of scale and comparison among systems are very much still alive as continuing themes. Body size determines overwhelmingly the scale at which organisms perceive and navigate through their physical world, and the contrasts between freshwater and marine ecosystems remain evident. Body size is a species trait with implications beyond scale, however, and we believe that the present volume shows that more similarities than differences are evident among the diverse aquatic systems considered. Indeed, several authors argue here that fundamental ecological processes are revealed by comparing marine, freshwater and terrestrial systems. In organizing this meeting, we were well aware of the increasing interest in body size from the wider ecological community over the past 30 years, as well as the technical challenge involved in exploring body-size data. Of course, the fascination with body size has a much longer history in ecology and was prominent in the writings, for example, of Alfred Wallace (1858) and Charles Elton (1927), the latter having discussed at length its relevance to trophic interactions (see review by Warren, 2005). It was R. H. Peters’ (1983) elegant exposition of the physiological, environmental and ecological correlates of body size that re-ignited modern interest, however, and which led indirectly to an explosion in the macroecological literature over the past ten years (Blackburn & Gaston, 2003), to the metabolic theory of ecology (Brown et al., 2004) and indeed to this present volume. All of the papers presented at the Hatfield meeting connect

x

PREFACE

with one or more of these themes and in many cases attempt to integrate aspects of body-size research that were previously treated separately. A focus on aquatic systems seemed appropriate because aquatic ecologists have historically been particularly prominent in the debate. Thus, Hardy (1924) was amongst the first to point out the significance of ontogenic (sized-based) shifts in the food webs supporting fisheries, Ryther (1969) illustrated the effects of predator and prey body sizes on food-chain length and global patterns of marine productivity, whilst Hutchinson (1959) provided a classic account of body size and species coexistence. It may well be that patterns and processes related to body size are particularly important in aquatic systems, or at least are more obvious. We asked the author(s) of each paper to examine the importance and role of body size in the systems in which they work. Essentially the book builds from the level of the individual and a consideration of body size as a species trait (Humphries; Atkinson & Hirst; Huryn & Benke; Townsend & Thompson), through food webs and communities (Woodward & Warren; Jones & Jeppesen; Schmid & Schmid-Araya), to body-size related macroecological patterns in aquatic systems (Finlay & Esteban; Rundle, Bilton & Foggo; Warwick), to dynamics and patterns in whole communities and ecosystems (Persson & De Roos; Petchey, Long & Morin; Jennings & Reynolds; Hall et al.; Cohen). Jim Brown and colleagues set the scene with a ‘wet’ exposition of metabolic theory, and although we did not ask contributors explicitly to test these ideas several did. The meeting certainly generated an old-fashioned sense of community and of excitement in what people had to say, though it was just as apparent how fragmented the community is, as was reflected in the examples chosen to illustrate particular points and the literature cited by authors from different ‘stables’ and backgrounds. We hope that this book reflects just a little of this excitement and serves as a useful synthesis of this area of ecology. Finally, we wish to thank all the contributors for their efforts and remarkable efficiency, the British Ecological Society and the Freshwater Biological Association for their support, and the local organizers at the University of Hertfordshire for all their hard work. Alan Hildrew, Dave Raffaelli, Ronni Edmonds-Brown.

References Blackburn, T. M. & Gaston, K. J. (2003). Macroecology: Concepts and Consequences. Oxford: Blackwell Science. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789.

Elton, C. S. (1927). Animal Ecology. London: Sidgwick & Jackson Ltd. Giller, P. S., Hildrew, A. G. & Raffaelli, D. G. (eds.) (1994). Aquatic Ecology: Scale, Pattern and Process. The 34th Symposium of the British Ecological Society. Oxford: Blackwell Science.

PREFACE

Hardy, A. C. (1924). The herring in relation to its animate environment. Part 1. The food and feeding habits of the herring with special reference to the east coast of England. Fisheries Investigations Series II, 7(3), 1–53. Hutchinson, G. E. (1959). Homage to Santa Rosalia, or why are there so many kinds of animals? American Naturalist, 32, 571–581. Peters, R. H. (1983). The Ecological Implications of Body Size. New York: Cambridge University Press. Ryther, J. H. (1969). Photosynthesis and fish production in the sea. Science, 166, 72–76.

Wallace, A. R. (1858). On the tendency of varieties to depart indefinitely from the orginal type. In C. R. Darwin and A. R. Wallace: On the tendency of species to form varieties, and on the perpetuation of varieties and species by natural selection. Journal of the Proceedings of the Linnean Socioty, Zoology, 20 August 1858, 3, 45–62. Warren, P. H. (2005). Wearing Elton’s wellingtons: why body size still matters in food webs. In Dynamic Food Webs: Multispecies Assemblages, Ecosystem Development, and Environmental Change, eds. P. C. de Ruiter, V. Wolters & J. C. Moore. San Diego: Academic Press.

xi

CHAPTER ONE

The metabolic theory of ecology and the role of body size in marine and freshwater ecosystems JAMES H . BROWN University of New Mexico, Albuquerque

ANDREW P . ALLEN National Center for Ecological Analysis and Synthesis, Santa Barbara

JAMES F . GILLOOLY University of Florida, Gainesville

Introduction Body size is the single most important axis of biodiversity. Organisms range in body size over about 22 orders of magnitude, from tiny bacteria such as Mycoplasma weighing 1013 g to giant Sequoia trees weighing 109 g. Such size variation is a pervasive feature of aquatic ecosystems, where the size spectrum spans at least 20 orders of magnitude, from the smallest free-living bacteria at about 1012 g to the great whales at about 108 g (e.g., Sheldon et al., 1972; Kerr & Dickie, 2001). Nearly all characteristics of organisms, from their structure and function at molecular, cellular and whole-organism levels to ecological and evolutionary dynamics, are correlated with body size (e.g., Peters, 1983; McMahon & Bonner, 1983; Calder, 1984; Schmidt-Nielsen, 1984). These relationships are almost always well described by allometric equations, power functions of the form: Y ¼ Y0 Mb

(1:1)

where Y is a measure of some attribute, Y0 is a normalization constant, M is body mass, and b is a scaling exponent (Thompson, 1917; Huxley, 1932). A longstanding puzzle has been why empirically estimated values of b are typically close to multiples of 1/4: 3/4 for whole-organism metabolic rates (Savage et al., 2004a) and rates of biomass production (Ernest et al. 2003), 1/4 for mass-specific metabolic rates and most other biological rates such as the turnover of cellular constituents (Gillooly et al., 2005a), population growth rates (Savage et al., 2004b) and rates of molecular evolution (Gillooly et al., 2005b), and 1/4 for biological times such as cell cycle time, lifespan and generation time (Gillooly et al., 2001, 2002). Recent theoretical advances in biological scaling and metabolism represent tremendous progress in solving this puzzle. The pervasive quarter-power Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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exponents are due to the fractal-like design of the networks and surfaces that supply energy and materials used by cells in biological metabolism (West et al., 1997, 1999). One additional advance has strengthened and extended this theoretical foundation. The well documented exponential effect of temperature on metabolic rate can be incorporated by adding a Boltzmann–Arrhenius factor, e E/kT, to Eq. (1.1). Whole organism metabolic rate or production, P, can then be expressed as: P ¼ P0 M3=4 eE=kT

(1:2)

where E is the activation energy, k is Boltzmann’s constant (8.62  105 eV/K), and T is absolute temperature in degrees Kelvin (Gillooly et al., 2001, 2002). Therefore, mass-specific metabolic rate, B, and most other rates can be expressed as: B ¼ P=M ¼ B0 M1=4 eE=kT

(1:3)

where B0 is another normalization constant. The addition of temperature to this model proved critical to the development of a metabolic theory of ecology (MTE) (Brown et al., 2004). MTE incorporates these fundamental effects of body size and temperature on individual metabolic rate to explain patterns and processes at different levels of biological organization: from the life histories of individuals, to the structure and dynamics of populations and communities, to the fluxes and pools of energy and materials in ecosystems. Brown et al. (2004) began to develop MTE in some detail, made many testable predictions, and evaluated some of these predictions, using data compiled from the literature for a wide variety of ecological phenomena, taxonomic and functional groups of organisms, and types of ecosystems. Here we apply the metabolic theory of ecology to focus on some important correlates and consequences of body size in marine and freshwater ecosystems. In so doing, we build on a rich tradition that extends back over a century. Many of the most eminent aquatic ecologists have contributed. Several themes have been pursued. With respect to population dynamics and species interactions, this includes work from Gause (1934), Hutchinson (1959), Brooks and Dodson (1965), Paine (1974), Leibold and Wilbur (1992) and Morin (1995, 1999). With respect to distributions of biomass, abundance and energy use across species, this includes work from Sheldon and Parsons (1967), Sheldon et al. (1972, 1977), Cyr and Peters (1996) and Kerr and Dickie (2001). With respect to food webs, this includes work from Lindeman (1942), Odum (1956), Hutchinson (1959), Carpenter and Kitchell (1988), Sprules and Bowerman (1988) and Cohen et al. (2003). Finally, with respect to nutrient relations and ecological stochiometry, this includes work from Redfield (1958), Schindler (1974), Wetzel (1984) and, more recently, Sterner and Elser (2002). Many of these themes have been addressed by the contributors to this volume.

THE METABOLIC THEORY OF ECOLOGY

MTE provides a conceptual framework for understanding the diverse effects of body size in aquatic ecosystems (see also Peters, 1983; Cyr & Pace, 1993; Cyr, 2000; Kerr & Dickie, 2001; Gillooly et al., 2002; Brown & Gillooly, 2003; Brown et al., 2004; Allen et al., 2005; Gillooly et al., 2006). MTE is based on wellestablished fundamental principles of physics, chemistry and biology, makes explicit, testable, quantitative predictions, and synthesizes the roles of individual organisms in populations, communities and ecosystems. The literature on body size and metabolism in general, and on aquatic ecosystems in particular, is too vast to summarize here. The references cited above and below are just a few of the relevant publications, but they will give the interested reader a place to start.

Background For what follows, we will assume that Eqs. (1.2) and (1.3) capture the fundamental effects of body size and temperature on metabolic rate. As the examples below will show, these equations do not account for all observed variation. They do, however, usually account for a substantial portion of the variation within and across species, taxonomic and functional groups, and in ecosystems where body size varies by orders of magnitude. Moreover, fitting Eq. (1.2) or (1.3) to data generates precise quantitative predictions that can be used as a point of departure to evaluate the many factors that may contribute to the residual variation. These include experimental and measurement error, phylogenetic and environmental constraints, influences of stoichiometry, and the effects of acclimation, acclimatization and adaptation. Since we present Eqs. (1.2) and (1.3) as assumptions, it is important to state that MTE and the underlying models for the scaling of metabolic rate and other processes with body size and temperature have received both enthusiastic support and severe criticism. We will not cite or review these issues and references here, but simply state that we are confident that most substantive criticisms have been or will be answered, and that the theory is fundamentally sound. This volume and this chapter are on the effects of body size on the structure and dynamics of aquatic ecosystems. Metabolic rate, and other rate processes controlled by metabolic rate, are strongly affected by both body size and temperature. We can ‘correct’ for variation due to environmental or body temperature by taking logarithms of both sides of Eq. (1.3) and rearranging terms to give: lnðBeE=kT Þ ¼ ð1=4Þ ln ðMÞ þ ln ðB0 Þ

(1:4) 5

where k is Boltzmann’s constant (¼ 8.62  10 eV/K) and E is the average activation of metabolic reactions (0.65 eV; see Brown et al., 2004). Equation (1.4) shows that, after correcting for temperature, ln(BeE/kT) is predicted to be a linear function of ln(M) with a slope of 1/4. Other allometric scaling relations can be similarly analyzed using equations that have different values for the

3

J. H. BROWN ET AL.

normalization constants and sometimes for the exponents, e.g. 3/4 for wholeorganism metabolic rate (Eq. (1.2)). In aquatic ecosystems, it is reasonable to assume that the body temperature of an ectotherm is equal to water temperature. Thus, coexisting species of prokaryotes, phytoplankton, protists, zooplankton, other invertebrates and fish can usually be assumed to have the same body temperature. Additionally, since daily and seasonal variations in water temperatures are relatively modest, it is often reasonable to take some average value. Correction for variation in temperature is particularly important when comparing locations or seasons that differ substantially in water temperature, and when comparing ectotherms and endotherms, which differ substantially in body temperature. In this chapter we have followed these procedures, and corrected for temperature variation when appropriate.

Individual level: metabolic rate, production and life-history traits We begin at the level of the individual organism. The first question is whether metabolic rate varies with body size as predicted by Eqs. (1.2) and (1.3). In Fig. 1.1, we present temperature-corrected data for whole-organism metabolic rates of aquatic unicellular eukaryotes, invertebrates and fish. Note that the predicted slopes of these relationships are close to 3/4. It is apparent that the observed values cluster around and do not differ significantly from these slopes. These data confirm a large literature on the body-size dependence of metabolic rates in a wide variety of aquatic organisms, from unicellular algae and protists to invertebrates and fish (e.g., Hemmingsen, 1960; Fenchel & Finlay, 1983). Note also that there is considerable variation around these relationships. It may appear to be random scatter, but further analysis would probably suggest that much of it is due to some combination of experimental error, differences in techniques, evolutionary constraints related to phylogenetic relationships,

30 In(metabolic rate *eE/kT)

4

fish invertebrates unicells

y = 0.74x + 20.89 2 r = 0.79

y = 0.73x + 19.74 2 r = 0.97

10 y = 0.70x + 18.24 r 2 = 0.97

–10

–30

0 ln(body mass)

30

Figure 1.1 The relationship between temperature-corrected metabolic rate, measured in watts, and the natural logarithm of body mass, measured in grams. Metabolic rate is temperature corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Gillooly et al. (2001).

THE METABOLIC THEORY OF ECOLOGY

ln(production * eE/kT)

40 fish algae zooplankton

15

y = 0.76x + 25.04 r 2 = 0.99

–10 –40

–10 ln(body mass)

20

Figure 1.2 The relationship between temperature-corrected biomass production rate, measured in grams per individual per year, and the natural logarithm of body mass, measured in grams. Metabolic rate is temperature corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Ernest et al. (2003).

body plan, stoichiometry, as well as acclimatization, acclimation and adaptation to different environmental conditions. The metabolism of an individual organism reflects the energy and material transformations that are used for both the maintenance of existing structure and the production of new biomass. Within taxonomic and functional groups, organisms allocate a relatively constant fraction of metabolism to production (Ernest et al., 2003). In endotherms, this is typically less than 10%, but in ectotherms it tends to be of the order of 50%. Consequently, rates of wholeorganism biomass production are predicted to scale according to Eq. (1.2), with an allometric exponent of 3/4, the same as whole-organism metabolic rate. Figure 1.2 shows that the temperature-corrected rates of production for algae, zooplankton and fish cluster closely around a common allometric scaling relation with an exponent of 0.76, almost identical to the theoretically predicted value of 3/4. This implies that the relative allocation of energy and materials to biomass production is indeed similar across most organisms. It follows from the above discussion and Eq. (1.3) that the mass-specific rate of ontogenetic growth and development should scale as M1/4, and therefore that developmental time should scale as M1/4. In Fig. 1.3, we present two examples, rates of ontogenetic development of zooplankton eggs in the laboratory (panel A) and fish eggs in the field (panel B) (Gillooly et al., 2002). This is a nice model system, because the mass of the egg indicates not only the size of the hatchling, but also the quantity of resources stored in the egg and expended in metabolism during the course of development. Note that the data for fish eggs in the field give an exponent, 0.22, very close to the predicted 1/4, but there is considerable unexplained variation. This is hardly surprising, giving the inherent difficulties in measuring both development time and temperature under field conditions. The data for development rate of freshwater zooplankton eggs measured under controlled conditions in the laboratory give an allometric exponent, 0.26, essentially identical to the predicted 1/4. The regression explains 84% of the observed

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J. H. BROWN ET AL.

(a)

(b) 26 In(hatching rate *eE/kT)

26 In(hatching rate *eE/kT)

6

24 y = –0.26x + 20.37 r2 = 0.84

22

24

y = –0.22x + 22.49 r2 = 0.24 22

–20

–7.5 ln(body mass)

–10

–8

–6

–4

ln(body mass)

Figure 1.3 The relationship between temperature-corrected hatching rate, measured in 1/days, and the natural logarithm of body mass, measured in grams, for zooplankton eggs in the laboratory (panel A) and fishes in the field (panel B). Hatching rate is temperature-corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Gillooly et al. (2002).

variation in the temperature-corrected data. Interestingly, for ontogenetic growth rates of adult zooplankton, Gillooly et al. (2002) have shown that stoichiometry, specifically the whole-body C:P ratio, explains most of the variation that remains after accounting for the effects of body size and temperature. This supports the ‘growth-rate hypothesis’ and the large body of theoretical and empirical work in ecological stoichiometry (Elser et al., 1996; Elser et al., 2000; Sterner & Elser, 2002). The growth-rate hypothesis proposes that differences in the C:N:P ratios of organisms are due to differences in the allocation of phosphorus-rich RNA necessary for growth. For these zooplankton, living in freshwater where phosphorus may be the primary limiting nutrient, rates of metabolism and ontogenetic growth are limited by whole-body concentrations of RNA. Not only does the C:P ratio explain most of the residual variation in development rates as a function of body size in zooplankton, but it is also related to the body-size dependence of development itself. Whole-body concentrations of phosphorus-rich RNA scale inversely with body size, with an exponent of approximately 1/4 in both aquatic and terrestrial organisms (Gillooly et al., 2005a). Therefore, this example shows how a quantitative prediction from metabolic theory can be used to assess the influence of other factors, such as stoichiometry, which may account for much of the remaining variation. Since times are reciprocals of rates, metabolic theory predicts that biological times should scale with characteristic powers of 1/4. Figure 1.4 shows data for one such time, maximal lifespan, for a variety of aquatic animals ranging from zooplankton to fish. The slope of this relationship, 0.23, is very close to the theoretically predicted value of 1/4, and the fitted regression accounts for the

THE METABOLIC THEORY OF ECOLOGY

In(lifespan/e E/kT)

–10 zooplankton amphipods molluscs fish

–20

y = 0.23x – 19.74 r 2 = 0.98

–30 –20

–10

0

ln(body mass)

10

Figure 1.4 The relationship between temperature-corrected maximum lifespan, measured in days, and the natural logarithm of body mass, measured in grams, for various aquatic organisms. Lifespan is temperature-corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Gillooly et al. (2001).

vast majority of variation (r2 ¼ 0.98). The enormous variation in body size across these organisms masks considerable unexplained residual variation. It is well established that even closely related animals of the same body size can differ in lifespan by at least an order of magnitude. If the first-order effect of temperature had not been removed, then there would have been even more variation, with species in cold-water environments living longer than those of similar size in warmer waters.

Population and community levels: growth, mortality and abundance There are two logical benchmarks to measure population growth rate: the maximal rate, rmax, and the rate of turnover at steady state. Data on rmax for a wide variety of organisms, from unicellular eukaryotes to invertebrates and vertebrates, have been compiled and analyzed by Savage et al. (2004b). These data give a slope of 0.23, very close to the predicted 1/4. We have extracted and plotted the subset of these data for aquatic organisms, including algae, zooplankton and fish in Fig. 1.5. The slope is a bit lower, 0.20, but the confidence intervals still include the predicted value of 1/4. We conclude that maximal population-growth rates scale similarly to mass-specific metabolic rate and follow Eq. (1.3). This is not surprising, since metabolism fuels individual production, which in turn fuels population growth, thereby determining rmax. The rate of population turnover, and hence birth and death rates, should scale similarly. Figure 1.6 shows the body-mass dependence of mortality rates of fish in the field. The fitted regression has a slope of 0.24, very close to the predicted value of 1/4. The 1/4 power scaling of natural mortality may come as a surprise to many ecologists because mortality in the field is generally thought to be controlled by extrinsic environmental conditions, such as predation, food shortage or abiotic stress, rather than to intrinsic biological traits such as metabolic rate. The majority of mortality may indeed be due to predation or

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J. H. BROWN ET AL.

30

In( rmax*eE/kT )

algae zooplankton fish

25

20

y = –0.20x + 21.90 r2 = 0.97 15 –30

–5

20

ln(body mass)

28

In(mortality rate *e E/kT)

8

Figure 1.5 The relationship between the temperature-corrected maximum rate of population growth (i.e. rmax), measured in 1/days, and the natural logarithm of body mass, measured in grams, for various aquatic organisms. Rmax is temperaturecorrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Savage et al. (2004b).

y = –0.24x + 25.04 r2 = 0.47

22

16 –5

7.5 ln(body mass)

20

Figure 1.6 The relationship between the temperature-corrected mortality rate of marine fishes in the field, measured in 1/years, and the natural logarithm of body mass, measured in grams. Mortality rate is temperature-corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Savage et al. (2004b).

other extrinsic factors, but birth and death rates must match, and the rate of production must offset the rate of mortality for a population to persist. Population-turnover rate is another of those phenomena which is controlled by metabolic rate and, consequently, shows characteristic 1/4-power scaling. Metabolic rate determines the rate of population turnover, but what about the abundances or steady-state densities of populations in the field? Based on data for mammals, Damuth (1981) showed that population density scales as M3/4. This is what would be expected if populations of a guild or trophic level had equal rates of resource supply, R, because the steady-state population density, N, should be proportional to the rate of resource supply divided by the resource use or field metabolic rate per individual, P, so N / R/P / M0/M3/4 / M3/4. Recent compilations of data on population density as a function of mass generally support this prediction (Damuth, 1981; Belgrano et al., 2002; Li, 2002; Allen et al., 2002; Brown et al., 2004). For example, Li (2002) showed that the densities of morphospecies of phytoplankton in the North Atlantic scaled as M0.78, where M is cell carbon mass. An important community-level consequence of population density or number of individuals per area, N,

THE METABOLIC THEORY OF ECOLOGY

scaling as M3/4 and whole-organism field metabolic rate or energy use per individual, P, scaling as M3/4, is that the rate of community energy use per unit area, E, is independent of body size: E / NP / M3/4M3/4 / M0. Damuth (1981) called this the energy equivalence rule. If the abundance and energy use of populations scale predictably with body size, these relationships are of potentially great interest to ecologists. However, care should be taken in making and testing these predictions of MTE for several reasons. First, the assumption of equal rates of resource supply is difficult to evaluate. It is likely that species in different guilds, functional groups and trophic levels will have quite different resource availability. This could even be true for members of the same guild or trophic level. Second, resource supply sets only an upper bound on population density. Predation, competition and other limiting factors may cause the steady-state density to be well below this limiting bound. Third, the above two factors can cause considerable variation, as much as several orders of magnitude, in the observed densities of species populations in the field. Fourth, data are often plotted with each point representing a species, but in organisms with indeterminate growth and consequently wide variation in body size, it may be difficult to estimate the average body mass and abundance of a species. If the organisms really do use the same resources, it is more logical to estimate the upper bound by summing the numbers of individuals of all species in a body-size interval. Ackerman et al. (2004) performed such an analysis for all of the fish coexisting at a site on the Great Barrier Reef, and found the predicted M3/4 scaling – except for the smallest size classes, which probably share food resources with invertebrates. We conclude that metabolic rate powerfully constrains the abundance of organisms in species populations, functional or trophic groups, and body-size categories, but, again, care should be exercised in making and testing predictions based on metabolic theory.

Ecosystem level: flux and storage of energy and materials Through their metabolism, organisms contribute to the flows of energy and elements in ecosystems. These flows include not only the quantitatively dominant components of the carbon cycle, but also those involving critical limiting nutrients, such as phosphorus or nitrogen, that together with carbon, comprise the ‘Redfield Ratio’. Metabolic theory provides a conceptual basis for predicting, measuring and understanding the roles of different kinds of organisms in the flux and storage of elements in ecosystems. The total biomass per unit area, W, is simply the sum of the body mass of all individuals. For organisms of similar size, it can be estimated by taking the product of the population, N, and the body mass, M. Similarly, the store of each element in living biomass per unit area, S, is: S¼

i X 0

½Xi Ni Mi

(1:5)

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J. H. BROWN ET AL.

1

In(carbon turnover rate)

10

phytoplankton wetlands

–2

y = –0.21x – 2.83 r2 = 0.80 –5 –20

–10

0

ln(body mass)

10

Figure 1.7 The relationship between carbon turnover rate, measured as 1/days, and the natural logarithm of average plant mass, measured in grams. Data have not been temperaturecorrected because environmental temperatures were not reported. Analyses from Brown et al. (2004) and Allen et al. (2005).

where X is the whole-body concentration of substance X, and the subscript i denotes a species, developmental stage or body-size class, functional or trophic group, which should be analysed separately for accurate accounting. To a first approximation, the turnover rate of these materials is proportional to massspecific metabolic rate, B, so the rate of flux, F, is F¼

i X

½Yi Ni Bi

(1:6)

0

where Y is an element-specific constant required because turnover rates vary widely for different kinds of organisms, depending in part on the form in which they are stored (e.g. structural carbon in plants, and calcium and phosphorus in the shells of molluscs and the bones of vertebrates). Knowing Y, it is also then possible to use the general mass and temperature dependence of metabolic rate to estimate the turnover rate of a particular element. We illustrate the potential applications of this framework with two examples. First, we show the relationship between the rate of carbon turnover and plant size for freshwater and marine ecosystems, where the primary producers are predominantly phytoplankton, and for wetlands, where the primary producers are predominantly herbaceous plants (Fig. 1.7). These data have not been temperature corrected due to difficulties in estimating the relevant temperatures in these ecosystems, so temperature probably accounts for substantial residual variation. Nevertheless, the regression has a slope of 0.21, close to the predicted value of 1/4, fits the data well for both phytoplankton in open waters and herbaceous plants in wetlands, and accounts for about 80% of the observed variation. Furthermore, Allen et al. (2005) show that this same relationship can be extended to include terrestrial ecosystems, where the dominant plants vary in size from herbs in grasslands to trees in forests.

THE METABOLIC THEORY OF ECOLOGY

Allen et al. (2005) further show how this framework can be extended to understand the roles of different sizes and temperatures of plants in the flux and storage of carbon, and hence in the carbon cycle at scales from local ecosystems to the globe. Belgrano et al. (2002) developed another extension, showing that plant density across the spectrum of plant sizes from algae to trees and across a range of ecosystem types from oceans, freshwaters, wetlands, grasslands and forests shows the predicted M3/4 scaling. These examples show how MTE can be applied to make more explicit and quantitative links between the processing of energy and elements at the individual level to the flux, storage and turnover of these elements at the level of ecosystems. Our second example concerns the role of metabolism in trophic relationships, including the structure and dynamics of food webs. Above, we have shown how MTE can be applied to understand the M3/4 scaling and the M0 energy equivalence observed empirically within many functional groups and trophic levels. The theory can also be applied to understand the body-size structure of food webs and the flow of energy and materials between trophic levels. Brown et al. (2004) developed quantitative expressions for the ratios for consumer:producer ratios of: (i) metabolic energy flux, F1/F0; (ii) biomass, W1/W0; and (iii) abundance, N1/N0; where the subscripts 0 and 1 denote any given trophic level and the next highest level respectively. For aquatic ecosystems, we can usually assume that all organisms (except for endotherms, which should be considered separately) are operating at approximately the same temperature. Then these ratios are: for energy flux: F1 =F0 ¼ i1 N1 M1 3=4 =i0 N0 M0 3=4 ¼ 

(1:7)

where i0 and i1 are the normalization constants for the field metabolic rates of the producers and consumers organisms, respectively; for biomass: W1 =W0 ¼ N1 M1 =N0 M0 / ðM0 =M1 Þ1=4

(1:8)

and for abundance: N1 =N0 / ðM0 =M1 Þ3=4

(1:9)

The ratio for energy flow, a, which must always be <1, is the traditional Lindeman efficiency that has been the subject of so much discussion and investigation in ecology. It is apparent from inspection of the above equations that the M3/4 scaling of production is an important factor affecting a. If the body-mass ratio of producer to consumer is large, and contributions to this symposium suggest that it is often in the range of 100–500 in aquatic ecosystems (see also Humphries, this volume; Woodward & Warren, this volume; Cohen, this volume), then a large component of the energy dissipated between trophic levels will be due simply to the allometry of production rates. In addition to body size

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and abundance, other factors contributing to a are: (i) the fraction of the metabolism at level 0 that is allocated to biomass production, or production efficiency, which appears to be approximately 50% across a wide variety of ectothermic organisms; (ii) the fraction of the individuals or biomass produced by trophic level 0 that is consumed by trophic level 1, i.e. the consumption efficiency; and (iii) the fraction of the energy content of this consumed resource that is actually absorbed and transformed in the metabolism of organisms at level 1, i.e. the assimilation efficiency, which has been measured for the diets of many kinds of consumers. The above framework can be applied to understand quantitatively how Lindeman efficiencies, rates of energy and material flow, biomasses and abundances vary within and between ecosystems as a consequence of the body sizes of the organisms at different trophic levels. For example, Brown et al. (2004) derive explicitly the conditions required to have the inverted ecological pyramids (i.e. ratios >1) of biomass or abundance that are sometimes observed empirically (see also Jones & Jeppesen, this volume). Additionally, if a is known, Eqs. (1.7) and (1.8) can be applied, and the body sizes of the organisms occupying adjacent trophic levels can be used to predict the ratios of biomass and abundance. Conversely, if the body-size ratios are known, the above equations can be used to explore the contributions of body size and the production, consumption and assimilation efficiencies to the Lindeman efficiency. More generally, the above framework represents a start at synthesizing the different approaches to food webs that have traditionally been taken by ecosystem and community ecologists. The former have used dE/dt currencies to quantify rates of energy and material flow, whereas the latter have used dN/dt currencies to focus on the dynamics of consumer populations and their resources. By considering explicitly the allometry of resource use and abundance, metabolic theory shows how these currencies are inextricably related (see also Yodzis & Innes, 1992; Kerr & Dickie, 2001; Brown & Gillooly, 2003; Brown et al., 2004; Gillooly et al., 2006).

Concluding remarks Much of ecology is concerned with the exchanges of energy and materials (i.e. elements) between organisms and their environments. These exchanges determine the life histories of individual organisms, the abundances and turnover of populations, the allocation of resources among coexisting species, and the fluxes and pools of energy and materials in ecosystems. These exchanges are direct consequences of metabolism as organisms take up energy and nutrients from their environments, transform them within their bodies, and allocate them to maintenance, growth and reproduction. The metabolic rates of organisms vary predictably, or scale quantitatively, with body size and temperature. The metabolic theory of ecology uses these scaling relations to make and test

THE METABOLIC THEORY OF ECOLOGY

predictions about the effects of energy and materials on the ecology of organisms and the roles of organisms on the fluxes and storage of energy and materials in ecological systems. The theoretical predictions provide baselines from which to measure and understand the influences of additional factors that contribute to the variation in and around empirical scaling relations for organisms in different phylogenetic lineages, functional groups and environments. The conceptual framework of MTE presumably applies to all organisms and ecosystems. Marine and freshwater organisms and ecosystems are no exception. Indeed, there is a rich tradition of empirical and theoretical work in biological oceanography and limnology that relates the structure, function and biotic composition of these systems to the body sizes of the organisms present and the temperatures at which they are operating. We have presented just a few examples to show more explicitly and quantitatively how the developing MTE can be applied. Many of the contributions to this symposium volume present additional examples. But all these studies together provide only a limited sample of the kinds of work that can potentially be done, and the breadth and depth of understanding that they can potentially contribute. Through fisheries, pollution, climate change and other impacts, humans are transforming marine and freshwater ecosystems faster than they can be studied in detail. More data are available for some systems, such as temperate lakes and streams and the surface waters of temperate oceans, than for others, such as tropical lakes and streams and the abyssal depths of the oceans. The metabolic theory of ecology provides a general, quantitative conceptual framework, grounded in accepted first principles of biology, physics and chemistry, not only for understanding the basic ecology of aquatic ecosystems, but also for applying this knowledge to conservation, management and policy.

References Ackerman, J. L., Bellwood, D. R. & Brown, J. H. (2004). The contribution of small individuals to density-body size relationships: examination of energetic equivalence in reef fishes. Oecologia, 138, 568–571. Allen, A. P., Brown, J. H. & Gillooly, J. F. (2002). Global biodiversity, biochemical kinetics, and the energetic-equivalence rule. Science, 297, 1545–1548. Allen, A. P., Gillooly, J. F. & Brown, J. H. (2005). Linking the global carbon cycle to individual metabolism. Functional Ecology, 19, 202–213. Belgrano, A., Allen, A. P., Enquist, B. J. & Gillooly, J. F. (2002). Allometric scaling of maximum population density: a common rule for

marine phytoplankton and terrestrial plants. Ecology Letters, 5, 611–613. Brooks, J. L. & Dodson, S. I. (1965). Predation, body size and composition of plankton. Science, 150, 28–35. Brown, J. H. & Gillooly, J. F. (2003). Ecological food webs: high-quality data facilitate theoretical unification. Proceedings of the National Academy of Sciences, 100, 1467–1468. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789. Calder, W. A. (1984). Size, Function, and Life History. Cambridge, MA: Harvard University Press.

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Carpenter, S. R. & Kitchell, J. F. (1988). Consumer control of lake productivity. Bioscience, 38, 764–769. Cohen, J. E., Jonsson, T. & Carpenter, S. R. (2003). Ecological community description using the food web, species abundance, and body size. Proceedings of the National Academy of Sciences, 100, 1781–1786. Cyr, H. (2000). Individual energy use and the allometry of population density. In Scaling in Biology, eds. J. H. Brown and G. B. West. New York: Oxford University Press, pp. 267–295. Cyr, H. & Pace, M. L. (1993). Allometric theory-extrapolations from individuals to communities. Ecology, 74, 1234–1245. Cyr, H. & Peters, R. H. (1996). Biomass-size spectra and the prediction of fish biomass in lakes. Canadian Journal of Fisheries and Aquatic Sciences, 53, 994–1006. Damuth, J. (1981). Population density and body size in mammals. Nature, 290, 699–700. Elser, J. J., Dobberfuhl, D. R., MacKay, N. A. & Schampel, J. H. (1996). Organism size, life history, and N:P stoichiometry. Bioscience, 46, 674–684. Elser, J. J., Sterner, R. W., Gorokhova, E. et al. (2000). Biological stoichiometry from genes to ecosystems. Ecology Letters, 3, 540–550. Ernest, S. K. M., Enquist, B. J., Brown, J. H. et al. (2003). Thermodynamic and metabolic effects on the scaling of production and population energy use. Ecology Letters, 6, 990–995. Fenchel, T. & Finlay, B. J. (1983). Respiration rates in heterotrophic, free-living protozoa. Microbial Ecology, 9, 99–122. Gause, G. F. (1934). The Struggle for Existence. Baltimore: Williams and Wilkins. Gillooly, J. F., Brown, J. H., West, G. B., Savage, V. M. & Charnov, E. L. (2001). Effects of size and temperature on metabolic rate. Science, 293, 2248–2251. Gillooly, J. F., Charnov, E. L., West, G. B., Savage, V. M. & Brown, J. H. (2002). Effects

of size and temperature on developmental time. Nature, 417, 70–73. Gillooly, J. F., Allen, A. P., Brown, J. H. et al. (2005a). The metabolic basis of wholeorganism RNA and phosphorus content. Proceedings of the National Academy of Sciences, 102, 11923–11927. Gillooly, J. F., Allen, A. P., West, G. B. & Brown, J. H. (2005b). The rate of DNA evolution: effects of body size and temperature on the molecular clock. Proceedings of the National Academy of Sciences, 102, 140–145. Gillooly, J. F., Allen, A. P. & Brown, J. H. (2006). Food web structure and dynamics: reconciling alternative ecological currencies. In Ecological Networks: Linking Structure to Dynamics in Food Webs, eds. M. Pasqual and J. A. Dunne. Oxford: Oxford University Press. Hemmingsen, A. M. (1960). Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital and Nordisk Insulin Laboratorium, 9, 6–110. Hutchinson, G. E. (1959). Homage to Santa Rosalia or why are there so many kinds of animals. American Naturalist, 93, 145–159. Huxley, J. S. (1932). Problems of Relative Growth. London: Methuen. Kerr, S. R. & Dickie, L. M. (2001). The Biomass Spectrum: A Predator-Prey Theory of Aquatic Production. New York: Columbia University Press. Leibold, M. A. & Wilbur, H. M. (1992). Interactions between food web structure and nutrients on pond organisms. Nature, 360, 341–343. Li, W. K. W. (2002). Macroecological patterns of phytoplankton in the northwestern North Atlantic Ocean. Nature, 419, 154–157. Lindeman, R. L. (1942). The trophic-dynamic aspect of ecology. Ecology, 23, 399–417. McMahon, T. A. & Bonner, J. T. (1983). On Size and Life. New York: Scientific American Books. Morin, P. J. (1995). Functional redundancy, nonadditive interactions, and supply-side

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dynamics in experimental pond communities. Ecology, 76, 133–149. Morin, P. J. (1999). Productivity, intraguild predation, and population dynamics in experimental food webs. Ecology, 80, 752–760. Odum, H. T. (1956). Efficiencies, size of organisms, and community structure. Ecology, 37, 592–597. Paine, R. T. (1974). Intertidal community structure. Experimental studies on the relationship between a dominant competitor and its principal predator. Oecologia, 15, 93–120. Peters, R. H. (1983). The Ecological Implications of Body Size. New York: Cambridge University Press. Redfield, A. C. (1958). The biological control of chemical factors in the environment. American Scientist, 46, 205–221. Savage, V. M., Gillooly, J. F., Woodruff, W. H. et al. (2004a). The predominance of quarter-power scaling in biology. Functional Ecology, 18, 257–282. Savage, V. M., Gillooly, J. F., Brown, J. H., West, G. B. & Charnov, E. L. (2004b). Effects of body size and temperature on population growth. American Naturalist, 163, 429–441. Schindler, D. W. (1974). Eutrophication and recovery in experimental lakes: implications for lake management. Science, 184, 897–899. Schmidt-Nielsen, K. (1984). Scaling: Why is Animal Size So Important? New York: Cambridge University Press.

Sheldon, R. W. & Parsons, T. R. (1967). A continuous size spectrum for particulate matter in sea. Journal of the Fisheries Research Board of Canada, 24, 909–915. Sheldon, R. W., Prakash, A. & Sutcliffe, W. H. (1972). The size distribution of particles in the ocean. Limnology and Oceanography, 17, 327–340. Sheldon, R. W., Sutcliffe, W. H. & Paranjape, M. A. (1977). Structure of pelagic food-chain and relationship between plankton and fish production. Journal of the Fisheries Research Board of Canada, 34, 2344–2353. Sprules, W. G. & Bowerman, J. E. (1988). Omnivory and food chain length in zooplankton food webs. Ecology, 69, 418–426. Sterner, R. W. & Elser, J. J. (2002). Ecological Stoichiometry: the Biology of Elements from Molecules to the Biosphere. Princeton, NJ: Princeton University Press. Thompson, D. W. (1917). On Growth and Form. Cambridge: Cambridge University Press. West, G. B., Brown, J. H. & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276, 122–126. West, G. B., Brown, J. H. & Enquist, B. J. (1999). The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science, 284, 1677–1679. Wetzel, R. G. (1984). Detrital dissolved and particulate organic carbon functions in aquatic ecosystems. Bulletin of Marine Science, 35, 503–509. Yodzis, P. & Innes, S. (1992). Body size and consumer-resource dynamics. American Naturalist, 139, 1151–1175.

15

CHAPTER TWO

Body size and suspension feeding STUART HUMPHRIES Department of Animal and Plant Sciences, University of Sheffield

Introduction Suspension-feeding animals are ubiquitous in aquatic ecosystems, and all major taxa have members for whom suspension feeding is the main foraging mode. Suspension feeders are often the chief primary consumers in aquatic systems but, because of the diverse nature of the particles they collect, they also contribute significantly via their effects as both secondary consumers and detritivores (Gili & Coma, 1998; Jørgensen, 1966). In removing particulate food from the surrounding water, suspension-feeding organisms act as mediators of energy flux between the photic zone and the deep sea, between continental waters and the benthic zone, and between local systems in freshwaters (Gili & Coma, 1998; Wildish & Kristmanson, 1997; Wotton, 1994). Their role in energy transfer means that they are key components of aquatic ecosystems, representing important pathways for energy flow, and are crucial determinants of the productivity of aquatic environments. Suspension feeders are characterized by the possession of an organ used to capture suspended particles from the water (feeding structure). The feeding structures utilized by suspension feeders are highly variable, and include appendages bearing hairs, mucus or silk nets, gill rakers and baleen plates, lophophores, tentacles, and ciliated and flagellated cells. Within a feeding structure, individual collecting elements are the first point of contact for food particles. Transport of particles (particle flux) to the feeding structure is achieved by the flow of water, provided either by active pumping or by external flow. Suspension feeders are generally categorized as belonging to one of two major groups, based on the extent to which ambient (external) water flow is utilized for feeding (LaBarbera, 1984; Vogel, 1994; Wildish & Kristmanson, 1997). Passive suspension feeders rely entirely on ambient flow to deliver food particles to their feeding structures, while active suspension feeders use energy to regulate water flow over or through their feeding structures using a biological pump (ciliary or muscular). However, further intermediate categorization is possible, with facultative-active suspension feeders able to switch between passive and active feeding, depending on ambient flow conditions. Combined passive-active suspension feeders (Wildish & Kristmanson, 1997) utilize both passive and active methods at the same time and to varying extents, while deposit-suspension feeders switch between Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

BODY SIZE AND SUSPENSION FEEDING

deposit-feeding (picking particles from the substratum) at low velocities, and suspension-feeding when deposited particles are resuspended by higher velocities. Body size is somewhat nebulous and difficult to specify when it comes to suspension feeders, as it is for other ecological aspects of body size in this volume. Whether to use volume, length, body mass or dry weight becomes problematic when members of the suspension-feeding functional group include gelatinous pelagic animals that have large physical size, but low carbon content as an adaptation to low food concentrations (Acun˜a, 2001). Analogously, suspension feeders with dense and massive shells, such as barnacles and bivalve molluscs, have a non-trivial proportion of metabolically inactive body mass. Similar arguments can be made for those suspension feeders that use external structures to capture food; examples include silk nets (Trichoptera), as well as mucus nets (polychaetes, appendicularians) and sheets (pelagic molluscs). Many benthic suspension feeders also exhibit a predominantly two-dimensional body plan. The majority of issues concerning body size, for instance in relation to scaling in aquatic versus terrestrial ecosystems (Schmidt-Nielsen, 1984; Denny, 1993; Alexander, 1998; Brown, Allen & Gillooly, this volume), clearly apply to suspension feeders. However, this chapter will focus on the organismal- and habitat-level implications of body size that are directly relevant to the process of suspension feeding.

The hydrodynamic implications of body size The effects of water velocity, viscosity and scale ( size of the object of interest) in any biological system can be understood most easily by using a parameter, the Reynolds number (Re), that describes the flow regime within or around that system. The Reynolds number is a scaling parameter that provides a measure (ratio) of the relative importance of inertial and viscous forces within a fluid, and describes the way in which fluids will behave at difference scales. The Reynolds number is given by Re ¼ ul/, where u is velocity, l is the linear length scale of interest, and  is the kinematic viscosity of the fluid. Crudely, for biological systems where size and speed are positively correlated (Vogel, 1994), low values (Re  1) indicate slow uniform (laminar) flow, while high values (Re  1000) indicate faster, more turbulent flow. More importantly, any combination of velocity, viscosity and scale that results in the same Re will result in a geometrically similar flow regime, as characterized by the ratio of inertial to viscous forces. Thus, doubling the length scale will result in a flow regime that can also be realized by doubling velocity or by halving kinematic viscosity. As a tool, Re provides us with a way to conceptualize the link between the size of an object and the flow characteristics it experiences. Few organisms are as directly dependent on these flow characteristics as suspension feeders: although modulated by behaviour and morphology, purely physical processes

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fundamentally determine the food-capture rate of suspension feeding animals. In this context body size can be seen as synonymous with flow regime, with Re relating as it does, a single measure of size to environmental conditions. In biological systems, small (and hence slow) organisms tend to operate under conditions where the fluid they are immersed in is dominated by viscous forces (low Re), while larger, faster organisms operate at higher Re, where inertial forces prevail (Vogel, 1994). While high Re characterizes the flows at a human scale, the behaviour of low Re flows are frequently counterintuitive. For instance, if a bacterium were suddenly to cease swimming, it would come to a halt in a distance much less that the diameter of a hydrogen atom (Berg, 1983). Lengths of suspension feeders vary over five orders of magnitude, from singlecelled protists to baleen whales, while the Reynolds number of such organisms in general ranges between Re  106 (bacteria) and Re  108 (large whales), or 14 orders of magnitude (Nachtigall, 2001). This provides a dramatic range of conditions in which suspension feeders operate, and leads to an array of adaptations to this feeding mode. Despite such large variations in body size, aerosol theory co-opted from engineering (Rubenstein & Koehl, 1977) suggests that there are only five inclusive mechanisms by which particles can encounter collecting elements: (i) direct interception, (ii) inertial impaction, (iii) gravitational deposition, (iv) diffusional deposition and (v) electrostatic attraction. Simple sieving (where particles are caught because they are larger than the gap between collecting elements) is generally added to this group, although in the process of sieving particles encounter the feeding structure via one of the five classic mechanisms. Direct interception involves streamline kinematics: particles travelling on a streamline that passes around the collecting element will come into contact with that element if they come within one particle radius. Inertial impaction relies on particles that are denser than the surrounding fluid failing to follow rapidly turning streamlines due to their inertia, while gravitational deposition relies on a particle’s mass causing it to cross streamlines and thus impact the collector. For smaller particles, diffusional deposition may be important, whereby Brownian motion of tiny (<1 mm) particles causes them to cross streamlines and impact the collecting element. Finally, electrostatic attraction may act to draw some particles towards collecting elements in non-electrolyte fluids. The obvious restrictions imposed by only five inclusive mechanisms for particle capture suggest that evolutionary convergence in feeding methods may be inevitable. Differences do exist, however, in the importance of the different mechanisms to particular organisms, a factor itself determined by morphology, particle type and availability, and to some extent by body size. What is now clear is that these particle-encounter mechanisms comprise an ‘envelope of the possible’, and are common to almost all suspension feeders (Rubenstein & Koehl, 1977; LaBarbera, 1984; Shimeta & Jumars, 1991; Vanderploeg, 1994).

BODY SIZE AND SUSPENSION FEEDING

Body size changes during ontogeny and evolution The flow regime that an organism experiences is critical to a number of physiological processes (Palumbi, 1986; Vogel, 1994; Rex, Montebon & Yap, 1995). Given that the body size of suspension feeders determines the flow regime around them, and considering the extent of growth in aquatic organisms, ontological shifts between regimes are common. Physical limits to growth and patterns of modularity (the way in which clones group together) are important in many groups with indeterminate growth, where size of feeding surfaces is traded against the risk of mechanical failure and respiratory costs of increased tissue volume. Feeding itself is highly dependent on flow, and hence size of the collecting elements within a feeding structure. Although it has been commonly assumed that the Re of collecting elements (based on element diameter) is much less than unity, there is mounting evidence that a large fraction of suspension feeders may operate in a 1  Re  100 regime (intermediate-Re), where neither viscosity nor inertia truly dominates (Shimeta & Jumars, 1991; Table 2.1 & Fig. 2.1a). The physics of fluid flow in this regime is underdeveloped, and little experimental work has been carried out to investigate the implications of this flow regime for the large number of suspension-feeding animals whose collecting elements are thought to operate in this intermediate-Re range. The few studies in this area have already shown some surprising shifts in the way feeding appendages operate with a transition to intermediate-Re (Koehl, 1983; Cheer & Koehl, 1987; Koehl, 1993, 1996, 2000, 2001). It has been shown that hair-bearing appendages used for functions such as suspension feeding, swimming, flying and olfaction, operate in fundamentally different ways depending on Re (based on the gap between hairs: Koehl, 1983; Cheer & Koehl, 1987; Koehl 1993, 1996, 2000, 2001). At very low Re these appendages act as paddles, pushing water in front of them, whilst at Re near unity they function more like leaky sieves with water passing easily between the hairs (Fig. 2.1b). The strong implications for suspension feeders are reinforced when the relationship between Re of the hair-gaps and body size is considered. Reynolds number in this instance is related to body size via both appendage size and speed of movement (proportional to limb length and body size). However, there is currently a lack of evidence for ontological transitions within species, as compared with between-species differences. This difference is probably a consequence of ‘leakiness’ having a low sensitivity to changes in size at very low Re (Koehl, 1995).

Limits to maximum body size The density of water is around 800 times greater than air, which (in addition to reducing sinking rates and hence promoting the existence of suspension feeding per se) provides substantial physical support not available to terrestrial organisms. As a result, both maximum body size and appendage elaboration in suspension feeders are somewhat less restricted by constraints related to

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Table 2.1 Partial list of suspension feeders likely to feed at intermediate-Re, based on estimates of flow local to feeding structures, and measurements of collecting-element diameter taken from the literature. Unless indicated, species are those identified from published drawings and photographs by Shimeta and Jumars (1991): 1. Humphries unpublished; 2. Johnson (1993); 3. Hentschel (1996); 4. Loo et al. (1996); 5. Anthony (1997); 6. Shimeta and Koehl (1997); 7. Allen (1998); 8. Jesling (2002). Taxon grouping

Species

Polychaeta

Eupolymnia heterobranchia2 Lanice conchilega1 Polydora ligni 3 Pseudopolydora kempi japonica Pseudopolydora paucibranchiata6 Pygospio elegans8 Sabella pavonina Scolelepis squamata Spio filicornis8

Echinodermata (Ophiuroids, Holothurians & Crinoids)

Amphiura filiformis4 Comaster multifidus Cucumaria miniata1 Fluorometra serratissima1 Oligometra serripinna Ophiopholis aculeata Ophiopteris antipodium Ophiothrix fragilis7 Psolus chitinoides

Cirripedia (barnacles)

Lepas pectinata

Copepoda

Centropages typicus

Stylasterina (Hydrozoan hard corals)

Stylaster californicus1

Octocorallia (soft corals & sea pens)

Paracyanthus stearnsi1 Sansibia spp.1 Stylatula elongata1 Xenia spp.1

Actinaria (sea anemones)

Anemonia viridis1 Anthopleura elegantissima Corynactis californica1 Metridium senile

Zoanthidea

Palythoa variabilis

Scleractinia (hard corals)

Acropora millepora5 Alveopora spongiosa1 Balanophyllia elegans1 Montipora digitata5 Pocillopora damicornis5 Porites cylindrica5

Insecta

Isonychia campestris Simulium bivittatum Simulium spp.1

BODY SIZE AND SUSPENSION FEEDING

(a)

Re = 10

Particle encounter rate

Re = 1

Log velocity (b) 1

Leakiness

0.8

0.6

0.4

0.2

0 0.00001

0.0001

0.001

0.01

0.1

1

Reynolds number

Figure 2.1 Functional transitions in relation to Reynolds number. (a) Generalized pattern of particle encounter for direct interception inflections indicate a transition in encounter rate with Re (redrawn from Shimeta & Jumars, 1991), (b) leakiness of an array of hairs, plotted against Re. Leakiness is defined as the volume of fluid passing between two elements (hairs) in an array, divided by the volume that would flow through the space if the elements were not present. Lines represent gap:element diameter ratios: squares 50:1, triangles 15:1, diamonds 5:1, circles 0.6:1 (redrawn from Koehl, 1995).

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physical support than in terrestrial organisms. However, physical restrictions on the size of feeding structures will start to appear as body size increases, in common with many other mechanical devices. Energetic optimality models suggest that growth should stop at some energetically optimal body size in both passive (Sebens, 1982, 1987) and active suspension feeders (Acun˜a, 2001; Humphries, unpublished). Nonetheless, it should be remembered that the size limit set by energy balance may never be met in animals with determinate growth (Sebens, 1987). The most obvious way to increase energetic intake from suspension feeding is simply to increase the size of the feeding structure. As long as (i) positive net energy gain is possible, and (ii) costs and gains increase at a similar rate with increasing size of the capture apparatus, suspension feeding will be viable given feeding structure(s) sufficiently large to collect enough food for reproduction and/or growth. However, this method of increasing energy gain will produce diminishing returns if the costs of producing and maintaining a larger feeding structure increase more rapidly than the gain provided by that structure. This is more than likely when body size is increased, as the metabolic costs of greater tissue volume tend to increase much faster than the gain from an essentially two-dimensional feeding structure. For instance, passive suspension feeders should theoretically have capture rates directly proportional to the surface area of their capture apparatus (i.e. increasing as body mass0.67) if their growth is isometric (Sebens, 1982, 1987). In active suspension feeders, gain rate is proportional to the volume of water processed per unit time, thus leading to a predicted proportionality to cross-sectional area, ciliated surface, or other apposite surface. Concurrently, basic metabolic costs will increase with any increase in body size, although not necessarily linearly (Fig. 2.2). As far as it is possible to generalize, metabolic costs are likely to scale as somewhere between body mass0.67 and body mass0.75 for most animals (Peters, 1983; Schmidt-Nielsen, 1984; White & Seymour, 2005). In addition to any possible metabolic drawbacks, an increase in size simply may lead to movement restrictions, or compromise function in some other way as for any other organism. One method of circumventing, or at least offsetting, the costs of constructing a larger feeding apparatus and a body to support it is to find a way of increasing the size of the feeding apparatus at a rate disproportionately more than that of the increase in body size (allometric scaling). For instance, colonial sea anemones, corals and gorgonians have a growth form that allows the surface area of their feeding apparatus to increase at a rate proportional to their mass rather than their surface area as might be expected of animals whose body surface is where their feeding structures are situated (Sebens, 1982, 1987). The flat-sheet or multiply-branched body form of these colonial or clonal animals allows their feeding surfaces to increase linearly with body mass as colony growth appears to occur through the production of new polyps (of equal size to the originals),

BODY SIZE AND SUSPENSION FEEDING

(a)

Energetic intake/cost (mJ/s)

25

20

15

10 5 0 0

0.005

0.01

0.015

0.02

0.025

0.03

Body size (mass, kg)

(b) 45 Energetic intake/cost (mJ/s)

40 35 30 25 20 15 10 5 0 0

0.01

0.02

0.03 0.04 Body size (mass, kg)

0.05

0.06

0.07

Figure 2.2 Cost:gain curves for two suspension feeders: (a) the mussel Mytilus edulis, and (b) the sea anemone Anthopleura xanthogrammica. Solid lines are gain functions, broken lines are cost functions. Redrawn from Sebens (1987).

rather than a general increase in the size of existing polyps. This method has its limitations, however, because while it enables escape from a size limit imposed by energetic constraints, other size limits may well be imposed, for instance, by suitable ambient velocities, substrata, local food depletion, local competition, or ‘self-shading’ (Sebens, 1982, 1987; Kim & Lasker, 1998; Okamura, Harmelin & Jackson, 2001). A method available to non-colonial animals is to modify existing body parts to act as feeding structures (sometimes even to the exclusion of their original function). Examples include the use of locomotory arms raised into the current in brittle stars, and the limbs of some euphausiid shrimps. By using such

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dual-function organs, these animals might profit by increasing the size of their feeding apparatus for a given body size. However, the above scaling arguments still hold for further increases in the size of feeding apparatus, and thus body size. A particularly interesting solution to the scaling problem is the use of external capture apparatus, usually silk or mucus nets, by animals such as the larvae of caseless caddis flies (Trichoptera) and many polychaete worms, respectively. Here, the solid substratum provides support and anchor points for a net that the animal constructs, and the animal is thus able to increase the size of its feeding structure without an increase in body size. The increase in filter area in relation to body size can be very large: one species of caseless caddis fly with a body mass of less than 6 mg regularly builds nets up to 20 cm long (Petersen, Petersen & Wallace, 1984). Although the costs of net construction are relatively high (in Polycentropus flavomaculata, the process of silk spinning and net construction raises metabolic rates by about 17% (Dudgeon, 1987)), they are likely to be considerably less than the metabolic costs of a body large enough to hold an internal feeding structure of similar size. Furthermore, the costs of building an external structure are ‘capital’ costs, in that they do not require sustained investment at a high level, as would equivalent volumes of metabolically active tissue. Use of an external feeding structure is also common in oceanic environments. Pelagic pteropod molluscs use large mucus nets suspended from their body to capture planktonic food. The low-turbulence environment of the open ocean allows them to construct fragile nets that are not constantly torn apart by forces generated by turbulent water movement (Harbison, 1992). Many pelagic suspension feeders probably also utilize another mechanism for increasing gain and reducing costs that is facilitated by their low turbulence environment: the development of gelatinous bodies. Pelagic tunicates appear to use metabolically inert gelatinous tissue to increase their body size so that they can support a larger filter without the energetic costs of increasing the volume of metabolically active tissue (Acun˜a, 2001). Indeed, some deep-sea species of appendicularians with bodies 75 mm long build external gelatinous ‘houses’ with diameters of up to 1 m (Ruppert & Barnes, 1994), presumably in response to the very low seston concentrations in their environment. Acun˜a’s (2001) argument is based on the scaling of gain to costs in a similar way to that discussed above, but invokes a quadratic increase in pumping costs with filter size, in comparison to a linear increase in gain as the driving force for the development of gelatinous bodies. As seen above, however, the same principle of costs increasing more rapidly than gains is equally applicable to passive suspension feeders (Sebens, 1987).

Particle capture as a predator–prey relationship The existence of a positive relationship between the body size of a predator to that of its prey (Peters, 1983) is currently only an assumption for suspension

BODY SIZE AND SUSPENSION FEEDING

maximum

0.065

Bead diameter (mm)

0.055

0.045

0.035

0.025 minimum 0.015

0.005 0.4

0.5

0.6

0.7 0.8 Animal length (mm)

0.9

1.0

1.1

Figure 2.3 The relationship between prey size and body size in the copepod Acartia tonsa capturing plastic beads. Maximum ingested bead size varies as Lprey ¼ 05.52  105 Lpred1.0397, while minimum bead size is constant across the body-size range studied. Redrawn from Wilson (1973).

feeders. Evidence from vertebrates eating ‘small-prey’ (Peters, 1983) suggests a relationship of the form Wprey ¼ 0.0018Wpred1.18, where W is mass in kg, with an exponent not significantly different from unity. For invertebrates, Warren and Lawton (1987) describe a positive relationship between mean prey length and predator length (L, in m) equivalent to the form Lprey ¼ 5.83  104Lpred0.984. Wilson (1973) gives Lprey ¼ 7.83  105Lpred2 – 6.61  105Lpred þ 4.4  105, for the maximum plastic bead diameter ingested by the copepod Acartia tonsa (Fig. 2.3). The latter data are also fit well by a power function with an exponent of close to unity (Lprey ¼ 5.52  105Lpred1.0397; Humphries, unpublished), but are valid only for one species with a small size range. The general predator–prey size relationship is also characterized by increasing variance in prey size as predator size increases (Peters, 1983; Warren & Lawton, 1987; Cohen et al., 1993). Mechanisms for this pattern in ‘traditional’ predators are thought to relate to the ability to switch to small prey when larger prey is unavailable, which becomes less feasible as predator size decreases. However, when considering suspension feeders a physical basis for the pattern can be proposed. If particles with a linear dimension greater than the filter-gap size are utilized (sieving) then the maximum prey size will be determined by the dimensions of the filter apparatus or mouth, and all particles larger than this critical size will be retained. Thus, if sieving is utilized by a particular species, a bimodal prey-size distribution is predicted (Silvester, 1983; Brown et al., 2005) and maximum prey size will increase isometrically with predator size.

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Minimum prey size, however, will be limited by hydrodynamic considerations (encounter rate has a minimum against particle size as diffusion falls off before other mechanisms increase rates; Rubenstein & Koehl, 1977; Shimeta & Jumars, 1991) and the problems of dealing with extremely small particles. It is reasonable to expect tuning of the size of filtering structures and collecting elements to profitable prey size (determined by energy content and distribution in the environment). Mean prey size (or other measure or central tendency) may not scale isometrically as expected for maximum prey size. Unfortunately, information on predator–prey size relationships for suspension feeders is scarce and a general analysis has not yet been attempted.

Body size and food availability (body size and solid–fluid interfaces) Although large size may directly increase the size range of particles available to an animal, body size can also influence the availability of particles through its effects on flow regime. Physical interactions involving availability and the deposition of particles depend on body size because of the link between body size and flow regime. When considering benthic suspension feeders, body size in conjunction with spatial positioning can determine the availability of suspended particles. Hydrodynamic studies have highlighted the influence of surface roughness on flow (Nowell & Church, 1979; Nowell & Jumars, 1984; Eckman, 1990; Abelson & Denny, 1997), and this has been observed to relate directly to animal size and positioning (Pawlik, Butman & Starczak, 1991; Friedrichs, Graf & Springer, 2000; Cardinale, Palmer & Collins, 2002). Any structure extending into the flow from the substratum will perturb the local flow pattern, and the formation and shedding of vortices from benthic suspension feeders can lead to differential deposition of particles downstream (Vogel, 1994; Abelson & Denny, 1997; Turner, 2000). In this case, the size of the structure or animal determines Re and thus a characteristic wavelength for vortex shedding. Vortices are shed at a rate determined by the Strouhal number (St), a dimensionless frequency, dependent on the shape and Re of the object (Vogel, 1994), and interact most strongly with the substratum downstream at a characteristic distance related to shedding rate (Fig. 2.4). Positive feedback may then occur as increased deposition leads to increased feeding rates and hence growth of downstream animals (Turner, 2000). A further consequence is that growth itself will alter the vortex shedding rate. An additional study (Abelson, Miloh & Loya, 1993) suggests that body morphology can determine the availability of food particles. As morphology in this instance is characterized by a slenderness ratio (height/diameter) body size per se may also play an important part, particularly if an animal’s slenderness ratio changes through ontogeny because of the change in Re associated with its linear dimension parallel to the flow. Since body size can influence sediment deposition in the local area, it will also have strong effects on the importance of benthic suspension feeders as ecosystem

BODY SIZE AND SUSPENSION FEEDING

Figure 2.4 (a) Deposition and erosion of sediment around a sedentary scallop resulting from the ‘horseshoe vortex’ that develops around a projecting structure in shear flow (viewed from above), and modulation of vortex formation (b) behind a protruding structure (at characteristic wavelength l, viewed from above), and (c) behind an accretive structure (promoting deposition at characteristic distances 2l behind the object, viewed from side). In (a) dark shading indicates erosion of sediment, lighter shading indicates deposition. Flow is from left to right in all cases. (a) redrawn from Grant, Emerson & Shumway (1993), (b) and (c) redrawn from Turner (2000).

engineers. In addition, many benthic species are known to mediate competitive interactions between species, to influence larval settlement, to control sediment resuspension, and to impact the feeding rates of neighbours through effects on the local flow environment arising from their morphology (Okamura, 1984, 1985, 1988; Johnson, 1990; Wildish & Kristmanson, 1997; Gili & LaBarbera, 1998; Friedrichs et al., 2000; Cardinale et al., 2002; Lindegarth, Jonsson & Andre´, 2002; Wotton, Malmqvist & Leonardsson, 2003; Pratt, 2004). Benthic suspension feeders can also take advantage of some of the hydrodynamic peculiarities of the fluid–solid interfaces at which they live. Being attached to a solid surface reduces the energy required to maintain position in the flow, and thus the animals can take greater energetic advantage of the water passing over or through feeding structures. However, the presence of velocity gradients produced as fluid moves over a solid surface, means that average flows near the interface are lower than in the bulk of the fluid some distance away (Vogel, 1994). These velocity gradients are generated because water passing over a solid surface obeys what is known as the no-slip condition, where water in contact with the surface does not move, propagating reduced velocities out into the water column through friction between fluid ‘particles’ (Vogel, 1994). While a velocity gradient can be seen as an advantage in some cases, by allowing animals to live in higher ambient velocities, in general the net result is a

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decrease in the rate of fluid passing over or through feeding structures. To counter this, many animals extend their bodies, or just their feeding structures, up through the velocity gradient where they experience increased ambient velocities. Depending on the velocities and turbulence of the fluid involved, the actual distance an animal may need to negotiate can vary greatly (Denny, 1993; Vogel, 1994). For instance, a barnacle on a wave-swept shore may experience velocity gradients of the scale of millimetres, while gorgonian corals on reef walls may need to overcome gradients many centimetres thick. The costs of maintaining position for such animals are increased somewhat, but are still likely to be below those of maintaining position without contact with the substratum. A further trick is utilized by larvae of the blackfly (Simulium), in that the larva’s body and feeding structures are used to generate vortices that travel back though the velocity gradient to dislodge food particles from the substratum, which can then be captured from the water column by the larva (Chance & Craig, 1986). Compensation also comes from the increase in gain resulting from feeding in higher velocities. Examples include sea pens and brittle stars, as well as corals and gorgonians, which also exhibit growth forms that, by reducing the area exposed to the flow, decrease the forces acting on their attachment to the substratum. Ideally, these animals want to increase the area exposed to food particles, but without increasing their resistance to water flow proportionately. The development of a velocity gradient is not limited to the substratum on which benthic suspension feeders live. Any solid–water interface will develop a velocity gradient and, for benthic suspension feeders, the thickness of this zone of reduced velocity on their body surface can be important for both feeding and respiratory exchange. For a given surface, the thickness of the velocity gradient that develops is related to Re, and hence to body size (the further downstream one goes, the thicker the layer of reduced velocities; Vogel, 1994). In general, larger animals experience thicker boundary layers that can result in decreased rates of diffusion and lower concentrations of oxygen close to their bodies.

Conclusions Clearly, body size is an important factor determining the ecology of the majority of organisms. With respect to suspension feeders, their direct connection to flow regime, and the dependence of flow regime on scale, reveals powerful physical control of many processes. The importance of suspension feeders to aquatic ecosystems further reinforces the interaction between body size and flow. The existence of non-linearities already investigated in some relationships hints at unexpected functional shifts in other areas. Dependence of feeding rate on body size presents both opportunities and challenges for suspension-feeding animals. Correlations between feeding rates and body size suggest that freeing feeding structures from the constraints of scaling with surface area can improve

BODY SIZE AND SUSPENSION FEEDING

the efficiency of energy acquisition and remove some of the restrictions on a maximum body size. Despite its potential to throw light on many ecological processes in aquatic systems, the relationship between food-particle size and body size across suspensionfeeding taxa is currently unknown. As a further consequence, we lack information on basic scaling relationships for both prey and morphology of suspension feeders, which may reveal more complex size-related niche differentiation. Our current level of understanding regarding body size in suspension feeders is relatively low, but can be developed by careful attention to both size and the influence of flow regime. External influences on body-size patterning via fluid motion are now recognized, but the potential for further novel relationships exists and deserves further consideration.

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appendages. Journal of Theoretical Biology, 105, 1–11. Koehl, M. A. R. (1993). Hairy little legs: feeding, smelling, and swimming at low Reynolds numbers. Contemporary Mathematics, 141, 33–64. Koehl, M. A. R. (1995). Fluid flow through hair-bearing appendages: feeding, smelling and swimming at low and intermediate Reynolds numbers. In Biological Fluid Dynamics, ed. C. P. Ellington and T. J. Pedley. Cambridge: The Company of Biologists Limited, pp. 157–182. Koehl, M. A. R. (1996). When does morphology matter? Annual Review of Ecology and Systematics, 27, 501–542. Koehl, M. A. R. (2000). Consequences of size change during ontogeny and evolution. In Scaling in Biology, ed. J. H. Brown and G. B. West. Oxford: Oxford University Press, pp. 67–86. Koehl, M. A. R. (2001). Transitions in function at low Reynolds number: hair-bearing animal appendages. Mathematical Methods in the Applied Sciences, 24, 1523–1532. LaBarbera, M. (1984). Feeding currents and particle capture mechanisms in suspension feeding animals. American Zoologist, 24, 71–84. Lindegarth, M., Jonsson, P. R. & Andre´, C. (2002). Physical and numerical modeling of the role of hydrodynamic processes on adult-larval interactions of a suspension-feeding bivalve. Journal of Marine Research, 60, 499–516. ¨. Loo, L.-O., Jonsson, P. R., Sko¨ld, M. & Karlsson, O (1996). Passive suspension feeding in Amphiura filiformis (Echinodermata: Ophiuroidea): feeding behaviour in flume flow and potential feeding rate of field populations. Marine Ecology Progress Series, 139, 143–155. Nachtigall, W. (2001). Some aspects of Reynolds number effects in animals. Mathematical Methods in the Applied Sciences, 24, 1401–1408.

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Pratt, M. C. (2004). Effect of zooid spacing on bryozoan feeding success: is competition or facilitation more important? Biological Bulletin, 207, 17–27. Rex, A., Montebon, F. & Yap, H. T. (1995). Metabolic responses of the scleractinian coral Porites cylindrica Dana to water motion. I. Oxygen flux studies. Journal of Experimental Marine Biology and Ecology, 186, 33–52. Rubenstein, D. I. & Koehl, M. A. R. (1977). The mechanisms of filter feeding: some theoretical considerations. American Naturalist, 111, 981–994. Ruppert, E. E. & Barnes, R. D. (1994). Invertebrate Zoology. Fort Worth: Saunders College Publishing. Schmidt-Nielsen, K. (1984). Scaling: Why is Animal Size so Important? Cambridge: Cambridge University Press. Sebens, K. P. (1982). The limits to indeterminate growth: an optimal size model applied to passive suspension feeders. Ecology, 63, 209–222. Sebens, K. P. (1987). The ecology of indeterminate growth in animals. Annual Review of Ecology and Systematics, 18, 371–407. Shimeta, J. & Jumars, P. A. (1991). Physical mechanisms and rates of particle capture by suspension feeders. Oceanography and Marine Biology Annual Review, 29, 191–257. Shimeta, J. & Koehl, M. A. R. (1997). Mechanisms of particle selection by tentaculate suspension feeders during encounter, retention, and handling. Journal of Experimental Marine Biology and Ecology, 209, 47–73. Silvester, N. R. (1983). Some hydrodynamic aspects of filter feeding with rectangular-mesh nets. Journal of Theoretical Biology, 103, 265–286. Turner, J. S. (2000). The Extended Organism: the Physiology of Animal-Built Structures. Cambridge, MA: Harvard University Press. Vanderploeg, H. A. (1994). Zooplankton particle selection and feeding mechanisms. In The Biology of Particles in Aquatic Systems, ed.

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R. S. Wotton. Boca Raton: Lewis Publishers, pp. 205–234. Vogel, S. (1994). Life in Moving Fluids. Princeton, Princeton University Press. Warren, P. H. & Lawton, J. H. (1987). Invertebrate predator–prey body size relationships: an explanation for upper triangular food webs and patterns in food web structure? Oecologia, 74, 231–235. White, C. R. & Seymour, R. S. (2005) Allometric scaling of mammalian metabolism. Journal of Experimental Biology, 208, 1611–1619.

Wildish, D. & Kristmanson, D. (1997). Benthic Suspension Feeders and Flow. Cambridge: Cambridge University Press. Wilson, D. S. (1973). Food size selection among copepods. Ecology, 54, 909–914. Wotton, R. S. (1994). The Biology of Particles in Aquatic Systems. Boca Raton: Lewis Publishers. Wotton, R. S., Malmqvist, B. & Leonardsson, K. (2003). Expanding traditional views on suspension feeders – quantifying their roles as ecosystem engineers. Oikos, 101, 441–443.

CHAPTER THREE

Life histories and body size DAVID ATKINSON The University of Liverpool

ANDREW G . HIRST British Antarctic Survey

Introduction This chapter demonstrates how investigating patterns of survival, reproduction, growth and development – life histories – can improve understanding and prediction in diverse areas of ecology ranging from microevolution and population dynamics of individual species, to ecosystem function and biogeochemistry. To make sense of the huge diversity of life history in nature, a first step is to derive a common set of traits, such as age and size at first reproduction, number and size of offspring, inter-clutch interval, and juvenile and adult survival. The effects of changes in the magnitude of each of these traits on the others (e.g. increased offspring size may be traded off against a reduction in offspring number), and their relationship to fitness or population growth under particular environmental conditions, can then be analyzed. This chapter initially outlines how this process, life-history analysis, is used in adaptive evolutionary models that predict adult and offspring size within species. As there are numerous reviews that introduce life-history analysis (e.g. Lessells, 1991; Roff, 1992; Stearns, 1992; Daan & Tinbergen, 1997; Stearns, 2000; Roff, 2002; Begon, Townsend & Harper, 2006), this chapter outlines only the salient features. While some applications of life-history analysis are beyond the scope of this chapter (e.g. elasticity analysis; Benton & Grant, 1999), here we will evaluate the importance of life-history analysis in understanding and predicting body-size variation and the scaling of many traits with body size, at various levels of ecological organization ranging from within-genotype variation (phenotypic plasticity and changes during ontogeny) to differences among ecological functional groups that affect ecosystem function and biogeochemistry. Specifically, the chapter first outlines two main ways of understanding and predicting the evolution of body size using life-history analysis: optimization (optimality) and adaptive dynamics. Key elements of these are described, followed by a discussion of some methodological issues, and examples of their ecological application. The second part of the chapter examines scaling relationships between body size and other traits of ecological importance, and follows Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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the same organizational structure (key elements, methodological issues, ecological applications).

Understanding and predicting the evolution of body size Key elements of life-history theory

Optimality models Life-history theory attempts to predict the life histories that evolve under particular selection pressures. Optimality models have been referred to as ‘classical life-history theory’ (summarized in Roff, 1992; Stearns, 1992, 2000), which predicts those life histories that will maximize some measure of Darwinian fitness in a population with stable age structure in particular selective environments. The key elements are a fitness definition, a relationship of traits to fitness, and tradeoffs among traits. Fitness definition Fitness has been defined in different ways in different lifehistory models (see Kozłowski, 1993; Mylius & Diekmann, 1995; Benton & Grant, 2000; Brommer, 2000; Brommer, Merila & Kokko, 2002; Brommer et al., 2004 for a discussion of alternatives). One widely used fitness measure in classical lifehistory theory is r, known as the intrinsic rate of natural increase. This population concept can be adopted for individuals or genotypes, such that the genotype with the highest r will grow more rapidly than all other genotypes. Maximization of r is equivalent to maximization of reproductive value at birth (Brommer, 2000), which is the number of descendants that a female newborn is expected to have over her lifetime, discounted by the rate at which the population is increasing (see below). Reproductive value (V) at birth can be represented as: X V¼ lx mx erx (3:1) where lx is the probability of surviving to age x and mx is the number of offspring produced at age x: their product when summed over the organism’s lifetime is lifetime reproductive success (LRS), which can be viewed as the individual organism analogue of the population-wide measure, net reproductive rate (or ratio) (Brommer et al., 2002). While it is easy to see the link between LRS of a genotype and its Darwinian fitness, a discount term is also needed because in an expanding population offspring produced now are worth more than those produced in the future, as they themselves can breed sooner. Thus the exponential term at the right of the equation is the discount term, which disappears in a stationary population as r becomes zero. This leaves LRS, which is often used as a fitness measure when no net population growth is assumed. As the equation for reproductive value can be expanded to incorporate separate juvenile and adult phases, with separate mortalities and durations between life-history events (juvenile development, duration between reproductive events), it is possible to calculate the combinations of traits that give the same

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reproductive value and plotting them to produce a fitness contour (e.g. Sibly & Atkinson, 1994). Trade-off curves can then be superimposed on fitness contours to identify the trait values that yield highest fitness.

Relationship of traits to fitness While the link between some phenotypic traits and fitness may be weak, many life-history traits are either components of fitness (age-specific survival and fecundity) or are strong correlates of fitness (e.g. growth rate, offspring size; Lessells, 1991). Blanckenhorn (2000) and Brown & Sibly (2006) summarized the typical fitness advantages of large size as increased fecundity, success in size-dependent competition for resources (including mates), escape from size-limited predators, greater diet breadth, and greater physiological homeostasis and hence tolerance of environmental fluctuations. Trade-offs A trade-off occurs when a genetically determined change in one trait that contributes to fitness has an inverse effect on the fitness contribution of other traits. An example of a trade-off in organisms with the same growth rate is when juvenile development is accelerated leading to earlier maturity, but this will be at a smaller size, which typically reduces the number of offspring a mother produces (Caswell, 1989), and may even reduce mating success and adult survival (Blanckenhorn, 2000). Possible costs of large adult size, summarized by Blanckenhorn (2000) and Brown & Sibly (2006), include: (i) increasing risks of dying before breeding because large size is achieved by extending the juvenile period (hence the period of mortality risk) or increasing growth rate (which may incur costs); (ii) increased risk of being killed by predators, parasitism or environmental stressors or reduced reproductive success because of reduced agility, increased detectability, higher energy requirements or heat stress; (iii) decreased lifetime reproductive success due to late reproduction; (iv) decreased rate of massspecific production, including reproduction. In optimality modelling, optimization is performed within a limited range of possible life histories that is determined by constraints such as geometry and physical and chemical laws. An example is the scaling of metabolic rate to body size raised to the power 3/4, which West, Brown & Enquist (1997) proposed was due to physical and geometrical constraints on the supply of resources to metabolizing cells as body size is increased (see also Brown, Allen & Gillooly, this volume). Variation not explained by this scaling relationship may then be amenable to other forms of explanation, such as variation in selection pressures, hence life-history analysis. Just how firmly the 3/4 power law constrains biological rates, will be discussed later in this chapter. Adaptive dynamics More recent modelling approaches that take account of realistic population dynamics, usually referred to as adaptive dynamics (Waxman & Gavrilets,

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2005), also require the relationships of traits to fitness and of trade-offs among traits used in optimality modelling. However, adaptive dynamics can be distinguished from classical life-history theory by its different fitness concept, regarding it as the ability of a phenotypic strategy to invade and persist in a population with realistic dynamics, i.e. frequency and density dependence. For instance, the optimal life history can change as population size varies, depending on which life-history phase (juveniles, adults) and which processes (growth, mortality) are most affected by density. Adaptive dynamics theory typically assumes an initially very rare mutation that codes for a trait value that is different from that in the initial population of ‘residents’. Fitness then refers to the ability of the mutation to ‘invade’ the population. Metz, Nisbet and Geritz (1992) formulated this as the average exponential growth rate of the invader, growing in the environment set by the resident. The models thus identify the evolutionarily unbeatable strategy, which is able to invade the population, taking account of the extent to which the fitness function, termed the invasion fitness, is dependent on trait frequencies and population densities (Mylius & Diekmann, 1995; Waxman & Gavrilets, 2005). Methodological issues

Determining trade-offs In trade-offs, investment in a trait can affect more than one other trait (Sibly & Calow, 1983): egg size, for example, can affect fecundity rates, mortality and growth rate of young, and development time of egg and juvenile. However, optimality models of life-history evolution usually deal with one trade-off at a time, presumably because this is both mathematically more tractable and more manageable for conducting empirical tests (though possibly at the expense of rigour). Knowing the shape of trade-offs is important for identifying life histories that are best adapted to particular environments. However, we still await accurate quantification of trade-offs, which has proved difficult because they should ideally be measured among individuals provided with the same resources, and which differ only in genes coding for one trait (e.g. offspring size). An alternative is to manipulate a trait and observe its consequences although this, too, is challenging, as it can be difficult to simulate alternative genotypes by manipulating the phenotype. When manipulating traits it is important, for instance, to ensure that the amount of resources provided to the organism is not adjusted (Lessells, 1991; Atkinson & Thorndyke, 2001). Frequency and density dependence Mylius and Diekmann (1995) advocated more effort towards accounting for adaptive dynamics, and argued that ‘the unpleasant fact that we usually know little about the way density dependence operates in real populations should not seduce us to pursue an ostrich-policy’. However, measuring selection in

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empirical studies typically examines short-term evolutionary change among extant genotypes (Brommer et al., 2002). Therefore, against the theoretical argument that invasibility (the ability to invade a population) is a more realistic measure of fitness than r or LRS, is the practical one that invasibility is not readily measured in natural populations, especially compared with LRS. Moreover, Stearns (2000) highlighted a number of the predictive successes of classical life-history theory, and suggested that these successes occurred because the theory focused on influences, such as age- and size-specific impacts on mortality and production, in an assumed stable, asexual population, rather than influences ignored by optimality theory, which include those central to adaptive dynamics (explicit population dynamics and frequency dependence). A general conclusion is that increased realism (e.g. adaptive dynamics) is likely to improve predictions, but lack of knowledge of actual dynamics, logistic problems in routinely measuring invasibility, and the established predictive successes of optimality theory, should prolong the use of the classical life-history approach and of easily measured fitness estimates such as LRS.

Predicting life-history plasticity Life-history theory not only predicts the mean value of a trait, but has been developed to predict the plastic response of a phenotypic trait in different environmental conditions (Stearns & Koella, 1986). Phenotypic plasticity occurs when a single genotype produces different phenotypes, including life histories. The magnitude of a trait’s plastic response to changes in an environmental variable is known as a reaction norm (Stearns & Koella, 1986; Stearns, 2000). A life history involves many developmental decisions that are made on the basis of physiological and environmental cues (the organism’s ‘state’), and lifehistory theory has incorporated dynamic optimization models (Houston & McNamara, 1999) to cope with sequential decisions. Reaction norms are important because they capture both the history of an individual’s development in a particular environment, and the evolutionary history of selection which has produced a set of adaptive responses to information about environmental conditions and physiological state. Thus a theory of reaction norms has to deal with two effects of the environment on a reaction norm. First is the proximate effect, in which environmental resources, stressors and information induce a change in life history. Second is the ultimate effect, in which the environment selects only those individuals whose life history response to environmental information leads to enhanced fitness. To illustrate this, life-history theory predicts that additional mortality on large individuals selects for smaller size at maturity, such as in species of Cladocera whose larger individuals are most at risk from fish predation (Brooks & Dodson, 1965). Thus, adaptive plasticity would involve reducing size at maturity in the presence of fish cues. Many studies have shown that, even in

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250 200

Mass (µg)

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150 100 50 0 CH

FH CL FL Fish kairomone-food level treatment

Figure 3.1 Mean body mass (þ95% confidence limits) at first reproduction of Daphnia magna. CH ¼ control (no fish kairomone) Daphnia at high food (1.5 mg C L1); FH ¼ Daphnia treated with fish kairomone at high food; CL ¼ control Daphnia at low food (0.5 mg C L1); FL ¼ Daphnia treated with fish kairomone at low food. Data are extracted from Figure 1 in Stibor & Navarra (2000), and redrawn.

the absence of planktivorous fish, the mere presence of fish chemical cues (kairomones) can induce earlier maturity at smaller body size (e.g. Tollrian & Harvell, 1998; Stibor & Navarra, 2000; Sakwinska, 2002; Weetman & Atkinson, 2002; Fig. 3.1). In contrast, when Cladocera are reared in the presence of chemical cues from smaller, invertebrate, predators such as the phantom midge larva, Chaoborus sp., which are more effective at killing small rather than large individual cladocerans, the cladocerans grow to a larger size (Stibor & Lu¨ning, 1994). In both these examples, the cladocerans are responding to environmental information (predator cues) about selection pressures (size-dependent mortality) to induce changes in adult size that appear to be adaptive. The prediction of optimal reaction norms depends strongly on the spatial structure of the population and the frequency with which a gene affecting the reaction norm encounters a particular environment out of the full set of environments experienced by the population (Houston & McNamara, 1992; Kawecki & Stearns, 1993). In an isolated habitat, the term r in Eq. (3.1) is the local intrinsic rate of increase in the habitat. But in meta-populations, where offspring may encounter different patches from their parents, the r term is not that for a given patch but the average for the population patches that the offspring may encounter (‘global r’). If the average population-growth rate in the patches likely to be encountered is 0, then the discount term in Eq. (3.1) disappears and the equation reduces to that for LRS. This fitness measure is used, for example, in reaction norm models of Berrigan and Koella (1994) that investigate effects of growth and mortality on optimal age and size at maturity, and is good news for field ecologists, as LRS is easier to measure than r (Kozłowski, 1993). Predictions of life-history theory differ depending on whether local or global r is maximized. For example, if global r is 0 and is assumed to be maximized by natural selection (i.e. other strategies have r < 0; Kozłowski, 1993), then the rate at which the local

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population increases has no effect on optimal age at maturity. In contrast, when maximizing local r, rapid population growth in that patch selects for earlier maturity as fitness is increased by producing offspring rapidly (as we argued in the discussion of Eq. (3.1)). Conditions favouring the evolution of adaptive plasticity in life histories include environmental change, which is predictable and which is encountered sufficiently frequently during evolution to have a strong selective effect. However, it should change sufficiently infrequently, or at least over a long enough period during ontogeny, to allow fitness benefits to accrue from lifehistory shifts that may take time to implement and/or be costly to reverse (Atkinson & Thorndyke, 2001; Doughty & Reznick, 2004). Testing the adaptive significance of body-size plasticity is a major challenge, but approaches have been identified to ensure that tests are rigorous (Gotthard & Nylin, 1995; Atkinson & Thorndyke, 2001; Doughty & Reznick, 2004). For instance, even though the plastic shifts in cladoceran adult size in response to predator kairomones appear to be adaptive, it is still necessary to check that the life-history responses were not caused by some other effect of the kairomones (e.g. toxic or nutrient) rather than their information content about predation risk.

Interpreting phenotypic variation Variation in a trait along an environmental gradient will result from the combined effects of genetic variation in the trait between individuals, phenotypic plasticity, and the differences in plasticity between genotypes (genotype  environment interaction). A reaction norm can be in the same direction as the selective effects of the environment on the trait: this is co-gradient variation. An example is how fish predation on large cladocerans can select among genotypes, favouring a reduced mean size at maturity, and can select for reaction norms that reduce age and size at maturity within clones in response to fish kairomones (Fig. 3.1). But counter-gradient variation can sometimes occur, where genetically based mechanisms evolve to resist environmental perturbation of a trait resulting in phenotypic similarity along an environmental gradient (Conover & Schultz, 1995). An example is provided by pumpkinseed sunfish, Lepomis gibbosus, which when small competes with bluegill sunfish, L. macrochirus (Arendt & Wilson, 1999). Raising pumpkinseed with bluegill, irrespective of whether the pumpkinseed were derived from lakes with or without bluegill, slowed pumpkinseed growth. However, pumpkinseed derived from lakes with bluegill grew faster than those from lakes without bluegill under all experimental treatments, following the predicted evolutionary acceleration of growth to allow passage through the competing size classes as quickly as possible (Arendt & Wilson, 1999; Fig. 3.2).

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Figure 3.2 Left: growth increments for different age classes of pumpkinseed sunfish in the wild; allopatric fish (solid symbol) are from a lake without bluegill sunfish; sympatric fish are from a lake with bluegill present. Numbers above or below symbols are mean sizes (mm) of fish for that age. Lines cross between ages 2 and 3, when pumpkinseed begin to feed mainly on snails, and when their growth rate is no longer constrained by interspecific competition. Right: instantaneous growth rates (IGR) for six pumpkinseed populations reared in enclosures. Solid symbols and solid lines represent allopatric populations; open symbols and broken lines represent sympatric populations. There is a significant decrease in growth rate as the density of bluegill increases, and the sympatric pumpkinseed grow faster than all allopatric pumpkinseed under all densities of bluegill. Thus, growth rate shows countergradient variation. Figures are from Arendt and Wilson (1999).

Ecological applications of life-history analysis

Fishing-induced evolution Life-history theory has mostly been used to predict body-size variation within species (e.g. Roff, 1992; Stearns, 1992; Berrigan & Koella, 1994; Day & Rowe, 2002). This will be important for the structure and functioning of aquatic ecosystems if the species plays an important role, for instance as a keystone predator. A prominent example of selection for smaller size and earlier reproduction comes from fisheries (Law, 2000; Jennings & Reynolds, this volume). However, when analyzing fisheries data, a major challenge is to separate genetic variation from plasticity and genotype  environment interaction. As well as evolutionary shifts in age and size at maturity, changes in these maturation traits can also result from changes in growth rates if stock depletion due to fishing leads to abundant food for the remaining fish, hence quicker growth (Lorenzen & Enberg, 2002), which can accelerate the optimum onset of maturity (Day & Rowe, 2002). However, a new statistical method has been devised for disentangling these different sources of phenotypic variation, which estimates from fisheries data the probabilities of maturing at each relevant age and size (Heino, Dieckmann & Godø, 2002a, b). This technique has now been used to

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identify a shift in maturation of northern cod Gadus morhua towards earlier ages and smaller sizes preceding collapse of the fishery in the late 1980s and early 1990s (Olsen et al., 2004). Such techniques are timely, as there is growing concern about the consequences of fisheries-induced evolution, which may ultimately lead to lower sustainable yields (Law, 2000; Conover & Munch, 2002; Walsh et al., 2006). Even where increased mortality occurs across a wide range of sizes and ages, selection is often expected to act against those genotypes that are slow to mature, hence typically at a large size, because the evolutionary response of juveniles to harvesting (on whom mortality selects earlier breeding) is often more sensitive than that of adults (on whom mortality selects delayed breeding) (Ernande, Dieckmann & Heino, 2004). However, the more obvious selection against larger adults comes from fisheries targeting larger fish (Law, 2000; Ernande et al., 2004). Genetic shifts in mature size of fish under mortality selection are most clearly seen where controlled experiments have been performed to test selection pressures and rates of evolution, but these tend not to be from commercial fisheries. One such system is provided by Trinidadian guppies Poecilia reticulata from streams containing sites that pose either high- or low-predation risks (Reznick & Ghalambor, 2005). In the high-predation environments studied by Reznick and colleagues predation on guppies appears to be spread across all size classes, whereas in lowpredation environments small individuals suffer greatest predation. A combination of experiments under identical rearing conditions (‘common garden’ experiments), predator introductions and transplantation between sites have demonstrated rapid evolution of smaller size at maturity in response to increased predation, and the reverse response when predation risks are reduced (Fig. 3.3). An artificial selection experiment on body size of the Atlantic silverside Menidia menidia found that populations where large fish were selectively harvested showed substantial declines in fecundity, egg volume, larval size at hatch, larval viability, larval growth rates, food consumption rate and conversion efficiency, and willingness to forage (Walsh et al., 2006). This experiment clearly demonstrates how selection for size affects numerous other traits that correlate with size, and that these changes generally reduce the capacity for population recovery. However, it is suggested here that in real fisheries, where populations have age structure, these maladaptive shifts in life histories may be subject to counterselection pressures because fish can be large not just because they grow fast, but also because they have managed to survive long enough to achieve large size. Rapid growth in the Atlantic silverside is associated with decreased swimming performance and higher susceptibility to predation (Walsh et al., 2006). Therefore, if slower growth is associated with higher survival, fishing of large individuals may not just remove fast growers (as in the experiment of Walsh et al., 2006) but also slow ones (good survivors), which will provide a counter-selection pressure on traits associated with capacity for population recovery.

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(a)

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Figure 3.3 Least squares means (1 SE, rarely extending beyond symbol) of size at maturity of adult male guppies, Poecilia reticulata, from high and low predation sites on the north slope (solid line) and south slope (broken line) of the Northern Range Mountains, Trinidad (data extracted from Figures 2c and 4d in Reznick and Ghalambour (2005), and redrawn: (a) data from field-collected fish; (b) data obtained under common garden conditions for each pair of high and low predation sites, though north slope populations were reared under lower food levels and at a different time from south slope fish). This illustrates co-gradient variation in adult size, with smaller size under high predation selection.

Understanding relationships with temperature, and improving biomass estimates The widespread inverse relationships between temperature experienced during ontogeny and both final body and offspring size in ectotherms (Atkinson, 1994; Atkinson et al., 2001) has been termed the ‘temperature–size rule’ (TSR; Atkinson, 1996). This plastic response of body size has been described as a ‘life-history puzzle’, because reduced growth rate (observed at lower temperatures) typically favours smaller, not the observed larger, body size (Berrigan & Charnov, 1994; Atkinson & Sibly, 1997; Day & Rowe, 2002; Angilletta & Dunham, 2003; Angilletta et al., 2004). However, life-history models can be produced that are capable of accounting for the TSR (Kozłowski, Czarnołe˛ski & Dan´ko, 2004), and these now need testing. The TSR has been quantified for diverse protists (Atkinson, Ciotti & Montagnes, 2003), which may be useful to ecologists wanting to estimate biomass and predict rates of production (if biomass is estimated by cell counts multiplied by an average cell volume for each species). Incorporating into biomass estimates the cell-volume reduction of 2.5% relative to volume at a reference temperature (158C) per 8C increase (Atkinson et al., 2003) could avoid errors of about 25% over a 108C range. However, as this result was derived for exponentially growing (log-phase) populations, and optimal size can be influenced by population growth rate (see discussion of Eq. (3.1), and section on Predicting life-history plasticity), further work should establish the relationship for non-growing populations.

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Loge cladocerans (µg ind–1)

2.5 2.0

winter spring/autumn summer

1.5 1.0 0.5 0 –1.5 0–100 100–200 >200 Fish CPUE (no. net–1 night–1)

Figure 3.4 Boxplot (median, 25, 75, 10 and 90% quartiles) of mean body weight of cladocerans (loge-transformed) for samples collected during summer, spring/autumn and winter versus the catch per net at night in multiple meshsized gill nets in 34 Danish lakes monitored one to three times (n ¼ 56–74). Fish sampling always occurred between 15 August and 15 September. Figure is from Jeppesen et al. (2004).

Shifts in the community size spectrum, and impacts on ecosystem function Differences in life history among higher taxa such as genera or families are usually interpreted as resulting from accumulated genetic differences driven by natural selection and phylogenetic history, with variation due to phenotypic plasticity being relatively small (Doughty & Reznick, 2004). However, whatever the cause of life-history variation, the environment can still select particular body sizes, and this can have substantial consequences for ecosystem structure and function (Hall et al., this volume; Huryn & Benke, this volume). Thus, the arguments used in previous sections about mortality effects on optimal adult size can be applied to collections of different-sized species. For instance, high mortality of large zooplankton species favours smaller species. In many lakes predation intensity by planktivorous fish has been shown to drive down the average size of zooplankters (e.g. Brooks & Dodson, 1965; Zaret, 1980; Jeppesen et al., 2004; Fig. 3.4). This removal of large grazers has profound effects on phytoplankton abundance, hence water clarity, and can even facilitate a switch between alternative stable ecosystem states (Moss, 1998; Jones & Jeppesen, this volume). A parallel shift in the community body-size spectrum is observed in heavily exploited marine fish communities, where landings have become increasingly dominated by smaller species (Jennings et al., 2002; Jennings & Reynolds, this volume). Again, size-selective mortality appears to cause decreases in the relative abundance of larger species as well as mean body size within species.

Life-history analysis and scaling relationships Key elements The magnitude of many biological phenomena, including life-history traits, increase with body size in a predictable way both within and across species and higher taxa (Brown & West, 2000; Brown et al., this volume). Typically, the magnitude of a trait is assumed to scale with body mass (M) according to a power

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function, trait value ¼ aMb, where a and b are constants. Thus, log (trait value) plotted against log M gives a straight line with slope b. A special case of scaling is when two traits (e.g. body mass at hatch and at maturity) have the same units and the value of one trait is directly proportional to the value of another: here, their ratio is a dimensionless constant or an invariant (Charnov, 1993), and a log-log plot of these values produces a slope of 1. Such invariants could underpin the form and shape of trade-offs that constrain life-history evolution, and if they extend across species could provide the basis of a general theory of life-history evolution, rather than a diverse array of species-specific models. Methodological issues Determining the scaling exponent A first issue is to ensure that the appropriate regression model is used, as the value of the scaling exponent is sensitive to whether the error is assumed to be confined just to the y-variable (as in a Type I regression), or is shared between the covariates (as in a Type II regression; McArdle, 2003). Thus, if there is a similar degree of error in both covariates, a Type II regression should be used.

Identifying invariant quantities in life histories A major problem is that the method generally used for identifying invariant quantities is flawed: thus, the very existence of invariant quantities will be in doubt until an alternative method is devised (Nee et al., 2005). The difficulty is that while it is true that for an invariant quantity the log-log regression of trait values will always produce a slope of 1, it is not true that a slope of 1 always implies invariance (Nee et al., 2005). The problem arises when the variable on the y-axis is a fraction of the x-variable, for instance mass at birth versus mass at maturity, so that the variables have been regressed against themselves. De Jong (2005) provides a graphical illustration of how combining data from very different invariant relationships for a variety of species into a single relationship for all species can produce the illusion of a single invariant quantity for all the species with a slope of 1, and high r2. A high r2 does not imply invariance, as the high r2 can arise when there is a wide range of values on the x-axis (Nee et al., 2005). This problem of detecting invariance may be more widespread than it first appears, as it can occur even when one variable does not appear initially to be a fraction of the other. For instance, the proposed invariant relationship between yearly clutch size b and adult mortality rate z has been shown by Nee et al. (2005) to involve correlation with itself. Specifically, if the animal produces E eggs in total over its adult lifetime of Y years, then its yearly clutch size b is E/Y and its annual mortality rate is 1/Y: therefore, b ¼ zE, a regression of ln(b) against ln(z) is expected to have a slope of 1.0, and r2 ¼ var[ln(z)]/(var[ln(z)] þ var[ln(E)]), which will be high if z has a wide range of values.

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Determining the effects of selection on scaling exponents The value of applying scaling laws to predict diverse ecological phenomena depends on the reliability of the underlying laws, and whether selection can alter the scaling exponent. Of particular recent interest is a theory that can predict life history, population growth and carrying capacity, species richness and rates of biomass production (reviewed by Brown et al., 2004; Brown et al., this volume). This theory incorporates a long-established, fundamental generalization in biology that respiration (metabolic) rate (R) ¼ aM3/4 (e.g. West et al., 1997; Savage et al., 2004). An important question is to what extent the scaling exponent, b, is fixed at 3/4? If this exponent varies with environment (e.g. pelagic vs. benthic) substantially across taxa with diverse body plans and of widely separated phylogenies, then a strong role for selection on this exponent is suggested, and a possible role for life-history theory. This is exactly what was found in a recent survey of 642 published regressions of scaling of laboratory-measured routine aerobic metabolic rate during ontogeny of invertebrates (Glazier, 2005; Glazier, 2006). Fifty per cent were significantly different from 3/4, and this rose to 70% in analyses with more statistical power (N  50 or where body mass ranges 2 orders of magnitude). Further, the exponent varied systematically with habitat: the mean exponent (95% CL) of pelagic species was nearly 1 (b ¼ 0.95  0.05, N ¼ 58) and was very highly significantly different (p < 0.0000000001) from that shown by benthic species (b ¼ 0.74  0.02, N ¼ 355). This distinction was robust, occurring between pelagic and benthic members of each of four diverse phyla, and even between pelagic larvae and benthic adults within species. This case of convergent evolution suggests a strong role for natural selection. Research is needed to discover whether near-isometric scaling of metabolic rate in pelagic species is associated with, for instance, size-dependent costs of locomotion or maintaining buoyancy, or size-dependent evolutionary responses to higher levels of predation. Relationship between intraspecific and interspecific allometries Typically, allometric relationships between some traits and body size across species use data from adults only (e.g. Savage et al., 2004). If it is assumed that natural selection has optimized body size through optimal allocation of resources to growth and reproduction independently in each species, then interspecific allometries become by-products of many body-size optimizations across the species included (Kozłowski & Weiner, 1997). This can produce different slopes for intraspecific and interspecific allometries. For instance, if one species (species A) is adapted to conditions that allow faster growth and reproduction than a related species B, then all else being equal, species A will have a higher mass-specific metabolic rate because of its faster rate of growth, and is predicted by simple evolutionary models to mature at a larger size (Kozłowski & Weiner, 1997; Daan & Tinbergen, 1997; Day & Rowe, 2002). Thus, in this case the interspecific allometric relationship will be steeper than the intraspecific ones.

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However, as different patterns of growth and mortality select different patterns of adult size and mass-specific metabolic rate, a variety of interspecific allometric slopes with varying amounts of scatter can result, depending on the species included in the comparison (Daan & Tinbergen, 1997). Further implications of this kind of reasoning for interspecific scaling of metabolism are discussed by Kozłowski, Konarzewski and Gawelczyk (2003). However, it may be inappropriate for ecologists to use interspecific allometries based just on adults to predict rates such as growth or mortality within ecological functional groups, as they ignore the majority of organisms – juveniles. Instead, allometric relationships should incorporate all relevant size classes of the different species in the community. Ecological applications

Estimating global patterns of mortality Here, scaling relationships and life-history analysis are applied to deducing the value of a difficult-to-measure life-history and demographic trait (mortality) from data on other life-history and demographic variables (fecundity, development period, reproductive rate). A specific example is the estimation of global rates and patterns of mortality in marine epipelagic copepods, where scaling with body size and temperature can be examined (Hirst & Kiørboe, 2002). Mortality is especially difficult to measure in the marine environment, which is physically dynamic and where planktonic populations cannot be easily followed through time. Consequently, mortality measurements in this group are relatively scarce, and confined to a narrow range of taxa, body sizes or environment types, which limit the ability to estimate the dependence of mortality on temperature and body mass. Therefore, Hirst and Kiørboe (2002) predicted mortality rates from data on fecundity rates, egg-hatch times, egg-to-adult times and sex ratios, all of which were available from more diverse sets of species, environments, body sizes and temperatures. Their initial assumptions (justified below) were that, on average, the populations were in steady-state, the mortality rate (d1) was age independent, and egg-production rate was constant for adult females irrespective of their age. With these assumptions the net reproductive rate, which is the number of offspring per female that survive until the next generation (R0), is derived from the rate of mortality, the development time (D, days ¼ time from being laid as an egg to moulting into adulthood), and the egg-production rate (m, eggs female1 d1) (Kiørboe & Sabatini, 1994): R0 ¼ ðm=ÞeD

(3:2)

Thus, for the population to be maintained, R0 has to equal S þ 1, where S is the ratio of adult males to females, as at steady-state each female must replace herself and produce the appropriate number of males given the sex ratio. The assumption of steady-state, averaged globally, must be approximately true

LIFE HISTORIES AND BODY SIZE

because copepods are neither going extinct nor taking over the world. The assumption of constant fecundity with age in copepods was made because this group has determinate growth: with no adult moults or great increase in adult body size. Equation (3.2) was then used to derive mortality-rate estimates for sac spawning species (i.e. those species that carry their eggs from laying up to the point of hatch), with the same value for mortality rates across eggs and posthatch stages. Approximately equal mortality across all stages including eggs has been demonstrated for sac spawners in the field (Ohman & Wood, 1996; Liang & Uye, 1997). Hirst and Kiørboe (2002) also altered this approach for broadcasting species (whose eggs do not remain attached to the female but rather are free) to allow for the highly vulnerable eggs of this group (see their study for details). When compared with the limited and highly variable measures of field mortality rates, the model predictions matched well with the average rates and patterns, and with adult longevity with respect to temperature and body size (Hirst & Kiørboe, 2002). The body-mass scaling of copepod mortality was compared with a general relationship for other marine organisms: pelagic invertebrates; the eggs, juveniles and adults of fish; and mammals (data from McGurk, 1986). Copepods have much flatter slopes than the general relationship (Fig. 3.5), suggesting that the smaller bodied copepods are avoiding mortality that other marine animals of a similar size are not. Copepods have especially well-developed predator sensory systems (the first antennae) and strong escape responses, which may in part account for their ability to escape mortality. Verity and Smetacek (1996) have suggested that the remarkably homogeneous body form observed across the range of free-living epipelagic copepods has resulted from strong predation pressures. Thus, life-history analysis can be applied to identify global patterns of vital rates in populations of diverse species belonging to a large taxonomic group (copepods). Copepods are the dominant metazoan grazers of marine phytoplankton, provide an important trophic link to fish, are key exporters of particulate organic carbon from the upper mixed layer of the ocean (see Kiørboe, 1998), and play a pivotal role in regenerating nutrients in the vast oligotrophic areas of ocean (Banse, 1995). Therefore, this application of life-history analysis is likely to be important for understanding oceanic ecosystem function and global biogeochemistry.

Improving predictions of global patterns of life history Gillooly et al. (2002) have produced a model of development times for animals, including egg-hatch times and egg-to-adult times, with the primary determinants being body mass and temperature. They corrected development times for mass (as development time/mass0.25) and plotted these against temperature (as Tc/(1 þ (Tc/273)), where Tc is the temperature in 8C: this term represented a

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101

100

Mortality rate (β, d–1)

48

10–1

10–2

10–3

10–4

Other pelagic invertebrates Fish eggs, juveniles and adults Marine mammals Copepods – sac spawners Copepods – broadcast eggs Copepods – broadcast post-hatch

10–5 10–8 10–7 10–6 10–5 10–4 10–3 10–2 10–1 100 101 102 103 104 105 106 107 108 Weight (W, g) 1

Figure 3.5 Mortality rates (b, d ) as a function of body dry mass (W, g ind1) for pelagic invertebrates (excluding copepods) and the eggs, juveniles and adults of fish, and marine mammals (from McGurk 1986). Regression through these data is given by a dotted line log10b ¼ 0.325log10W  2.086 (r2 ¼ 0.826, p < 0.001). Predicted relationships from Hirst and Kiørboe (2002) are given for broadcast eggs (solid line), broadcasters post-hatch and sac spawners (dashed line). For broadcasters post-hatch and sac spawners body masses are taken as adult masses, whereas for the broadcast eggs egg masses are used. All copepod data corrected to 158C using a Q10 value of 2.0. Figure adapted from Hirst and Kiørboe (2002).

correction to relate temperature to zero Kelvin, used in biochemical kinetics theory (Hochachka & Somero, 2002)). They initially suggested that these plots would produce lines with universal slopes and intercepts. Thus, egg-hatch times should share a common slope and intercept, as should egg-to-adult times. However, Gillooly et al. (2003) have since acknowledged that intercepts are non-universal, stating ‘In our model, the coefficient a allows for variation in intercepts with metabolic rate B0, and hence for differences in development times depending on which taxa, environmental conditions and developmental stages are measured’. Variability in the intercepts of development times versus temperature have been explored further by Hirst and Lo´pez-Urrutia (2006). Using marine plankton and nekton groups as a case study, with data compiled from the copepods, chaetognaths, appendicularians, cephalopods, fish, euphausiids and mysids, they found that although differences are often taxonomically based, other factors can be important too. Specifically, after allowing for temperature and mass, a significant proportion of the variability that remains in egg-hatch times can be accounted for by the vulnerability (mortality) of the eggs. Eggs that are protected in some way, such as carried by the female, laid in

LIFE HISTORIES AND BODY SIZE

free-floating clumped masses, or attached to the substratum, have temperaturecorrected hatch times that are on average 3.3 times longer than those for unprotected free planktonic eggs at equivalent egg masses. Furthermore, not only can differences in the egg-hatch time be observed, but data on the two- to four-cell cycle times in marine invertebrate embryos also demonstrate similar separation on the basis of egg protection strategy (Strathmann, Staver & Hoffman, 2002). Differences in egg-hatch times not only occur between taxa on the basis of egg-protection strategy, but also within single taxa such as the copepods. As the sac-carried eggs of copepods are around an order of magnitude less vulnerable than are broadcast eggs (see previous section), the patterns found in this analysis qualitatively agree with expectations from an evolutionary perspective: the period of time animals spend in some life-history stages appears to be negatively related to their vulnerability. There is also clear evidence of trade-offs between different life-history attributes. The shorter hatch times in broadcasting copepods are not short enough to offset the higher mortality in the egg stage in comparison to sac spawners (i.e. for a given number of eggs laid there will be, on average, more hatchlings from sac spawners than broadcasters). Broadcasters appear to make up for this reduced survival over the egg period in other ways: although the two groups have similar amounts of energy to invest in eggs (Hirst & Bunker, 2003), broadcasters achieve a higher rate of fecundity than sac spawners by producing relatively smaller eggs (Bunker & Hirst, 2004). It is interesting that although sac-spawning copepods are not uncommon in the marine environment, the broadcasters are generally dominant, whereas in freshwater almost all pelagic copepods are sac spawners. It is suggested here that a broadcast strategy would simply be too costly on egg survival in freshwaters, where the water column is relatively shallow and benthic predation intense, so that any eggs which settled out would have poor chances of survival.

Conclusion This chapter has shown how life-history analysis can predict the evolution of body size in different environmental conditions, and can help explain the scaling of important vital rates with body mass and temperature. Like the book as a whole, this chapter illustrates the importance of body size throughout ecology, including microevolution, population dynamics, and the structure and functioning of communities. Functional relationships between organism life histories and higher levels of ecological organization, including ecosystem functioning, are becoming increasingly appreciated, and act both up and down levels of organization. The importance of community structure on life history (including adult and offspring size), is highlighted, for instance, in recent models of optimal life history that invoke selective pressures that depend on the community size spectrum (Thygesen et al., 2005), and on indirect

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(community) consequences when altering predation rates (Gardmark, Dieckmann & Lundberg, 2003). On the other hand, the importance of life-history trade-offs in determining community structure is illustrated, albeit in a terrestrial system, by the way continuously varying life histories and trade-offs can allow multiple competitors to coexist (Bonsall, Jansen & Hassell, 2004), suggesting that such trade-offs may be fundamental to understanding the structure of ecological communities.

Acknowledgements DA’s research is supported by NERC and EU Framework 6 funding; AGH is supported as part of the BAS DISCOVERY 2010 Programme. We thank two anonymous referees for helpful comments.

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CHAPTER FOUR

Relationship between biomass turnover and body size for stream communities ALEXANDER D . HURYN University of Alabama

ARTHUR C . BENKE University of Alabama

Introduction A crucial requirement for the analysis of energy flow through freshwater food webs is the accurate and precise estimation of secondary production (Benke et al., 1988). The rate of production (or biomass-turnover rate) is often expressed as either annual production-to-biomass ratios (annual P/B) or daily biomassgrowth rates (g, Appendix I). Invertebrate production and annual P/Bs have now been estimated on a taxon-specific basis for a relatively wide range of freshwater habitats, streams and rivers in particular, and often this has been done within a community context (see reviews by Benke, 1993 and Huryn & Wallace, 2000). The relationships between body size and either daily or annual P/B for freshwater invertebrates have been assessed using empirical approaches (Banse & Mosher, 1980; Plante & Downing, 1989; Morin & Bourassa, 1992; Benke, 1993; Morin & Dumont, 1994). The results of such studies provide strong evidence that annual P/B is negatively related to body size (Appendix I; Fig. 4.10). However, recent efforts showing remarkably high P/Bs for some benthic macroinvertebrates in both warm-water (e.g. Benke, 1998; reviewed by Huryn & Wallace, 2000) and cool-water streams (e.g. Nolte & Hoffman, 1992) suggest that the results of these early studies – Banse and Mosher’s (1980) still widely cited analysis, for example – greatly underestimate biomass turnover. Furthermore, because they are based on meta-analytical approaches incorporating comparison of populations taken from many different communities, these earlier studies do not allow the analysis of factors constraining patterns of P/B as a function of the body size of individual taxa within single communities. The allometric relationship between body size and bioenergetic variables has captured the interest of ecologists for some time (reviewed by Peters, 1983; Schmidt-Nielsen, 1984; Glazier, 2006). Recent studies of the role of metabolic constraints as determinants of the relationship between body size and production have advanced earlier efforts by producing a conceptual framework that explicitly links metabolic theory with ecological theory (Brown et al., 2004; Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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Brown, Allen & Gillooly, this volume). This conceptual framework (i.e. the ‘metabolic theory of ecology’; Brown et al., 2004) provides a number of specific predictions about the relationship between body size and bioenergetic variables over a wide range of ecological scales. In this paper we test selected predictions that relate to the relationship between body size and P/B for stream animal populations and communities. We chose to focus on the P/B because it is a powerful variable that summarizes the dynamic relationship between growth rate, biomass and production (Appendix I).

The predictions We used detailed community-level production budgets for four streams (described below) to test a priori predictions about the relationship between body size (M, mg or mg dry mass (DM) or ash-free dry mass individual1) and population density (N, no. individuals m2), biomass (B ¼ M  N, mg m2), production (P, mg dry mass or ash-free dry mass m2 yr1), and the P/B (yr1). We chose to analyze the relationship of each of the major production variables (N, B, P) with body size because they all interact to contribute to the ultimate relationship of body size with P/B (Appendix I). As will be seen, each of the predictions described below is derived from the theoretical framework proposed by Brown et al. (2004).

Prediction 1 Density (N, number of individuals m2) will decrease as body mass increases (M, mg individual; Fig. 4.1). Some previous studies (e.g. Brown et al., 2004; Woodward et al., 2005a) have indicated that N / M0.75 when the relationship is fitted to a power curve using least-squares regression. This relationship is expected if the following conditions are met: (1) requirement for resources by individuals scales as M0.75, (2) population size increases until limited by resources (i.e. equilibrium density), and (3) total resource use will be independent of M because resources are used at equal rates by members of each size class within a given population (Brown et al., 2004).

log abundance (N, individuals m–2) log biomass (B, mg m–2) log production (P, mg m–2 yr–1) log P/B (P/B, yr–1)

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7

B ∝ M0.25

6

P ∝ M0

5 4

P/B ∝ M –0.25

3 2 1

N ∝ M –0.75

0 1

2

3

4

5

6

body size (M, mg individual–1)

Figure 4.1 Predicted relationships between individual body mass and areaspecific abundance, biomass, production and the P/B. The predictions follow Brown et al., 2004.

BIOMASS TURNOVER AND BODY SIZE

Prediction 2 Assuming that a population is at equilibrium density (i.e. N / M0.75), population biomass (B ¼ M  N, mg dry mass or ash-free dry mass m2) will increase with body mass, such that B / M0.25 (Fig. 4.1). This relationship is attributed to a lower rate of flow of energy and resources through the bodies of large versus small organisms (indicated by time-specific P/B, see Appendix I, Fig. 4.10) as a result of lower metabolic costs (see Prediction 3, below; Brown et al., 2004). Prediction 3 Biomass turnover rate (P/B, yr1) will decrease with increasing M, because organisms with large body sizes often have longer development times (or CPIs, Appendix I) compared with organisms with small body sizes. The decrease in P/B is proportional to M0.25 (Fig. 4.1), which is equivalent to dividing P / M0 (see Prediction 4, below) by B / M0.25. P/B / M0.25 is identical to the relationship of the empirically derived mass-specific metabolic rate with M (Brown et al., 2004). Prediction 4 Production (P ¼ B  P/B, mg dry mass or ash-free dry mass m2 yr1) will be independent of body size (Brown et al., 2004). This is because the product of B / M0.25 and P/B / M0.25 is equivalent to P / M0 (Fig. 4.1). Each of these predictions is subject to the assumptions that resource supply and temperature are constant across body-size classes. These assumptions appear to be reasonable for population and taxon-specific production statistics extracted from within single and independent stream communities rather than for data that are pooled across communities. This is an important distinction because most studies of the relationship between body size and components of production are based on the analysis of variables pooled across a diverse assemblage of communities and ecosystems (e.g. Banse & Mosher, 1980; Benke, 1993; Morin & Dumont 1994; Brown et al., 2004), yet the factors believed to constrain these variables – such as temperature and nutrient and organic carbon supply – operate within communities and ecosystems (see Cyr & Walker, 2004).

Study streams We used data from four streams for our tests of these predictions – the Ogeechee River, Georgia; Upper Ball Creek, North Carolina; and Sutton Stream and Stony Creek, New Zealand. Each stream has perennial flow and we assume that trophic resources limit community secondary production rather than physical factors such as disturbance (see assumptions related to Prediction 1). Since our data sets are based on discrete communities we are able to assume that representatives of the different body-mass classes within each system were subject to similar resource and temperature regimes. We chose these streams because the production dynamics of their communities has

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been studied in depth. What is also particularly significant, however, is the way production was estimated for each community. Special effort was made to include all taxa of macrofauna and temporary meiofauna (e.g. retained by 100 to 250 mm mesh sieves), and production calculations for each community were independent of one another. In other words, production calculations were based entirely on system-specific and taxon-specific growth rates and lifehistory studies. This is an important point because many estimates of production are based on CPIs, P/Bs, or growth rates that have been derived from other species and/or systems. This is clearly problematical for analyses that require independent data.

Ogeechee River The Ogeechee is a low-gradient coastal plain river in which the major stable habitat is submerged wood (snags). Mean daily water temperature ranges from 2.0 to 30.88C (annual mean 19.38C) and mean annual discharge is 67 m3 s1. The densities, biomass, production and annual P/B values for its snag-inhabiting community, which is composed of more than 40 invertebrate taxa, were estimated during 1982 (Benke & Parsons, 1990; Benke & Jacobi, 1994; Benke & Wallace, 1997; Benke, 1998; Benke et al., 2001; Benke, 2002). Twenty snag samples were collected at least monthly. Care was taken to obtain the full range of insect size classes by using a 100 mm mesh sieve. Individual growth studies were done for many of the small fast-growing taxa (selected Diptera and Ephemeroptera) so that accurate taxon-specific estimates of biomass turnover (annual P/B) could be obtained. The snag community is extremely productive, when compared with the shifting-sand community of the main channel. Total annual snag production during the study was 109.3 g DM m2 (snag surface area) for primary consumers, 30.8 g DM m2 for omnivores, and 7.5 g DM m2 for predators. Upper Ball Creek Upper Ball Creek is a fishless, high-gradient headwater stream in the Appalachian Mountains of western North Carolina, USA. Its catchment is heavily forested and relatively undisturbed. Annual mean daily water temperature and discharge are 8.48C and 20 L s1, respectively. Production of its macroinvertebrate community (71 taxa) was estimated for one year during 1982–1983 (Huryn & Wallace, 1986, 1987a, 1987b; Huryn, 1990). Twenty samples were taken at monthly intervals at random locations within a 400-metre reach using a Surber sampler fitted with a 232 mm mesh net or a coring device. Samples were processed using a 100 mm sieve. Individual growth studies were done for many of the small fastgrowing taxa (Chironomidae) and slow growing taxa (crayfish) so that accurate taxon-specific estimates of biomass turnover (annual P/B) could be obtained. Annual macroinvertebrate production was 5.1 and 1.9 g ash-free dry mass m2 for primary and secondary consumers, respectively.

BIOMASS TURNOVER AND BODY SIZE

Sutton Stream and Stony Creek Sutton Stream and Stony Creek are moderate-gradient headwater streams in the Lammerlaw Range of the South Island of New Zealand. The river valleys are incised and rugged with schist bedrock. Vegetation is largely exotic pasture grasses and native tussock grasses that are extensively grazed by livestock. The 400-metre study reaches selected at each site have no canopy, although there are shrubs along the stream margins. Mean daily water temperature ranged from 0.0 to 17.48C (annual mean ¼ 5.68C) in Sutton Stream, and from 0.0 to 16.48C (annual mean ¼ 6.08C) in Stony Creek. Mean annual discharge of Sutton Stream is 568 L s1; discharge of Stony Creek is 461 L s1. Sutton Stream is inhabited by introduced brown trout (Salmo trutta); Stony Creek is inhabited by native river galaxias (Galaxias eldoni). These fish species are the top predators in both systems. Production was estimated for a one year period during 1991–1992 for 37 taxa in Sutton Stream and 42 taxa in Stony Creek (Huryn, 1996a, 1996b, 1998). Samples used to estimate invertebrate production were collected from each stream approximately monthly during 1991–1992. Sixteen benthic samples were taken from random locations approximately monthly using a 900 cm2 Surber sampler fitted with a 232 mm net. Samples were processed using a 250 mm sieve. Individual growth studies were done for many of the small fastgrowing taxa (Leptophlebiidae) and slow-growing taxa (Potamopyrgus) so that accurate taxon-specific estimates of biomass turnover (annual P/B) could be obtained. Fish production was also estimated using standard methods (Huryn, 1996a, 1998). Annual primary consumer production for Sutton Stream was 11.2 g ash-free dry mass m2, secondary consumer production was 2.1 g m2, and trout production was 2.1 g m2. Primary, secondary and Galaxias production in Stony Creek were 7.7, 0.9 and 0.2 g m2 yr1, respectively. Trout predation in Sutton Stream exerted strong top-down control on prey production. In comparision, Galaxias predation in Stony Stream had minor energetic consequences for prey production (Huryn, 1998).

Tests of predictions The average individual mass for each taxon was estimated as B/N ¼ M (mg individual1) for each stream community. Two basic approaches were used. The first approach consisted of summing production statistics for taxa occurring within discrete body-size classes. M was log10 transformed and each taxon assigned to the appropriate body-size class (log10M ¼ 0.5–0.99, 1.0–1.49 . . . 6.5–7.49). The N, B and P values for each taxon in each size class were then summed as suggested by Brown et al. (2004). A P/B was then calculated for each size class using summed values. Plots of body-mass category versus log10 transformed N, B, P and P/B were then prepared and least-squares regression was used to fit a linear model to the plots. The second approach assessed the relationship

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between M and N, and M and P/B, using individual taxa rather than size classes. The purpose of this analysis was to assess the variability of the relationship between M and N, and M and P/B within independent communities. Scaling coefficients for log10 N, B, P and P/B versus log10 M were obtained from least-squares linear-regression models. Predicted scaling exponents were assumed to be statistically indistinguishable from observed exponents when they fell within two standard errors (SE) of the latter. Results The scaling exponents for N versus M (taxa summed within size classes) ranged from 0.99 to 0.59 (Fig. 4.2). All regressions were significant (p < 0.05). The scaling exponents were negative and within one (Ball Creek, Sutton Stream, Stony Creek) or two SE of the predicted exponent of 0.75 (Fig. 4.3). The scaling exponents for B versus M (summed taxa) ranged from 0.13 to 0.29 (Fig. 4.4). Only the regression for Ball Creek was significant, however (p < 0.04). Nevertheless, the relationship between B and M was similar for all streams, with positive exponents that were within one SE of the predicted exponent of 0.25 (Fig. 4.3).

Ball Creek log10N = 4.52 – 0.76 log10M (r2 = 0.95, p < 0.001)

Ogeechee River log10N = 5.35 – 0.99 log10M (r2 = 0.88, p < 0.001)

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Stony Creek log10N = 4.68 – 0.91 log10M (r2 = 0.78, p < 0.01)

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Figure 4.2 Log-log plots of population density (N ¼ individuals/m2) against M (summed taxa, mg/individual) for the snag-community of the Ogeechee River and benthic communities of Ball Creek, Sutton Stream and Stony Creek. The largest body-size class for Ball Creek is occupied by crayfish. The largest body-size classes for the latter two streams are occupied by invertivorous fishes. The grey line indicates the predicted slope of the relationship between log10N and log10M (N / M0.75). The black line indicates the slope derived from least-squares regression of the data.

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BIOMASS TURNOVER AND BODY SIZE

Figure 4.3 Summary of regression coefficients describing the slopes of the relationships between body size (M) and N, B, P/B and P for the snag-community of the Ogeechee River and benthic communities of Ball Creek, Sutton Stream and Stony Creek. The solid black lines indicate predicted slopes of the relationships (i.e. N / M0.75, B / M0.25, P/B / M0.75 and P / M0). The error bars are 1 SE.

The scaling exponents for annual P/B versus M (summed taxa) ranged from 0.24 to 0.27 (p < 0.01) for Ball Creek, Sutton Stream and Stony Creek, and were remarkably similar to the predicted exponent of 0.25 (Figs. 4.3 & 4.5). The scaling exponent for the Ogeechee River (0.50, p < 0.01), however, diverged substantially from this prediction (Figs. 4.3 & 4.5). The regression of P versus M was not significant, as predicted, for Ball Creek, Sutton Stream and Stony Creek, with scaling exponents ranging from 0.13 to 0.03 (Fig. 4.6). Each of these fell within one SE of the predicted exponent of 0 (Fig. 4.3). The scaling exponent for the Ogeechee River, however, indicated a strong negative relationship between P and M (summed taxa, Fig. 4.6) and, like the P/B values estimated for this community (Fig. 4.5), showed a significant departure from the expected exponent (Fig. 4.3). Production by the snag community of the Ogeechee River was much greater than the other streams, as indicated by the relative height of the normalization constant for the relationship between P and M (summed taxa, Fig. 4.6). This is to be expected, given the three- to four-fold greater average annual temperature of the Ogeechee River compared with the other streams (Brown et al., 2004). The scaling exponents for N versus M (individual taxa) ranged from 0.79 to 0.52 (Fig. 4.7). Those for the Ogeechee River and Ball Creek fell within one SE,

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Ball Creek log10B = 1.72 + 0.21 log10M (r2 = 0.54, p < 0.04)

Ogeechee River log10B = 2.38 + 0.13 log10M (r2 = 0.12, p = 0.402)

log10B (mg/m2)

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Stony Creek log10B = 1.77 + 0.13 log10M (r2 = 0.06, p = 0.590)

Sutton Stream log10B = 1.29 + 0.29 log10M (r2 = 0.27, p = 0.230)

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Figure 4.4 Log-log plots of population biomass (B ¼ mg/m2) against M (mg/individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10B and log10M (B / M0.25). The black line indicates the slope derived from least-squares regression of the data.

and those for Stony Creek and Sutton Stream fell within two SE, of the predicted slope of 0.75. The scaling exponents for P/B versus M (individual taxa) ranged from 0.41 to 0.18 (Fig. 4.8). The exponents for Stony Creek and Sutton Stream fell within one SE, and the exponent for Ball Creek fell within two SE, of the predicted exponent of 0.25. Only the exponent of the Ogeechee River (0.41) departed significantly from the predicted value. Although greater variability is apparent in both the departure of the observed scaling exponents from those expected, and the relatively low r2 of the regression models, the pattern of concordance of observed-to-predicted scaling exponents among communities, using individual taxa (>37 taxa per stream), was essentially the same as that observed for the analysis using taxa summed within size classes (seven to eight size classes per stream). Discussion Annual biomass turnover rates for benthic freshwater macroinvertebrates range over four orders of magnitude, from <1 to >200 (Butler, 1982; Benke, 1998; Huryn & Wallace, 2000). Although annual P/Bs for taxa with relatively

BIOMASS TURNOVER AND BODY SIZE

Ball Creek log10P/B = 1.22 – 0.24 log10M (r2 = 0.75, p < 0.006)

log10 annual P/B

Ogeechee River log10P/B = 2.46 – 0.50 log10M (r2 = 0.89, p < 0.001)

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Figure 4.5 Log-log plots of annual P/B (yr1) against M (mg/individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10P/B and log10M (P/B / M0.25). The black line indicates the slope derived from least-squares regression of the data.

small body size (e.g. M  <25 mg DM) may range over several orders of magnitude, there is little doubt that taxa within this size range are capable of generating among the highest rates of biomass turnover reported for eukaryotes. Although often overlooked in studies of community production, due to small body size and low population biomass, the identification and quantification of the P/Bs of such taxa is crucial to understanding the dynamic attributes of food web links (Benke & Wallace, 1997; Woodward et al., 2005b; Stead et al., 2005). The factors controlling rates of biomass turnover are myriad, but aside from food quality and supply the two most influential factors are probably temperature and body size. A number of studies based on empirical approaches have explicitly demonstrated the positive effect of temperature (Benke, 1993; Morin & Dumont, 1994) and the negative effect of body size of freshwater invertebrates (Banse & Mosher, 1980; Benke, 1993; Morin & Dumont, 1994; Plante & Downing, 1989; Morin & Bourassa, 1992) on time-specific biomass turnover rates. Mechanistic explanations for the relationship between P/B and food quality and temperature are obvious; explanations of the relationship between P/B and body size are not. Numerous and diverse explanations have been suggested, but none is yet universally accepted, greatly complicating the theoretical basis for

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Ball Creek log10P = 2.94 – 0.02 log10M (r2 = 0.03, p = 0.705)

Ogeechee River log10P = 4.83 – 0.37 log10M (r2 = 0.60, p < 0.02)

log10 annual P(mg/m2)

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Stony Creek log10P = 3.09 – 0.13 log10M (r2 = 0.07, p = 0.556)

Sutton Stream log10P = 2.77 – 0.03 log10M (r2 = 0.00, p = 0.887)

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Figure 4.6 Log-log plots of annual P (P ¼ mg m2 yr1) against M (mg/ individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10P and log10M (P / M0). The black line indicates the slope derived from leastsquares regression of the data.

predicting scaling exponents (Cyr & Walker, 2004). For our analysis, we selected the recently formalized metabolic theory of Brown et al. (2004) as a framework for posing testable predictions about the relationship between components of production and body size. Their metabolic theory is grounded on the assumption that processes driven by metabolism at all ecological scales are subject to quarter-power scaling, and that individual metabolism scales as M0.75 due to the fractal-like architecture of internal distribution systems (Woodward et al., 2005a). For our test of selected predictions of this theory, we specifically focused on several independent communities because factors constraining bioenergetic relationships among animals should be most effectively expressed at the community scale (Cyr & Walker, 2004). The results of our analysis indicate that the scaling exponents describing the relationship between N, B, P/B and P for the communities of Ball Creek, Sutton Stream and Stony Creek showed a high level of concordance with the predicted quarter-power scaling relationships. Among the analyses of the different production variables, the relationship between P/B and M (summed taxa) showed the highest level of precision, with the scaling exponent varying from only 0.24 to 0.27, which bracketed the predicted exponent (0.25), and with

BIOMASS TURNOVER AND BODY SIZE

log10N (individuals/m2)

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Figure 4.7 Log-log plots of population density (N ¼ individuals/m2) against M (individual taxa, mg/individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10N and log10M (N / M0.75). The black line indicates the slope derived from least-squares regression of the data.

r2 values ranging from 0.75 to 0.86. The close agreement shown for these scaling exponents with that predicted by metabolic theory seems extraordinary when considering the large ecological differences between streams, e.g. forest vs. grassland; with fish vs. without fish; strong top-down control vs. weak topdown control (cf. Huryn & Wallace, 1987b; Huryn, 1998), and the fact that consumers from two to three trophic levels were included in the analysis. In contrast with the temperate stream communities used in our analysis, however, the scaling exponents for P/B against M, and P against M for the snag community of the subtropical Ogeechee River showed relatively large and significant departures from predicted values. This lack of concordance between observed and predicted scaling exponents indicates fundamental differences between the production dynamics of the different stream communities. Similar departures from predictions of the metabolic theory have been observed for aquatic ecosystems with strongly size-structured trophic chains (Jennings & Mackinson, 2003; Brown & Gillooly, 2003). For these systems, and presumably others with a strong correlation between body size and trophic level, it has been suggested that inefficient transfers of biomass between trophic levels may result in a step-wise reduction in the slope of the biomass–body size relationship (Jennings & Mackinson, 2003; Brown & Gillooly, 2003). Depending upon the

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Ogeechee River log10P/B = 2.14 – 0.41 log10M (r2 = 0.51, p < 0.0001)

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Figure 4.8 Log-log plots of annual P/B (yr1) against M (individual taxa, mg/ individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10P/B and log10M (P/ B / M0.25). The black line indicates the slope derived from least-squares regression of the data.

value of the actual trophic efficiencies and the relative sizes of predator and prey, the relationship of both N and B vs. M may be altered (e.g. N / M0.75 ! N / M1.0; B / M0.75 ! B / M0; Brown & Gillooly, 2003) which will have consequences for P vs. M (e.g. P / M0.25 rather than M0 when B / M0). Considering that the scaling exponents for B and N vs. M for the Ogeechee River were not significantly different from 1 and 0, respectively (e.g. Fig. 4.3), the expectation of a scaling exponent substantially <0 for P vs. M seems reasonable. On the other hand, there appears to be little substantive support for this explanation of the difference between scaling exponents among the temperate streams. The relationship between trophic position and M was plotted for the taxa occurring in each of the four stream communities, based on general knowledge of feeding habitats of their fauna for the three temperate streams, and actual gut analysis for members of the snag community of the Ogeechee River (Benke & Wallace, 1997; Benke et al., 2001; Fig. 4.9). A comparison of the resulting plots shows that a rather broad spectrum of body size is apparent for primary and secondary consumers in all communities, with little indication of a greater correlation between body size and trophic position in the Ogeechee River than for the temperate streams. Another major factor to consider in an attempt to explain the discrepancy in scaling of P/B vs. M among stream communities is the ecological characteristics

BIOMASS TURNOVER AND BODY SIZE

trophic level or position

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Figure 4.9 Plots of annual trophic level or trophic position against log10M (individual taxa, mg/ individual) for four stream communities (see Fig. 4.2 for details). Trophic position (sensu Benke & Wallace, 1997) for taxa from the Ogeechee River was estimated on the basis of gut content analysis. Trophic level for taxa from the remaining three communities was presumed on the basis of published feeding habits and limited gut analysis.

of the Ogeechee snag-habitat itself. A significant proportion of the production of the snag community is subsidized by organic seston (suspended particles) that is continuously delivered from habitats upstream. This high-quality and abundant food source supports exceedingly high densities of filter-feeding organisms on the snags (Benke & Parsons, 1990; Benke & Wallace, 1997; Benke, 1998). This is reflected, to some degree, by the high densities of small organisms in the Ogeechee River community compared with the temperate streams (Figs. 4.2 & 4.7). Other types of primary consumers, however, must browse organic matter directly from the surface of the snag (Benke & Jacobi, 1986, 1994; Benke, 1998). Differences in resource quality and supply rate, along with the relative metabolic costs of radically different feeding strategies, could potentially cause scaling exponents to depart from predicted values due to a confounding effect of source of food (e.g. seston vs. biofilm) and body size. Knowledge of the comparative bioenergetics of these different feeding guilds, and whether these are confounded with the size-distribution of the integrated snag community, is required to assess this hypothesis properly. In summary, the overarching hypothesis of metabolic theory, that the commonality of metabolic processes across scales from cellular to ecosystem explains the relationship between body size and N, B, P and the P/B, was clearly not rejected for our sample, albeit small, of temperate-stream communities. This finding suggests that the following conditions may be of primary importance in determining

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community-scale patterns of production in temperate streams: (1) trophic resource demand scales as M0.75, (2) resources are used at equal rates by members of each body-size class, and (3) N is maintained at an equilibrium density (Brown et al., 2004). Our finding is particularly relevant to studies of stream productivity because it suggests that, within temperate-stream communities, the interaction of individual body mass and metabolism and population abundance results in levels of secondary production that are essentially constant across the entire spectrum of body sizes occurring within macrofaunal communities. In comparison with the temperate stream communities, the overarching hypothesis of metabolic theory was rejected for the snag-dwelling community of the Ogeechee River, indicating a fundamental difference between community structure and function between stream types. This finding should stimulate the formulation of questions concerning processes underlying differences between body size and the secondary production of stream communities and demonstrates the strength of the theoretical framework of Brown et al. (2004) as an investigative tool. We conclude by briefly considering the ‘predictive’ power of the metabolic theory of ecology, and its application to studies of ecological productivity. The empirical relationships that form the grist for current metabolic theory (e.g. Brown et al., 2004) do have relatively high predictive power in the sense that scaling exponents produced using data sets integrating numerous and often phylogenetically diverse taxa representing a large range of body sizes vary little among different data sets. Analyses of data sets representing a smaller number of closely related taxa (e.g. different orders of benthic insects), however, may show exponents that diverge radically from predictions (e.g. Benke, 1993; Morin & Dumont, 1994). Further, even within single communities, the range of residual variance of the dependent variable for typical plots of N, B, P/B or P against M for specific taxa may range over several orders of magnitude (Figs. 4.7 & 4.8). It remains unclear whether these exceptions are true departures from metabolic theory or are attributable to systematic factors, such as a low signal-to-noise ratio, that occur when the range of body size used in analyses is constrained. Given this level of uncertainty, the predictive power of metabolic theory for determining production statistics (i.e. P, P/B) for single populations or even communities is of dubious value. The predictive power of metabolic theory does hold great promise for identifying important questions about general relationships between body size and metabolic processes within and across broad scales of ecological pattern and process.

Appendix I A primer on secondary production and the P/B Production is generally defined as the formation of biomass through time (Benke, 1993; Benke & Huryn, 2006). It is essentially the increase of an individual’s mass over time scaled to the population or community levels of ecological

BIOMASS TURNOVER AND BODY SIZE

organization. When scaled beyond the level of the individual, production is a flow or flux per unit of time (e.g., amount of biomass formed per unit of area per unit of time, mg m2 yr1 or mg m2 d1). Estimating secondary production is labor intensive, when compared with estimates of abundance or biomass alone. One must also be able to either follow cohorts through time, know biomassspecific growth rates (for instance, mg mg1 d1), or know mean developmental times (cohort production interval or CPI, d) (Benke & Huryn, 2006). The rate of production is conveniently expressed as either the cohort or timespecific (e.g. daily or annual) biomass turnover. The cohort biomass turnover (P/B over the length of the CPI) ranges within one order of magnitude (2–8, Fig. 4.10, left), and 5 has long been used as a proxy for expected cohort P/B (Waters, 1969). This relative consistency is due to the limited range of the logarithm of the ratio of the mass of the final to initial larval mass (Waters, 1987). The cohort P/B shows a strong positive relationship with body size because the relative increase in body mass during the CPI is greatest for taxa attaining a large body mass (Fig. 4.10, left). The cohort P/B can be easily converted to a time-specific biomass turnover rate if one knows the approximate length of a population’s CPI because the annual P/B is approximated as 5  365/CPI. For example, if a CPI ¼ 30 days, then the associated annual P/B  5  365/30  60. In this example, biomass would replace itself 60 times throughout the year and the biomass turnover time would be 365/60 or 12 days. Similarly, the daily P/B can be approximated as 5  1/30  0.17. The daily P/B is essentially the same as g, the daily biomass growth or turnover rate (see Benke & Huryn, 2006, for algorithm used to calculate g). In summary, an organism with a CPI that approximates 1-year will show annual P/Bs ranging from 2 to 8. One that has a CPI  1-year will show a low annual P/B (e.g. <2, Huryn & Wallace, 1986), and one that has a CPI  1-year will show a high annual P/B (e.g. >20, Benke, 1998). The annual P/B for most species of freshwater invertebrates was once widely believed to vary from <5 (species with CPIs longer than a year) to about 5–10 (species with CPIs  6 months to 1 year; Waters, 1977; Banse & Mosher, 1980). However, detailed studies of species in warm-water systems have shown that CPIs can be <1 month and daily g can be >0.1 d1; thus, annual P/B can be substantially greater than 10 or even 100 (Benke & Parsons, 1990; Benke & Jacobi, 1994; Benke, 1998; Jackson & Fisher, 1986; reviewed by Huryn & Wallace, 2000). In fact, some species living in coldwater environments can also have relatively high growth rates and short CPIs (Huryn & Wallace, 1986; Nolte & Hoffman, 1992) resulting in annual P/B ranging well above 20 (reviewed by Huryn & Wallace, 2000). Two very different life-history patterns underlie high rates of biomass turnover. The first is a single generation year1 followed by a long period of developmental quiescence (e.g. resting egg). In such cases, biomass will be present in

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1000

P/Bc = 6.608 M0.11 (r2 = 0.48, p < 0.001, df = 32)

annual P/B

10

cohort P/B

100

P/Ba = 4.367 M –0.22 (r2 = 0.31, p < 0.001, df = 525)

10 1

10000

100

1000

1

10

0.1

0.01

M (mg)

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 10000

0.1

1 0.001

70

M (mg)

Figure 4.10 Left: plot of estimates of cohort P/B and individual body mass for a broad range of taxa. Cohort P/B was estimated as the natural logarithm of the ratio of final mass to egg or hatchling mass. Body mass was estimated as the geometric mean of the product of final mass and egg or hatchling mass. Data from Anderson et al., 1998; Benke & Wallace, 1980, Berg & Hellenthal, 1992; Brown & Fitzpatrick,1978; Harvey et al., 1980; Huryn, 1996a; Huryn (unpublished data). Right: plot of annual P/B and individual body mass (M) for a broad range of taxa. Data were taken from the literature. Body mass was estimated as B/N, where B is average population biomass (mg/m2) and N is average population density (individuals/m2). Note that the slope of N versus annual P/B (0.22) is similar to that predicted using metabolic theory (0.25; Brown et al., 2004). The relationship between M and P/B was marginally improved by using mean annual temperature (T) and M as independent variables (log10P/ Ba ¼ 0.9796 þ 0.0273 T (8C)  0.2196 log10 M; r2 ¼ 0.42, p < 0.001, df ¼ 454). Data from Benke, 1998; Bergtold & Traunspurger, 2005; Bowles & Allen, 1991; Bowles, 1990; Brown & Fitzpatrick, 1978; Butler, 1982; Chadwick & Huryn, 2005; Collier & Winterbourn, 1990; Dixon & Wrona, 1992; Dudgeon, 1995, 1996, 1997, 1999; Eggert & Burton, 1994; Gı´slason & Gardarsson, 1988; Grafius & Anderson, 1979; Grafius & Anderson, 1980; Griffith et al., 1994; Hall et al., 1980; Harding & Winterbourn, 1993; Huryn & Wallace, 1987a, b; Huryn, 1996a, 1998; Huryn et al., 1995; Iverson, 1980; Jop & Stewart, 1987; Jop & Szczytko, 1984; Kobuszewski & Perry, 1994; Linklater & Winterbourn, 1993; Lobinske et al., 1996; Mackay & Waters, 1986; Marchant & Hehir, 1999; Marchant & Scrimgeour, 1991; Marchant, 1986; Marchant et al., 1985; Mitchell & Smock, 1991; O’Doherty, 1985; Parker & Voshell, 1983; Phillips et al., 1994; Ramı´rez & Pringle, 1998; Robinson et al., 1992; Rodgers, 1982; Roeding & Smock, 1989; Sallenave & Day, 1991; Sanchez & Hendricks, 1997; Scho¨nborn, 1977; Scrimgeour, 1991; Short & Ward, 1980; Short et al., 1987; Smith & Smock, 1992; Smock et al., 1985; Stagliano & Whiles, 2002; Stead et al., 2005; Takeda & Grzybkowska, 1997; Waters & Hokenstrom, 1980; Whitmore & Huryn, 1999; Willis & Hendricks, 1992; Winterbourn, 1974, 1996.

BIOMASS TURNOVER AND BODY SIZE

significant quantities for a small proportion of the year (short CPI), which will lead to a high annual P/B. Even taxa achieving a relatively large body mass can have relatively high annual P/Bs if they follow this life-history pattern (Huryn, 2002). The second pattern – of greater interest from a bioenergetic perspective – is multiple generations year1, each with a short CPI. This pattern is common for many stream invertebrates, such as chironomid midges, black flies and many baetid mayflies (Benke & Parsons, 1990; Benke & Jacobi, 1994; Benke, 1998). Given the universal constraints of eukaryotic anabolism, organisms with the very short CPIs (e.g. <1 month) tend to have a very low body mass. Given this simple relationship it should not be surprising therefore that body size and development time are correlated and that body size is closely related to annual and daily P/B (Fig. 4.10, right). Yet there are so many exceptions to this relationship, as suggested by the wide scatter of data when annual P/B is plotted against body mass (Fig. 4.10, right), that it can hardly be considered a rule. This is because taxa with a small body mass exhibit a wide range of annual P/Bs – from very low to very high – while those with a large body mass tend to have low annual P/Bs. For example, annual P/Bs for the often diminutive larvae of the family Chironomidae (Diptera) range over four orders of magnitude (<1–258; Butler, 1982; Benke, 1998; reviewed by Huryn & Wallace, 2000) while their biomass usually ranges within a single order of magnitude. Obvious factors underlying this variation are those directly affecting anabolic processes, such as temperature and food quality and quantity. For example, it should be no surprise that temperature, along with body size, explains a significant amount of variation in time-specific P/Bs among populations (Plant & Downing, 1989; Benke, 1993; Morin & Dumont, 1994; also see sources cited in the caption of Fig. 4.10). Furthermore, much variation in these data is because animals are from multiple ecosystems representing a wide range of other factors such as food quality and quantity. In spite of the poor fit (Fig. 4.10, right; r2 ¼ 0.31), it is clear that high annual P/B can be demonstrated in small size classes. The significant bioenergetic role that taxa with small body size may play within food webs should never be underestimated. Although population biomass is usually low for such taxa, high annual P/Bs can lead to enormous levels of production of macrofaunal invertebrates (e.g. 65–135 gm DM m2 yr1, Jackson & Fisher, 1986; Benke, 1998; reviewed by Huryn & Wallace, 2000). Unfortunately, empirical knowledge of the production dynamics of meiofaunal benthic invertebrates as well as the smaller size-range of macrofauna remains primitive. Recent attempts at quantifying meiofaunal production for stream and lake benthic invertebrate communities indicate that levels may be similar to those estimated for macrofauna (Bergtold & Traunspurger, 2005; Stead et al., 2005).

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Waters, T. F. (1969). The turnover ratio in production ecology of freshwater invertebrates. American Naturalist, 103, 173–185. Waters, T. F. (1977). Secondary production in inland waters. Advances in Ecological Research, 10, 91–164. Waters, T. F. (1987). The effect of growth and survival patterns upon the cohort P/B ratio. Journal of the North American Benthological Society, 6, 223–229. Waters, T. J. & Hokenstrom, J. C. (1980). Annual production and drift of the stream amphipod Gammarus pseudolimnaeus in Valley Creek, Minnesota. Limnology and Oceanography, 25, 700–710. Whitmore, N. & Huryn, A. D. (1999). Life history and production of Paranephrops zealandicus in a forest stream, with comments about the sustainable harvest of a freshwater crayfish. Freshwater Biology, 42, 1–11. Willis, L. D. & Hendricks, A. C. (1992). Life history, growth, survivorship, and production of Hydropsyche slossonae in Mill Creek, Virginia. Journal of the North American Benthological Society, 11, 290–303. Winterbourn, M. J. (1974). The life histories, trophic relations and production of Stenoperla prasina (Plecoptera) and Deleatidium sp. (Ephemeroptera) in a New Zealand river. Freshwater Biology, 4, 507–524. Winterbourn, M. J. (1996). Life history, production and food of Aphrophila neozelandica (Diptera: Tipulidae) in a New Zealand Stream. Aquatic Insects, 18, 45–53. Woodward, G., Ebenman, B., Emmerson, M. et al. (2005a). Body size in ecological networks. Trends in Ecology and Evolution, 20, 402–409. Woodward, G., Spiers, D. C. & Hildrew, A. G. (2005b) Quantification and resolution of a complex, size-structured food web. Advances in Ecological Research, 36, 85–135.

CHAPTER FIVE

Body size in streams: macroinvertebrate community size composition along natural and human-induced environmental gradients COLIN R . TOWNSEND University of Otago, New Zealand

ROSS M . THOMPSON Monash University, Australia

Introduction Communities contain a diversity of species and a spectrum of life forms. A consequence of evolutionary processes is that lists of species from different communities tell us almost nothing about how similar they are ecologically. On the other hand, by quantifying the life-history traits represented, we can discern similarities and differences among communities and gain an understanding of the functional relationships between traits and habitats. In response to Southwood’s (1977) contention that habitat provides the templet upon which evolution forges characteristic life-history strategies, we are interested in the extent to which life-history traits of macroinvertebrates can be directly mapped onto stream habitat axes. More recently, stream researchers have used the metaphor of environmental filters (Poff, 1997) that can eliminate certain traits and produce similar trait compositions in similar habitats (Statzner, Dole´dec & Hugueny, 2004). Trait-specific selective forces along environmental gradients may act over evolutionary time, as Southwood (1977) contended, or over an ecological time scale, selecting for successful strategists from the potential pool of colonists. The earliest categorization of species traits in stream ecology related to trophic role. Cummins (1974) identified grazer-scrapers, fine particle collectors (gatherers or filterers), large particle shredders and predators. Stream ecologists now use this trophic categorization to focus on the similarities and differences of communities in different parts of the world (e.g. Winterbourn, Rounick & Cowie, 1981; Thompson & Townsend, 2000; Fenoglio, Bo & Cucco, 2004), in different parts of the river continuum (e.g. Vannote et al., 1980; Grubaugh, Wallace & Houston, 1996) and in different kinds of terrestrial setting (e.g. Thompson & Townsend, 2000; Woodward & Hildrew, 2002). Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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Recognizing that a further fundamental feature of stream ecosystems is their flow-related disturbance regimes, Townsend & Hildrew (1994) developed predictions about how disturbance might be linked to species traits related to resistance (the capacity to withstand the disturbance) and resilience (the capacity to recover rapidly after a disturbance). There have now been many tests of these predictions (e.g. Resh et al., 1994), with support, for example, for the hypotheses that more frequent disturbance should be associated with traits that confer resilience (adult mobility, habitat generalism, rapid population growth) or resistance (clinging behaviour, streamlined/flattened morphology, several life stages outside the stream) (Townsend, Dole´dec & Scarsbrook, 1997). Others have sought to match further habitat features to the representation of traits, including the size and heterogeneity of the substratum (Bourassa & Morin, 1995; Gayraud & Phillipe, 2001; Schmid, Tokeshi & Schmid-Araya, 2002) and hydraulic variables (Statzner, Gore & Resh, 1988; Hart & Finelli, 1999; Merigoux & Dole´dec, 2004). Among the diversity of physiological, morphological and behavioural traits (related to gathering resources, surviving in the face of various threats, and reproduction), body size has a pivotal position. The size structure of communities can be directly influenced by ecological drivers including size-selective predation (particularly by fish), size-related risk of dislodgement by hydraulic forces, and the provision of streambed size-related refugia that may counter predation or dislodgement risks. But we can also expect indirect links between size and habitat dimensions because size is related to many other traits. For example carnivores and shredders are over-represented in bigger size classes, reflecting the larger size of their food particles. Moreover, species that are resilient because of short life cycles, rapid growth and high reproductive rates, are also usually small (Townsend et al., 1997). Furthermore, size may be positively correlated with competitive status (Bourassa & Morin, 1995) and negatively correlated with the possession of an aquatic imago stage and ovoviviparity (Statzner et al., 2004) as well as vulnerability to environmental contaminants (Hendriks & Heikens, 2001). The focus of this chapter is the match between body size and influential abiotic and biotic environmental gradients. We explore relationships with disturbance, substratum particle size and hydraulic stress, and with primary productivity and fish predation. We also test hypotheses in the context of human-influenced habitat gradients, comparing streams in forested, native grassland and pastoral settings. In the next section, we review previous stream studies of body-size patterns before proceeding to our analysis of a new database for tributaries in the south of New Zealand.

Different approaches for matching body size with environmental gradients The advantage of experimental over descriptive studies is their comparative simplicity, controlling (ideally) for all factors except the environmental gradient

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of interest. Although beset by complexity, descriptive studies, on the other hand, have the advantage of naturalness: but to be detectable, matches between body size and environmental gradients must be powerful enough to outweigh background noise. In the descriptive and experimental studies reviewed below, body size has been dealt with in two ways. Some researchers record the size of every individual present, while others use the shortcut of ascribing to all individuals in a given taxon the full size normally attained (‘maximal size’ below). The size range of invertebrates also varies, with a few studies including the meiofauna (42–500 mm; Fenchel, 1978) while most have focused on macroinvertebrates alone. Invertebrates are invariably sampled to include both those living on the surface and those in the top 5–10 cm of the substratum. Descriptive studies of abiotic gradients Townsend and Hildrew (1994) predicted that small size would be more prevalent in more frequently disturbed habitats, but that this pattern would be muted where spatial heterogeneity was high. The conceptual basis for the first prediction is that resilience in the face of frequent and intense disturbances would be provided by young age at reproduction, many descendants per reproductive cycle and many reproductive cycles per year, features that are themselves linked to small size. The second prediction derives from the idea that some streams possess a greater variety and quantity of physical refugia, such as large substratum particles and interstitial spaces in the bed. In these cases, larger species may still do well even in the face of disturbance. These hypotheses were tested in a suite of 54 stream sites scattered throughout a large river catchment in New Zealand. Disturbance regime was quantified by recording the movement on several occasions through a year of painted particles representative of those present on the bed of each stream. A refugium index was calculated from a set of component scores for the proportion of the streambed where shear stresses were low (<0.771 dynes cm2), the percentage of bed particles that were large (>128 mm wide), and the depth of interstitial space below the streambed. The proportion of the community made up of smaller individuals (maximal body size <10 mm long) was indeed greater in streams with more disturbed beds and low refugium scores (Fig. 5.1a), a relationship that was not evident in the subset of streams with higher refugium availability (Fig. 5.1b). High discharge events often produce a mosaic of patches, where substratum has variously been scoured out, deposited or left unaffected (Matthaei, Peacock & Townsend, 1999). After bed patches have been disturbed, faunal recovery is sometimes size related. Thomson (2002) noted after moderate floods in an Australian river that invertebrates tended to be larger (later instars) than before the event, indicating recolonization mainly by larger invertebrates that survived in refugia in the stream. After a large flood that disturbed much more of the streambed, on the other hand, invertebrates were smaller (early instars)

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(a) % of Individuals

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80

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40 0.0 0.2 0.4 0.6 0.8 1.0 Intensity of disturbance

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Figure 5.1 Relationship between a bed disturbance index in 54 stream sites and percentage of individual macroinvertebrates whose maximal length was less than 10 mm (a) in the 27 sites where refugium availability was lowest and (b) in the 27 sites where refugium availability was highest. The index measures the average proportion of bed particles that are moved by high discharge events in each stream. Intensity and frequency of disturbance are highly correlated in this case. (Based on data from Townsend et al., 1997.)

than before, suggesting recolonization was mainly via ovipositing adults. In a finer scale study in a New Zealand stream, Matthaei and Townsend (2000) compared recovery after high discharge events in bed patches where scouring or deposition had occurred. Smaller Deleatidium mayflies and Hydora beetles characterized patches of scour, and larger Chironomidae but smaller Simuliidae were associated with depositional areas, indicating both that recolonization may be size related but also taxon specific. The size structure of the streambed may have a more direct influence on trait representation too. Bourassa and Morin (1995) compared, for nine Canadian streams, the relationship between invertebrate body size (minimum size 63 mm) and substratum particle size, by sampling relatively uniform patches of stream bed consisting of sand, fine gravel, course gravel, cobble or small boulder. Coarser substrata, with their correspondingly larger interstitial spaces, might be expected, on average, to support larger invertebrates. Bourassa and Morin (1995) found a significant, but weak, trend towards larger average size in coarser substrata. In a related context, the presence of large wood (derived from forested riparian zones) has been shown in North American streams to be positively associated with large-bodied insects (Richards et al., 1997; Johnson, Breneman & Richards, 2003). Gayraud and Philippe (2001) focused on the amount of interstitial space in the streambed rather than the bed particles themselves. Their French study sites all contained pebbles and cobbles, but the less porous beds were associated with a greater preponderance of fine sediment. The results supported the hypothesis that the relative abundance of small invertebrates (maximal size 1–5 mm), which are capable of penetrating the substratum, should be greater in beds with low porosity, whereas larger invertebrates (5–10 mm) would be better represented in more porous streambeds that provide considerable interstitial space.

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Small body size is predicted to be beneficial in disturbed hydraulic conditions because it permits invertebrates to remain within the boundary layer. Snook and Milner (2002) found that small maximal size (<10 mm) was possessed by almost all individuals where hydraulic stress was highest in streams in the Pyre´ne´es (Boundary Reynolds number >30 000), whereas a mix of small and larger invertebrates occurred in less turbulent conditions. Merigoux and Dole´dec (2004) obtained contradictory results in their hydraulic study of invertebrates in contrasting patches in a French river. In this case maximal body size was actually larger in the more extreme conditions of high hydraulic stress (estimated as shear stress on the bed). They argued that morphological and behavioural traits, such as the ability to cling to the substratum or the breadth of gills that aid in anchoring, may increase with individual size and outweigh the predicted disadvantage of large size under hydraulically stressed conditions. Flash floods in desert streams are particularly intense disturbances. They can cause more than 90% mortality in the juvenile stages of stream insects, but recolonization is rapid via oviposition of aerial adults (Lytle, 2002). Thus, timing of emergence may play a critical role in persistence of taxa in flood-prone systems. Modelling the joint action of a seasonal limit for reproduction by the caddisfly Phylloicus aeneus in the absence of a flood, and of the probability that one or more floods might occur before this limit is up, led to two size-related predictions (Lytle, 2001). First, because individuals can use the adult stage as a refuge from floods but, by emerging early, pay an opportunity cost in lost growth (and fecundity), larger juveniles are expected to emerge early while smaller juveniles should risk more of the flood season in order to continue growing. Second, because no floods occur in some seasons, smaller individuals should risk all and emerge towards the end of the reproductive season, producing a second decline in body size in years where floods do not occur before the end of the season. In his study of three Chihuahuan desert streams over two years, Lytle (2002) indeed found that in most years there were two periods of emergence and two consecutive declines in body mass at emergence. To test whether these were associated with increasing flood probability and end of the reproductive season, respectively, he used maximum-likelihood methods to compare a null model with one incorporating a reproductive time constraint and several others that added flood disturbances into the mix. The latter performed best, indicating that flood dynamics played an important role in determining body-size patterns, a pattern consistent with natural history observations in similar systems (Scarsbrook & Townsend, 1993). Descriptive studies of biotic gradients Bourassa and Morin (1995; see above) extended their work on substratum grain size in Canadian streams to study the relationship between invertebrate body

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size and phosphate concentration. They reasonably assumed that phosphate availability was related to stream primary productivity, noting higher algal chlorophyll a and total invertebrate abundance in more phosphorus-rich streams. Average body size was marginally but significantly higher in nutrient-rich (total phosphorus > 40 mg L1) than nutrient-poor sites (< 25 mg L1). It may be that larger invertebrates are more competitive at gaining food or space in productive environments. In contrast, larger invertebrates might be at a disadvantage in the presence of large predators such as fish. Size-selective predation may reduce average body size in a community by reducing the mean size of prey species that occur there, or by driving larger taxa extinct. In his study of two neighbouring New Zealand streams that differed in terms of the presence of brown trout (Salmo trutta), Huryn (1998) found that of the ten largest invertebrate taxa, in nine cases individuals were on average significantly smaller in the stream with trout. Primary productivity was considerably higher in this stream, so it seems that size-selective predation has overridden any tendency towards larger size with greater productivity. Note that the New Zealand crayfish Paranephrops zealandicus, a very large invertebrate, is rare or absent from streams where brown trout occur (Usio & Townsend, 2000). Moreover, crayfish themselves seem capable of exerting size-selective predation, reducing the density of larger representatives of carnivorous chironomids (Usio & Townsend, 2004). Descriptive studies of complex gradients Given the multiplicity of factors that can influence macroinvertebrate size-class structure, it may be surprising that patterns are sometimes detectable when complex gradients are the focus of attention. Dole´dec et al. (2006) classified macroinvertebrates into five maximal size classes (<5 to >40 mm), and compared their representation in replicate New Zealand streams whose catchments were in each of four land-use classes: ungrazed native tussock grass, grazed tussock, ‘improved’ pasture (sheep or cattle), and heavily stocked pasture (deer or dairy). Average invertebrate size increased with agricultural intensity, perhaps reflecting higher stream productivity fuelled by increased nutrient concentrations in more intensively farmed pasture, or higher levels of contaminants, which may influence small animals disproportionately (Hendriks & Heikens, 2001; and see below). Altitude represents another complex gradient because hydraulic conditions, disturbance regimes and substratum size often vary along the length of streams. In a Europe-wide study, Statzner et al. (2004) found that the representation of small individuals (maximal size 2.5–5 mm) declined, and larger ones (10–20 mm) increased with increasing altitude. The pattern was clear but, as with the landuse study, its cause was not. The authors speculated that oxygen richness in the cold, turbulent upstream areas might have facilitated respiration of larger

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animals, or that the larger interstitial spaces associated with mountain cobble streams were responsible. Experimental studies Experimental studies of body-size patterns can be expected to provide the clearest demonstration of underlying mechanisms. Taniguchi and Tokeshi (2004) established artificial substrata whose surface irregularities were quantified according to their fractal geometry. The substratum plates were cut from natural serpentine bed material to create five levels of complexity of cavity sizes by attaching 0.3 cm thick stone squares of different dimensions (20  20 cm, 10  10 cm, 5  5 cm, 2.5  2.5 cm) to a basal plate of constant area (20  20 cm). Replicate plates were left in a flashy Japanese stream for 36 days, repeating the experiment in summer, winter and spring. Invertebrate body size declined with habitat complexity in all seasons. In other words, smaller individuals were commoner on substrata that provided smaller interstices, most likely acting as refuges against dislodgement in the current (or possibly against predation). Thus, there seemed to be a match between crevice size and invertebrate size. Downes et al. (1998) also found a higher proportion of small invertebrates in substrata with small crevices than on crevice-free substrata. Taniguchi and Tokeshi’s (2004) well-controlled experiment is illuminating, but they wisely point to the importance of considering habitat complexity in conjunction with other environmental factors. Thus, they left some of their plates to be colonized by algae and to accumulate detritus for one month prior to the experiment (removing any accumulated invertebrates after the preconditioning period). Across the range of substratum complexity, by the end of the experiment, mean body size was greater on plates that had previously accumulated food resources. This accords with the prediction that larger invertebrates may have a competitive advantage in more productive situations, although greater growth rates on preconditioned plates cannot be ruled out. Another biotic variable to be treated experimentally is predation. Flecker and Townsend (1994) established replicate artificial channels containing natural substratum in a New Zealand stream, allowing algae and invertebrates to colonize before establishing three predation treatments – no fish, native galaxiid fish or exotic brown trout (Salmo trutta). After ten days the channels with the voracious trout contained half the density of large invertebrate carnivore species compared with those with native or no fish. Moreover, as with Taniguchi and Tokeshi’s (2004) productivity pattern, the effects of fish predation on invertebrate size structure can be moderated by structural complexity. Thus, in enclosures in a Californian river, the presence of roach (Hesperoleucas symmetricus) and steelhead (Oncorhyncus mykiss) in a six-week experiment reduced the density of large invertebrate predators when the substratum consisted of boulders but not gravel (Power, 1992). This supports the hypothesis that refuges provided in

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gravels are of an appropriate size to reduce fish foraging efficiency on the invertebrate carnivores, and is in accord with observations that fish modify stream invertebrate behaviour and the amount of foraging time invertebrates spend away from refuges (e.g. Kohler & McPeek, 1989; McIntosh & Townsend, 1994). In an experiment involving an invertebrate predator (the caddisfly larva Plectrocnemia conspersa) and its stonefly prey (Leuctra nigra), Hildrew and Townsend (1977) noted that larger prey were more vulnerable than smaller ones in a substratum of small stones whose interstices were too small to shelter the large individuals. While the impact on stream communities of exotic chemicals, including pesticides and metals, has yet to be systematically assessed, laboratory studies have highlighted the likely importance of body size. Vulnerability to dissolved contaminants can be expected to be greater in insects that use dissolved oxygen, obtaining much of it through exchange epithelial surface, than those that breath air. Buchwalter, Jenkins and Curtis (2002) tested in the laboratory the hypothesis that stream insects with relatively large areas of exchange epithelium would be more likely to accumulate the insecticide chlorpyfiros from their environment. They estimated relative differences in exchange epithelium by measuring permeability to labelled water and found, for both the dissolved-oxygen breathers and the air breathers, that water permeability was strongly related to pesticide uptake rate. However, as predicted the dissolved-oxygen breathers had, in general, much higher uptake rates. In turn, water permeability was positively related to body size, reflecting higher surface-area-to-volume ratios in small individuals. Across a wide range of aquatic taxa, Hendriks and Heikins (2001) have documented a general inverse relationship between body weight and rate constants for the uptake of inorganic substances, as found for chlorpyfiros (a class of organophosphate insecticides). However, sensitivity to contaminants depends also on metabolic differences and detoxification mechanisms that vary across taxa. In a study involving representatives of the Ephemeroptera, Trichoptera and Plecoptera, uptake of cadmium and zinc was generally not related to size, but rather to the relative numbers of ionoregulatory cells present (Buchwalter & Luoma, 2005). On the other hand, Kiffney and Clements (1996) directly explored the relationship between size and toxicity (of a mining-related mixture of cadmium, copper and zinc) in four stream invertebrates (Ephemeroptera and Plecoptera) and found that the mean size of individuals at the end of the experiment was higher in the metal treatment than the control because smaller individuals were significantly more likely to die. Even high concentrations of nitrate in stream water (characteristic of agriculturally polluted streams) can be toxic to stream invertebrates, due to the conversion of oxygen-carrying pigments to forms incapable of carrying oxygen: once again, the strongest effects are generally felt by the smallest individuals (Camargo, Alonso & Salamanca, 2005).

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Two conclusions can be emphasized about the potential influence of chemical contaminants associated with agriculture or mining. First, where they occur, invertebrate community size structure may be shifted towards larger taxa and/or larger individuals within taxa. Second, other environmental influences that impact on size-class structure may make individuals in the community more, or less, susceptible to exotic contaminants.

Analysis of a new database for New Zealand streams Having reviewed the variety of environmental gradients that can underlie patterns in invertebrate size-class structure in streams, we now turn to a new database of actual macroinvertebrate body sizes from 18 tributaries in the Otago region of the South Island of New Zealand. This is a descriptive study in which we test a variety of hypotheses derived from the review above. Our predictions were that body size would be negatively correlated with disturbance intensity, positively correlated with substratum grain size and substratum heterogeneity, and positively correlated with algal productivity. We predicted that invertebrate predator size would be negatively correlated with the presence of the voracious brown trout and also tested the null hypothesis that the complex land-use gradient would bear no relationship to community body-size structure. Methods

Study sites The tributaries and study reaches have been described in detail elsewhere (Thompson & Townsend, 2004, 2005). In brief, the study sites were 30-metre reaches incorporating pools and riffles in second- or third-order streams with cobble or pebble beds. Four land uses were represented: native tussock grassland (seven sites), improved pasture grassland (three), native podocarp forest (two), and exotic conifer forest (six). Each site was sampled once for fish, macroinvertebrates and a range of physicochemical factors in the summer of 1994/5 (tussock, pasture and native forest sites) or 1997/8 (pine forest sites). Two of the tussock sites (Dempsters and Sutton) were also sampled in the spring and autumn of 1996 to assess seasonal effects. Fish The presence or absence of predatory fish was ascertained by electro-fishing, and each site was classed as having no fish, brown trout, native galaxiid fish, or both trout and galaxiids. Note that where the fish co-occur, there are generally very low densities and biomasses of each (Townsend, 2003). Macroinvertebrates Ten randomly located Surber samples (area 0.06 m2, mesh size 250 mm) were taken at each site to sample benthic macroinvertebrates with a minimum size

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of 1.5 mm. Thus, we excluded meiofaunal species; but note that meiofauna are not commonly seen in samples from these streams (Thompson & Townsend, 2005). Macroinvertebrates were measured (to the nearest 0.25 mm), identified to the best level of taxonomic resolution possible (Winterbourn & Gregson, 1989; Thompson & Townsend, 1999) and ascribed to a functional feeding group.

Physicochemical conditions Several ecologically relevant aspects of habitat were measured (Table 5.1). Algal production was estimated using a radioactive carbon isotope (7 mL of (14C) NaHCO3 (185 Mbq ml1)) using stream substrata placed in portable chambers (Fuller & Bucher, 1991; Thompson & Townsend, 1999). Means and standard deviations of substratum grain size were calculated for 100 random substratum particles at each site. For ten of the sites, detailed information was also available on disturbance regime (Townsend et al., 1997; these are ten of the sites in Fig. 5.1). It is important to note, however, that for the sites considered here there had been no major disturbance events in the 90 days preceding their sampling. Statistical analyses Size frequency histograms were generated for visual comparison of size distributions, and overlain with mean, upper quartile and lower quartile values for each stream. For statistical analysis the data for each site were converted to the proportion of the total number of macroinvertebrates that occurred in 1 mm size bins. Seasonal data at two sites were analyzed separately: size frequency histograms were constructed and visually compared. To test for effects of the various predictors on body size, mean, lower and upper quartiles were calculated for each site for all macroinvertebrates combined and for each functional feeding group. Where fewer than ten individuals occurred in a functional feeding group for a site, these data were excluded from analysis because the real size range of the taxon was not considered to have been adequately sampled. Analysis of variance was used to test for effects of land-use category and fish regime on each of the body-size parameters. Means and quartiles of body size were plotted and regressed separately against primary production, substratum particle size and variability, and disturbance. The summer data were also used in a principal components analysis to generate an ordination of sites and to explore multivariate influences. This ordination was overlain with information on primary production, substratum particle size and variability and, for ten sites, disturbance. For those sites with complete data sets, an optimal subsets Mantel test (BIOENV in Primer 5) was used to ascertain what combination of ecological attributes was best able to predict distribution of individuals across size classes.

Site

Blackrock Broad Canton Dempsters German Healy Kye Burn Little Kye Stony Sutton North Col Powder Berwick Venlaw Aka A Aka B Catlins Control

Catchment

Lee Lee Lee Three O’Clock Kye Burn Kye Burn Kye Burn Kye Burn Sutton Sutton Silver Silver Meggatburn Mimihau Akatore Akatore Craggy Tor Narrowdale

Pasture Pasture Pasture Tussock Tussock Tussock Tussock Tussock Tussock Tussock Native forest Native forest Pine forest Pine forest Pine forest Pine forest Pine forest Pine forest

Land use T T T TG TG G T TG – T T T T T – – G G

Fish 46.57 43.46 26.25 28.55 62.21 39.76 42.20 84.57 28.36 45.94 na na na na na na na na

Disturbance (% particles) 27.74 35.06 23.04 85.38 88.29 61.75 19.34 11.14 22.45 6.70 0.32 3.85 14.64 4.01 9.62 7.28 9.45 2.66

Algal production (mg(C) m2 h1) 57.43 34.75 81.19 118.93 59.61 96.75 122.02 34.19 182.63 106.22 91.29 79.83 39.00 122.20 38.02 55.33 50.29 19.89

Average substrate (mm)

70.06 35.99 96.44 99.03 62.13 83.35 113.90 21.25 120.57 112.88 83.36 84.91 38.55 102.76 49.89 36.60 44.36 17.60

SD substrate (mm)

Table 5.1 Aspects of the habitat templet included in the new analysis of 18 New Zealand streams. Disturbance is expressed as the average percentage of painted bed particles that moved during sampling periods over the year. T ¼ brown trout present, G ¼ native galaxiids present, SD ¼ standard deviation of 100 bed particles, na ¼ not available.

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Results The size frequency histograms are shown in Fig. 5.2. Invertebrates ranged from 1.5 mm to 25 mm, with mean lengths between 2.5 and 4.9 mm and with the majority of individuals across all sites in this size range. Invertebrate abundances were significantly influenced by land use (F3,14 ¼ 22.33, p < 0.01), with native forest sites having significantly more individuals than other categories, and pasture and tussock sites having significantly higher abundances than pine forest sites (Tukey’s post-hoc tests). There was no evidence of strong seasonal variability in body size for the two sites where data were available, and no apparent pattern involving functional feeding groups. Contrary to our predictions, body size was not significantly related to disturbance (Fig. 5.3a), average substratum particle size (Fig. 5.3b) or algal productivity (Fig. 5.3c). However, body size seemed to increase from low to intermediate substratum variance but to decrease again in the most heterogeneous substrata (Fig. 5.3d). Grazers and, in particular, shredders were mainly responsible for this pattern. There was a significant effect of land use on body size overall and, separately, for grazers, shredders and collector gatherers (Fig. 5.4). Invertebrates were larger (both mean and upper quartile lengths) in pasture streams, driven mainly by the presence of larger collector gatherers. Native forest sites were typified by the absence of small grazers, resulting in significantly greater lower quartile lengths for that functional feeding group than in other land uses. However, interpretation of a land-use effect as independent from a fish effect was confounded by the presence of trout in all native forest streams (see below). Tussock streams were typified by small body sizes across all functional groups. The fish regime had a significant effect on the body size of predatory invertebrates, with sites containing only brown trout having smaller individuals, as predicted (Fig. 5.5). In the principal components analysis of the proportion of individuals in each size class, streams scoring highly on Principal Component 1 (PC1) had a high percentage of mainly very small individuals (1.5–4 mm), while those scoring highly on Principal Component 2 (PC2) had a higher proportion of intermediate sized individuals (4–10 mm). Overlaying the physicochemical data on to the ordination (Fig. 5.6) indicated a trend for high scores on PC1 to be correlated with high algal productivity, substratum particle size and substratum variability. A Mantel test including all of the predictors supported this with the best model (Spearman’s Correlation 0.198) including algal production and average substratum particle size, and all of the ten best models incorporated those factors. Because PC1 was positively correlated mainly with the smallest size classes, these results run counter to our predicted positive relationships between size and both productivity and substratum particle size.

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Body size (mm)

Figure 5.2 Size frequency histograms of macroinvertebrates from 18 New Zealand stream sites. The presence of brown trout (e.g. Blackrock) or native galaxiid fish (e.g. Healy) is indicated by icons. Bar colour indicates land use: grey ¼ improved pasture, black ¼ native tussock grass, white ¼ native podocarp forest, hatched ¼ exotic pine forest. Means are indicated by solid lines flanked by dotted lines showing upper and lower quartiles.

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Figure 5.3 Relationships between body size of all macroinvertebrates combined and (a) disturbance intensity, (b) algal productivity, (c) mean substrate size and (d) standard deviation of substrate size. Mean lengths are shown, with bars extending to upper and lower quartiles. Each relationship is for 18 stream sites, except for disturbance for which only 10 sites were available. The humped shape relationship in (d) is described by the regression equation y ¼ 0.0003x2 þ 0.0355x þ 2.7723 (R2 ¼ 0.37).

Body-size patterns along environmental gradients and their utility for biomonitoring In the earlier analysis of the relationship between disturbance regime and body size, Townsend et al. (1997) quantified size as the maximum achievable by individuals in each taxon, and found that smaller invertebrates were more prevalent in the more intensely and frequently disturbed sites. In the current study of a subset of these sites, where body sizes were individually measured, no such relationship was seen. While this might be an artefact related to our selection of sites, it seems more likely to be a function of the long period of stable flow preceding our study (at least 90 days without a significant flow event). In the earlier study, sites had been disturbed much more recently. It may be that the stronger representation in streams with extreme disturbance regimes of species having small maximal sizes is the result of natural selection. On the other hand, few individuals survive to maximal size and the results for

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Figure 5.4 Averages (with standard error bars in mm) for mean (grey bars), lower (white bars) and upper (black bars) quartile body lengths of macroinvertebrates from 18 New Zealand streams in four land-use classes. Bush ¼ native podocarp forest.

actual sizes in the current study concur with Townsend et al.’s (1997) suggestion that time without disturbance would be likely to blur any relationship with body size. Patterns of body size at a site at any moment in time are likely to result both from the sum of evolutionary forces (determining maximal size obtainable) and time since disturbance (determining current body size). Our predictions that body size would be positively related to algal productivity and substratum grain size were not supported. Indeed our multivariate analysis indicates, if anything, that body size was smaller in more productive environments and/or those with coarser substrata, running counter to the predictions. This highlights the problem of testing single-factor predictions in

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Principal Component 2 – 16.3% of variation

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10

Figure 5.5 Averages (with standard error bars in mm) for mean (grey bars), lower (white bars) and upper (black bars) quartile body lengths of predatory invertebrates from 18 New Zealand streams in three fish classes. The middle set of histograms, for sites containing only brown trout, indicates that trout are responsible for reducing body size. Fish icons as in Figure 5.2.

8 6 4 2 0

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Figure 5.6 Principal components ordination of the proportion of invertebrates in different size classes, with symbols scaled by values of physicochemical variables: (a) disturbance, (b) algal productivity, (c) substrate size and (d) substrate variability. See Table 5.1 for units. White circles in (a) indicate no disturbance data.

a multivariate (descriptive) setting. Other things being equal, it may be that body size will be larger in more productive streams (reflecting greater competitive status of larger species or, more mundanely, a more adequate diet) or in streams with larger substratum particles (because of the provision of appropriate living

BODY SIZE IN STREAMS

spaces or refuges). But other things are not equal and, to be honest, we would have been surprised to find a clear relationship between size and algal productivity in the present study: stream invertebrates depend on both detrital and algal resources and the relative importance of these differs dramatically in forested and grassland streams. In contrast, we found in the same set of streams a positive relationship between food-chain length and algal productivity (Townsend et al., 1998; Thompson & Townsend, 2005). Patterns with individual factors must be particularly strong if they are to be detectable in our multivariate investigation. This may be the case for substratum particle size heterogeneity, where body size increases from low to intermediate heterogeneity before declining again, perhaps reflecting the (unmeasured) details of the fractal nature of our streambeds (Schmid & SchmidAraya, this volume). The availability of interstitial spaces and refugia in streambeds is likely to be a complex interaction between the size of substratum particles, degree of infilling by fine sediments and the shapes of bed particles. Streams in this study with high heterogeneity tended to include very small particles, which filled interstitial spaces. Low heterogeneity streams were typified by small particles, which may not develop interstitial spaces. In contrast, the sites with intermediate heterogeneity lacked very small particles but included large particles, providing a range of interstitial habitats. We also obtained results supporting the prediction that brown trout, through sizeselective predation, would limit the size of predatory invertebrates in the streams. Turning to patterns in the complex land-use gradient, the larger body sizes in pasture than tussock streams is consistent with higher algal productivity in pasture (because of higher nutrient concentrations), although this is not supported by our short-term productivity measures. Alternatively, the pattern may relate to an unmeasured but potentially important effect of greater concentrations of contaminants in pasture settings. We have seen that contaminants can have stronger adverse effects on smaller invertebrates because of their larger surface-area-to-volume ratios; this is an area that merits further investigation. In conclusion, macroinvertebrate body-size patterns are sometimes apparent, but they rarely account for a large proportion of variation along the dimensions of interest. This is no doubt partly because several factors operate simultaneously (even in partially controlled experiments) and, if these engender different size-related outcomes, the patterns will be muted or obscured. An additional problem is that different macroinvertebrates may have different solutions to environmental stressors. For example, species characteristic of disturbed settings might be ‘resistant’ large animals that are clingers or streamlined, or ‘resilient’ small animals with rapid recolonization and high population-growth rates. Moreover, there may be large animals whose resilience depends on their ability to move away before the disturbance reaches full intensity, to return

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after it has passed. In other words, both multiple stressors and taxon-specific solutions can conspire to reduce the likelihood of detecting clear patterns. We believe that our understanding of the structure and functioning of stream ecosystems has increased because of size-focused studies, but can this understanding be used to develop biomonitoring tools? Robson, Barmuta and Fairweather (2005) note that body size has appeal as a taxon-free and easy-to-measure metric. In addition, it bears relationships, either directly or indirectly, to a variety of humaninduced stressors. Size alone will certainly not furnish sufficient predictive power, however, when prioritizing rivers for rehabilitation or measuring river improvement. On the other hand, body size, in combination with other traits related to trophic role, survival and reproduction, may be used to create river health metrics of more general utility than those that depend simply on taxonomic composition or species diversity (e.g. Charvet, Kosmala & Statzner, 1998; Gayraud et al., 2003; Statzner et al., 2004; Dole´dec et al., 2006). The potential advantages of trait-based metrics are two-fold. First, a multiple-trait index is likely to be applicable across large geographic areas despite taxonomic differences. Second, the representation of particular traits can be expected to throw light on the mechanisms underlying stressor impacts, providing focus for management efforts.

Acknowledgements Thanks to Sylvain Dole´dec for supplying Fig. 5.1. RT was funded by the Biodiversity Research Centre at the University of British Columbia.

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with new data for freshwater invertebrates. Chemosphere, 58, 1255–1267. Charvet, S., Kosmala, A. & Statzner, B. (1998). Biomonitoring through biological traits of benthic macroinvertebrates: perspectives for a general tool in stream management. Archives fu¨r Hydrobiologie, 142, 415–432. Cummins, K. W. (1974). Structure and function of stream ecosystems. BioScience, 24, 631–641. Dole´dec, S., Phillips, N., Scarsbrook, M., Riley, R. H. & Townsend, C. R. (2006). A comparison of structural and functional approaches to determining landuse effects on grassland stream communities. Journal of the North American Benthological Society, 25, 44–60. Downes B. J., Lake P. S., Schreiber E. S. G. & Glaister A. (1998). Habitat structure and regulation of local species diversity in a

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Hildrew, A. G. & Townsend, C. R. (1977). The influence of substrate on the functional response of Plectrocnemia conspersa (Curtis) larvae (Trichoptera: Polycentropodidae). Oecologia, 31, 21–26. Huryn, A. D. (1998). Ecosystem-level evidence for top-down and bottom-up control of production in a grassland stream system. Oecologia, 115, 173–183. Johnson, L. B., Breneman, D. H. & Richards, C. (2003). Macroinvertebrate community structure and function associated with large wood in low gradient streams. River Research and Applications, 19, 199–218. Kiffney, P. M. & Clements, W. H. (1996). Size-dependent response of macroinvertebrates to metals in experimental streams. Environmental Toxicology and Chemistry, 15, 1352–1356. Kohler, S. L. & McPeek, M. A. (1989). Predation risk and the foraging behaviour of competing stream insects. Ecology, 70, 1811–1825. Lytle, D. A. (2001). Disturbance regimes and life history evolution. American Naturalist, 157, 525–536. Lytle, D. A. (2002). Flash floods and aquatic insect life-history evolution: evaluation of multiple models. Ecology, 83, 370–385. Matthaei, C. D. & Townsend, C. R. (2000). Longterm effects of local disturbance history on mobile stream invertebrates. Oecologia, 125, 119–126. Matthaei, C. D., Peacock, K. A. & Townsend, C. R. (1999). Scour and fill patterns in a New Zealand stream and potential implications for invertebrate refugia. Freshwater Biology, 42, 41–58. McIntosh, A. R. & Townsend, C. R. (1994). Interpopulation variation in mayfly anti-predator tactics: differential effects of contrasting predatory fish. Ecology, 75, 2078–2090. Me´rigoux, S. & Dole´dec, S. (2004). Hydraulic requirements of stream communities: a

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case study of invertebrates. Freshwater Biology, 49, 600–613. Poff, N. L. (1997). Landscape filters and species traits: towards mechanistic understanding and prediction in stream ecology. Journal of the North American Benthological Society, 16, 391–409. Power, M. E. (1992). Habitat heterogeneity and the functional significance of fish in river food webs. Ecology, 73, 1675–1688. Resh, V. H., Hildrew, A. G., Statzner, B. & Townsend, C. R. (1994). Theoretical habitat templets, species traits, and species richness: a synthesis of long-term ecological research on the Upper Rhone River in the context of concurrently developed ecological theory. Freshwater Biology, 31, 539–554. Richards, C., Haro, R. J., Johnson, L. B. & Host, G. E. (1997). Catchment and reach-scale properties as indicators of macroinvertebrate species traits. Freshwater Biology, 37, 219–230. Robson, B. J., Barmuta, L. A. & Fairweather, P. G. (2005). Methodological and conceptual issues in the search for a relationship between animal body-size distributions and habitat architecture. Marine and Freshwater Research, 56, 1–11. Scarsbrook, M. R. & Townsend, C. R. (1993). Stream community structure in relation to spatial and temporal variation: a habitat templet study of two contrasting New Zealand streams. Freshwater Biology, 29, 395–410. Schmid, P. E., Tokeshi, M. & Schmid-Araya, J. M. (2002). Scaling in stream communities. Proceedings of the Royal Society London, Series B, 269, 2587–2594. Southwood, T. R. E. (1977). Habitat, the templet for ecological strategies. Journal of Animal Ecology, 46, 337–365. Snook, D. L. & Milner, A. M. (2002). Biological traits of invertebrates and hydraulic conditions in a glacier-fed catchment (French Pyre´ne´es). Archives fu¨r Hydrobiologie, 153, 245–271.

Statzner, B., Gore, J. A. & Resh, V. H. (1988). Hydraulic stream ecology: observed patterns and potential applications. Journal of the North American Benthological Society, 7, 307–360. Statzner, B., Dole´dec, S. & Hugueny, B. (2004). Biological trait composition of European stream invertebrate communities: assessing the effects of various trait filter types. Ecography, 27, 470–480. Taniguchi, H. & Tokeshi, M. (2004). Effects of habitat complexity on benthic assemblages in a variable environment. Freshwater Biology, 49, 1164–1178. Thomson, J. R. (2002). The effects of hydrological disturbance on the densities of macroinvertebrate predators and their prey in a coastal stream. Freshwater Biology, 47, 1333–1351. Thompson, R. M. & Townsend, C. R. (1999). The effect of seasonal variation on the community structure and food-web attributes of two streams: implications for food-web science. Oikos, 87, 75–88. Thompson, R. M. & Townsend, C. R. (2000). New Zealand’s stream invertebrate communities: an international perspective. In New Zealand Stream Invertebrates: Ecology and Implications for Management, ed. K. Collier and M. Winterbourn. Christchurch, New Zealand: New Zealand Limnological Society, pp. 53–74. Thompson, R. M. & Townsend, C. R. (2004). Land-use influences on New Zealand stream communities: effects on species composition, functional organization, and food-web structure. New Zealand Journal of Marine and Freshwater Research, 38, 595–608. Thompson, R. M. & Townsend, C. R. (2005). Energy availability, spatial heterogeneity and ecosystem size predict food-web structure in streams. Oikos, 108, 137–148. Townsend, C. R. (2003). Individual, population, community and ecosystem consequences of

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a fish invader in New Zealand streams. Conservation Biology, 17, 38–47. Townsend, C. R. & Hildrew, A. G. (1994). Species traits in relation to a habitat templet for river systems. Freshwater Biology, 31, 265–275. Townsend, C. R., Dole´dec, S. & Scarsbrook, M. R. (1997). Species traits in relation to temporal and spatial heterogeneity in streams: a test of habitat templet theory. Freshwater Biology, 37, 367–388. Townsend, C. R., Thompson, R. M., McIntosh, A. R. et al. (1998). Disturbance, resource supply and food-web architecture in streams. Ecology Letters, 1, 200–209. Usio, N. & Townsend C. R. (2000). Distribution of the New Zealand crayfish Paranephrops zealandicus in relation to stream physicochemistry, predatory fish and invertebrate prey. New Zealand Journal of Marine and Freshwater Science, 34, 557–567.

Usio, N. & Townsend C. R. (2004). Roles of crayfish: consequences of predation and bioturbation for stream invertebrates. Ecology, 85, 807–822. Vannote, R. L., Minshall, G. W., Cummins, K. W., Sedell, J. R. & Cushing, C. E. (1980). The river continuum concept. Canadian Journal of Fisheries and Aquatic Sciences, 37, 130–137. Winterbourn, M. J. & Gregson, K. L. D. (1989). Guide to the aquatic insects of New Zealand. Bulletin of the Entomological Society of New Zealand, 9. Winterbourn, M. J., Rounick, J. S. & Cowie, B. (1981). Are New Zealand stream ecosystems really different? New Zealand Journal of Marine and Freshwater Research, 15, 321–328. Woodward G. & Hildrew A. G. (2002). Food web structure in riverine landscape. Freshwater Biology, 47, 777–798.

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CHAPTER SIX

Body size and predatory interactions in freshwaters: scaling from individuals to communities GUY WOODWARD Queen Mary, University of London

PHILIP WARREN University of Sheffield

Introduction Body size is an attribute of individual organisms. It affects, or at least is correlated with, a considerable array of physical, physiological and behavioural characteristics that determine where individuals occur and what they do (Elton, 1927; Peters, 1983; Brown et al., 2004; Woodward, Speirs & Hildrew, 2005c). Such ubiquity makes body size an obvious candidate source of general rules that can be derived from selective processes acting on individuals, but which can also be applied at higher levels of ecological organization (Cousins, 1980; Peters, 1983; Dickie, Kerr & Boudreau, 1987; Yodzis & Innes, 1992; Cohen et al., 1993; Gaston & Blackburn, 2000; Cohen, Jonsson & Carpenter, 2003; Emmerson & Raffaelli, 2004). Although body size was identified as a key link between natural history aspects of population dynamics and community structure many decades ago (e.g. Hardy, 1924; Elton, 1927; Hutchinson, 1959), these early ideas have languished somewhat until relatively recently. In the last two to three decades a plethora of allometric body-size scaling relationships have been described and used to derive mechanisms to explain, or parameters to model, general patterns in natural systems (e.g. Peters, 1983). Recently, it has been suggested that basal metabolic rate is the fundamental constraint that underpins many of the size-related patterns and processes observed in natural systems, and that a metabolic theory of ecology could, eventually, attain similar importance to that of the genetic theory of evolutionary biology (Brown et al., 2004; Brown, Allen & Gillooly, this volume). One effect of size taking a more central place in ecological thinking is that it provides a means of integrating approaches based on biomass and energy flux with those based on abundances and populations (e.g. de Ruiter, Neutel & Moore, 1995; Reuman & Cohen, 2005; Woodward et al., 2005a–c). Within terrestrial ecology, the role of body size has been explored extensively at very large spatial scales, particularly in response to latitudinal gradients Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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(e.g. Rapaport’s rule; Ricklefs, 2004), whereas in aquatic systems it has played a far more prominent role in thinking about community structure. This can be attributed to several important differences between terrestrial and aquatic systems. First, body size is a concept that is applicable to many plants and detrital particles in aquatic systems, particularly in pelagic systems, because of the way many organisms feed, and the fact that material is carried in suspension. Second, predation, which is often clearly size dependent, has long been recognized as a structuring force in aquatic systems, whereas a greater emphasis in terrestrial systems has been placed on the role of lateral competitive interactions within a single trophic level, or on plant–herbivore–parasitoid food chains, which form a major component of terrestrial systems but where size has a less obvious role (e.g. Lehman & Tilman, 2000). Finally, the size distribution of particles (including organisms) is relatively easy to measure in aquatic systems with automated counting systems: these include flow cytometry of algae and ciliates using Coulter1 counters (Pitta, Giannakourou & Christaki, 2001), continuous plankton recorders attached to ocean-going vessels (Beare et al., 2003) and remote sensing of fish populations using passive integrated transponder (PIT) tags (Achord, Levin & Zabel, 2003). It is perhaps not surprising, then, that there has been a greater focus on the role of body size in determining the structure and dynamics of aquatic food webs (e.g. Kerr, 1974; Cousins, 1980, 1985; Woodward & Hildrew, 2001, 2002b; Schmid-Araya et al., 2002a; Woodward et al., 2005a–c) than in terrestrial systems, with the notable exception of soil food webs which also include traditional predators and prey and size-delimited trophic levels (e.g. de Ruiter et al., 1995). Empirical data on body-size patterns and effects from aquatic systems have stimulated thinking about community organization and, in parallel with this, size has for some time been drawn into theoretical ideas about aquatic community dynamics (e.g. Kerr 1974; Cousins, 1980, 1985; Emmerson & Raffaelli, 2004; Reuman & Cohen, 2005). However, the demands of theory for data, both for parameterization and for testing predictions, has increasingly outstripped their availability, both in terms of numbers of studies and also the scale at which data are collected (Brown & Gillooly, 2003). For example, food-web studies – both empirical and theoretical – usually deal with species, or higher taxonomic (or other) aggregations, where the averaging of characteristics such as size obscures many of the details of what individuals are actually doing. At the other end of the scale, laboratory experiments often focus on size effects within limited size ranges of individuals of one or two species, while community theory often seeks to apply such results across species. Perhaps the greatest bridging of scales comes with macroecological relationships, where the effects of size on fundamental processes such as metabolic rate, are linked to large-scale patterns in species distributions and diversity (Brown, 1995; Gaston & Blackburn, 2000). What such analyses make explicit is that the patterns that arise at

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macroecological scales are the result of species interactions at the population scale which, in turn, are driven by the activities of individuals. Here we consider some of the consequences of using body size to understand the organization of trophic links as we scale from the individual to the community, with a focus on size constraints on feeding and the body-size distributions of organisms in food webs. We draw mainly on examples from freshwater systems, especially benthic ones, where most of our own work has been based, and two data sets in particular: the invertebrate food webs from an acidic pond (Skipwith Pond, Warren, 1989) and an acidic woodland stream (Broadstone Stream, Woodward & Hildrew, 2002b). We must also make an important caveat at this point: we are restricting ourselves to ‘traditional’ predatory relationships, so parasitic interactions will not be considered in this chapter. There are two reasons for this: first, very little is known of parasites in freshwater food webs, where they appear to be far rarer than in marine and terrestrial systems, and second, parasites often show inverse (or no) clear relationships with body size of their ‘prey’ (e.g. Huxham, Beaney & Raffaelli, 1996; Memmott, Martinez & Cohen, 2000).

Feeding and size: processes at the individual level Organisms are subject to natural selection for strategies and morphological, behavioural and physiological adaptations that maximize foraging efficiency, subject to other constraints (Schoener, 1971; Pyke, Pulliam & Charnov, 1977; Stephens & Krebs, 1986). Such adaptations can include body size itself (Schoener, 1969; Lundberg & Persson, 1993), but also the many specialized feeding adaptations that aquatic organisms exhibit (Humphries, this volume). The trade-offs inherent in maximizing foraging efficiency inevitably restrict the range of resource types that are exploited effectively (Pyke et al., 1977; Pyke, 1984; Stephens & Krebs, 1986), and size plays a key role here because it is a component of both the costs (e.g. handling time) and benefits (e.g. prey energy content) of foraging. Size constraints on foraging can arise at each of the individual stages of the predation sequence, from the initial encounter to the rate of digestion of ingested prey (Thompson, 1975; Persson et al., 1998; Woodward & Hildrew, 2002c). They can also arise at different points within each stage: for instance, attack rate has several subcomponents that commonly scale with body size, including the reactive distance of the predator (e.g. Breck & Gitter, 1983), the speed of movement of both predator and prey (e.g. Fry & Cox, 1970; Breck & Glass, 1973), and the probability of capture (e.g. Smyly, 1980; Pastorok, 1981). Handling time also comprises elements that are often strongly size dependent: these include, in order of temporal sequence, pursuit and subduing time, ingestion time, and digestion time (Woodward & Hildrew, 2002c). Thus, while the energetic reward of prey to a predator is likely to increase with prey mass, the costs of consuming it are also likely to be size dependent, but in more complex

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ways, since the subcomponents may not all scale with size in the same way (Thompson, 1975; Kislalioglu & Gibson, 1976; Hewett, 1980; Pastorok, 1981; Eggleston, 1990; Tripet & Perrin, 1994; Persson et al., 1998; Aljetlawi, Sparrevick & Leonardsson, 2004). The interaction of these costs and benefits will yield a sizedependent profit function, which should, according to foraging theory, drive diet choice (Stephens & Krebs, 1986). Thus, size is embedded in the relationships that determine the feeding adaptations selected for in individuals and this, in turn, shapes the fundamental trophic niche: i.e. the range of prey types a species is equipped to consume. Evidence for size-dependent foraging comes mostly from systems that contain single predator and prey species, where size can be varied independently of other things. Such studies in aquatic systems support the idea that both attack rate and handling time are related to predator–prey size differences (Thompson, 1975; Kislalioglu & Gibson, 1976; Hewett, 1980; Scott & Murdoch, 1983; Spitze, 1985; Eggleston, 1990; Woodward & Hildrew, 2002c; Tripet & Perrin, 1994; Aljetlawi et al., 2004), although the exact nature of the relationships varies. Handling time tends to decrease as predators become larger relative to their prey (see references above and Fig. 6.1). Attack rate has been suggested to follow a unimodal relationship (Persson et al., 1998; Persson & De Roos, this volume), although experimental results have yielded increasing, decreasing and humpbacked forms (see references above). Some of this variation is because individual prey species encompass only limited size ranges, so experiments sample different parts of the profitability curve, and some is probably due to fundamental 2

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Figure 6.1 (a) Handling time (i.e. from prey capture to complete ingestion) for Cordulegaster boltonii as a function of predator body mass. Prey ¼ one Nemurella pictetii (head-capsule width ¼ 1.0 mm). (b) Maximum daily consumption of N. pictetii by C. boltonii as a function of predator body mass.

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differences in the feeding biology of the organisms involved (Aljetlawi et al., 2004). Nonetheless, such experiments have, at least in some cases, provided evidence to support the idea that size-selective predation is directed towards the most profitable prey (e.g. Kislalioglu & Gibson, 1976; Pastorok, 1981; Turesson et al., 2002). Although optimal foraging theory predicts that consumers will feed on prey of a certain size range, for the reasons outlined above, this selectivity can manifest itself at a variety of temporal scales, from instantaneous decisions about feeding on individual prey, which can respond to dynamic variables such as hunger level and predation risk, through to the evolution of feeding adaptations, such as gape size and mouthpart morphology. The latter are essentially fixed traits for an individual at any given time and provide the size selection ‘envelope’. This fundamental food-size niche sets the size limits to predation for an individual. Within these limits, prey may or may not be taken, or may be taken with greater or lesser frequency, as a result of more dynamic foraging decisions (e.g. Turesson et al., 2002), or through variation in the efficiency of the foraging processes within those limits (e.g. Pastorok, 1981). This set of processes emphasizes the predators’ view of size selection, and the detail of these processes comes from studies of single species of prey with single species of predators (e.g. Woodward & Hildrew, 2002c). If we are to extrapolate to the broader food web these ideas have to be generalized across many prey and predator species, and the simplest way to do this is to assume that prey are equivalent in all respects except size. However, since the precise scalings between body size and the costs and benefits will not be exactly the same for each species (e.g. proportions of digestible tissue to total weight, mechanisms for avoiding capture, etc.) species will have their own profit functions on the size axis. In reality, however, many of these more subtle differences might not be perceived by aquatic predators, at least not during the initial stages of the predation process. Predators do not have any inherent reason to recognize taxonomic distinctions unless they correspond to relevant functional differences from the predator’s perspective (i.e. those that affect foraging). This raises the question of what proportion of the variation in the occurrence of feeding interactions between a predator and a suite of prey is determined by size, as opposed to other factors associated with prey type? If size predominates, then modelling the patterns and determinants of trophic links in multispecies systems becomes easier, as feeding can essentially be modelled as contiguous on a single niche axis (e.g. Williams & Martinez, 2000). Evidence from the Broadstone Stream food web supports the view that body size is the primary determinant of diet: the first axis of an ordination of predators’ diets represented a gradient in relative body size between predators and their prey, whilst other effects, such as foraging strategy and spatial overlap were less important (Fig. 6.2, redrawn after Woodward & Hildrew, 2002b). The relative contribution of taxonomic (or rather the morphological, physiological

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Figure 6.2 Detrended correspondence analysis ordination biplot of the diets of macroinvertebrate predators within Broadstone Stream (redrawn after Woodward & Hildrew, 2002b), showing a clear effect of body size along the first axis and the influence of microhabitat use along the second axis. Predator species scores are labelled in bold italics as initials, denoting genus (in decreasing order of mean body mass: Cordulegaster boltonii – C; Sialis fuliginosa – S; Plectrocnemia conspersa – P; Macropelopia nebulosa – M; Trissopelopia longimana – T; Zavrelimyia barbatipes – Z), followed by numbers, denoting sizeclasses within species (low numbers representing the smallest size class). Prey taxa are labelled as in Appendix 2 of Woodward & Hildrew (2002b). The arrows linking the seven size classes of the top predator Cordulegaster (C1–C7) depict the ontogenetic shifts in diet from the smallest to the largest individuals of this species. The smallest and largest ‘prey’ species found in the guts of the predators are denoted with stars and highlighted in bold type (cyclopoid copepods and C. boltonii, respectively). The solid line drawn parallel to the x-axis separates the epibenthic ambush predators from the interstitial searching predators, barring two exceptions (C5 and M3).

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Figure 6.3 Results of laboratory feeding trials, in which 11 species of freshwater invertebrate predators were presented, in separate, replicated trials, with a range of prey species of different sizes (Warren, unpublished data). Each vertical line of points is the set of results for a single predator species (plotted at the average predator size used in the trials). Each potential predator:prey interaction is represented by a semicircle: the lefthand semicircles, in black, indicate a prey species that was eaten, and the open semicircle to the right indicates a prey species upon which predation did not occur. The horizontal bars are the mean prey sizes taken by each predator.

and behavioural) differences to determining the presence of an interaction can be seen more explicitly in data from experimental feeding trials, where intraspecific size ranges of predators and prey were limited, but predators were exposed to a wide range of prey species that differed substantially in size (Fig. 6.3). Intriguingly, although prey sizes spanned almost four orders of magnitude, the spread of prey sizes taken was wide and there was little evidence of systematic changes in the likelihood of prey being consumed along the size axis, within the limits of prey size taken. The interspersion of species that were consumed with those that were not indicates size was not a good predictor of whether individual species will be consumed within the prey range taken. Put another way, feeding was not contiguous on the size axis. For the eleven predators examined here, the proportion of prey species (whose sizes lay between the largest and smallest prey taken) that were actually eaten ranged from 0.27 to 0.86. So, whilst at one level there are clearly quite subtle responses of predators to size differences among prey, it is important to bear in mind that most of these relationships come from intraspecific size variation. Using these relationships to scale up and generalize across diverse prey types might be more complex. The prey-size niche of individual predators does not explain all the variation in prey choice, but seems to have certain basic characteristics that recur across many predator types. The first is that individual predators tend to take prey

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smaller than themselves. The second is that larger predators tend to take larger prey individuals on average, but this is chiefly because the prey maximum increases with predator size. The prey minimum tends to increase more slowly than the maximum; with the result that the prey-size range increases with predator size (Woodward & Hildrew, 2001, 2002b): the mechanisms behind this are probably complex, but it is likely to be driven by a combination of both predator gape limitation and the size distribution of the potential prey assemblage. The consequence of this scaling is that the diets of individual predators shift with changing predator body size: a phenomenon documented by Hardy (1924) in one of the earliest published food webs, and termed metaphoetesis by Hutchinson (1959). Ontogenetic dietary shifts with growth are well known but often overlooked in food-web studies, where each ‘node’ is effectively averaged over all developmental stages (Woodward & Hildrew, 2001; Woodward et al., 2005c), or in some cases represents only certain parts of the developmental sequence. Given that organisms can move through three or more orders of magnitude of body mass over the course of their development, if the prey-size niche shifts in proportion then dietary changes can be profound, and the consequences for interpretation of feeding interactions when individuals are aggregated to species can be considerable: indeed, ontogenetic differences within species can far exceed taxonomic differences among species (Woodward & Hildrew, 2001, 2002b).

Scaling to species Although size constraints and predator–prey interactions operate at the level of individuals, when examining consequences for community structure we are usually interested in partitioning the interactions so as to make discrete associations between species, which are the entities in the system to which other dynamic metrics are relevant (e.g. population growth rate). Recurrent sizedependent patterns reported from species-averaged webs include ‘upper triangularity’ and nested feeding niches within food-web matrices, such that (in general) predators feed on prey that are smaller than themselves and diet width expands with predator size (Fig. 6.4). Analysis of a recently compiled metadatabase of consumer resource body-size ratios (Brose et al., 2005) shows a wide range of possible values for predatory invertebrates, although the average is close to two orders of magnitude in both marine (log-ratio 1.8  0.08 SE) and freshwater (log-ratio 1.9  0.06 SE) systems (Fig. 6.5). Marine systems display a wider range of ratios than is the case in freshwaters, presumably because the greater volume of habitat space can support far larger consumers, in addition to phylogenetic constraints: freshwater food webs are often dominated by insects, whereas these arthropods are vanishingly rare in marine systems, where they are replaced by other taxa, such as crustaceans, that can attain far larger body sizes. Despite the average log-ratio being close to two, there are some prey

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Figure 6.4 Species-averaging effects in food webs. (a) Community matrix for Skipwith Pond with species ordered according to body length (mm), with black circles representing feeding links and white circles representing the average size across all prey species for each predator. (b) Community matrix for the Broadstone Stream food web, with species ordered according to body mass, with circles representing feeding links, and the area of each circle corresponding to per capita interaction strength (logtransformed). (c) Individual predation events for the Broadstone Stream food web (n ¼ 1825 observations). The solid diagonal lines in all three plots represent the 1:1 line.

that are considerably larger than their predators, particularly in marine systems. This situation arises particularly where modular organisms, such as cnidaria, are involved, whose true ‘mean individual’ body mass is difficult to assess. However, it seems likely that many instances of predators being smaller than their prey in summary webs relate to species averaging effects, because whilst links are portrayed as being between species pairs, this is not the same as there being feeding interactions between all individuals of those species. All that is required to obtain a feeding interaction between species is that individuals from some part of the size spectrum of the consumer population feed on individuals from some part of the size spectrum of the resource population. In addition, if the positions and shapes of the feeding niches themselves are a function of predator size, and there is a frequency distribution of predator sizes that make up a population, the feeding niche of the species (or population) is itself the

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Figure 6.5 Distribution of predator:prey body-mass ratios for feeding links in aquatic systems. Boxplots (a) and (b) show species-averaged consumer-resource ratios for species pairs taken from the Brose et al. (2005) data set, for freshwater and marine food webs, respectively. The adjacent boxplots (c)–(f) in the lower panel show the effects of averaging at different scales of resolution within the Broadstone Stream food web. Boxplot (c) depicts the species-averaged values for the Broadstone Stream food web, as taken from the community matrix and the summary trivariate plot. Boxplot (d) depicts species averaging by links (i.e. the average body mass of consumers and that of the prey found in their guts for each species pair – thus this includes only individuals involved in a predation event, such that each link is a mean of the consumer-resource ratio of the two protagonist species involved). Boxplot (e) shows values from all individual predation events. Note that the trivariate plot understimates the true consumer-resource size disparity by about one order of magnitude – thus the predators are feeding on a subset of the prey size spectrum. At the finest scale of resolution (i.e. within-individual distributions), the right-hand boxplot (f) shows the distribution of prey body masses from the gut of a single predator within the Broadstone Stream food web (n ¼ 99 prey individuals of 13 species).

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Figure 6.6 Scaling from the individual to species-averaged food webs. Panel (a) shows resource use of a single predator (solid square symbol) feeding on one of a pair of prey species (each having a distribution of individuals of different sizes). The predator exploits different sizes of prey with differing effectiveness within the upper and lower size limits of its feeding niche. Only a portion of the size spectrum of the prey species is exploited, with upper- and lower-size refugia being evident. Curve B here represents non-exploited ‘prey’ species outside the predator’s size envelope of potential prey. (b) Resource use by four different predator individuals of different life stages, reflecting ontogenetic shifts in diet as a predator grows. (c) The distributions of body sizes of both consumers and resources, across a predator population comprising of many individuals of different sizes of both predator and prey (square symbols represent the average body size of each species). (d) Trophic interactions depicted as single links between single nodes, which are the species represented by their average size (square symbols), as in species-averaged food webs.

summation of the feeding niches of the consumer individuals (Fig. 6.6). Most studies suggest that consumer species are, on average, about one to four orders of magnitude larger than their prey, in terms of body mass (Woodward et al., 2005b) as in the Brose et al., (2005) database. However, because the size of the protagonists is rarely measured for individual acts of predation, but taken from the average size of individuals across the entire population, these reported ratios are likely to be somewhat misleading. The effect of species averaging can be seen in the Broadstone Stream food web where, if we calculate the average consumer-resource ratio by dividing across the total number of feeding links within the summary food web (i.e. all species pairs of predators and prey,

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with sizes being the average size of each species), as is often done in studies comparing consumer-resource body-size ratios (e.g. Brose et al., 2005), the true ratio of predator and prey body mass is underestimated by about one order of magnitude, when compared with that obtained as the average of the size ratios of individuals involved in actual feeding events (e.g. Fig. 6.5c vs. Figs. 6.5d & 6.5e). This is because species averaging effectively assumes that all sizes of predator population are equally likely to feed on all sizes of prey; but this is rarely likely to be the case. One consequence is that the triangularity in the species-averaged feeding matrix disappears, as the preponderance of smaller than average prey is revealed in the predators’ diets. Taking averages at the species level gives a log-normal distribution of body-mass ratios, with a mean close to one: i.e. predators are, on average, about ten times larger than their prey. A similar-shaped distribution is obtained when this is repeated for individual feeding links, but predators are, on average, now about 100 times larger than their prey (Fig. 6.5). Consequently, species averaging severely underestimated the true size disparity between consumers and resources, such that the prey that were actually consumed were considerably smaller than those that potentially could be consumed, highlighting the potential importance of size refugia from predation at the two extremes of a prey species’ size spectrum. Ontogenetic size refugia can arise where individuals that survive to become large become invulnerable to predators (Fig. 6.6b prey species B) and examples from aquatic systems are well known (Bechara, Moreau & Hare, 1993, Chase, 1999; Woodward et al., 2005c). The effects of these partial overlaps of feeding niche and prey-size distribution will depend on the contribution that individuals in the exploited part of the spectrum make to the reproductive output of the population. Interactions of this sort, where parts of species’ populations interact intensely and others little or not at all, can in theory lead to complex dynamics that differ considerably from the dynamics expected if all individuals are equivalent. This phenomenon often also has a temporal component: for instance, where the numbers of individuals in the different parts of the size spectrum vary over time through reproductive pulses (De Roos & Persson, 2002; Scheffer & Carpenter, 2003; Bystro¨m, 2006; Persson & De Roos, this volume). Clearly, although combining information from all sizes of predators and prey, and across sampling occasions, is the standard method for constructing most food webs, such species-averaged webs, whilst depicting a correct representation of the linkages between species, mask the effects of size partitioning, ontogenetic and seasonal shifts, and the potential for intraspecific size-refugia from predation. It is difficult from existing food-web data to get a clear measure of the magnitude of this effect but, for example, within the Skipwith food web about 36% of links are present only at certain life-stage combinations of consumer and resource: some of this variation (and certainly much more in terms of frequency of interaction rather than just presence) can be attributed to individual size

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effects. This raises wider questions about the conventional construction of food webs, such as whether the perceived prevalence of omnivory, cannibalism and feeding loops (species A eats species B eats species A) reported in summary webs might be an artefact of species averaging. Complex feeding loops (A eats B eats C eats A) among predators, determined by body size, produce dynamics that are often highly unstable in standard Lotka-Volterra population-based models (Polis, 1991) and should therefore be rare in nature. However, aquatic food webs are typically rich in omnivory (feeding across several trophic levels) and feeding loops, especially in invertebrate-dominated systems (Woodward & Hildrew, 2002a). Many of these interactions represent ‘life-history’ omnivory, and in extreme cases this can give rise to feeding loops and reversals in trophic status, whereby large individuals of small species prey upon small individuals of species that are ultimately larger (Woodward & Hildrew, 2002b). This often occurs when generations overlap, which can also introduce a seasonal dimension to shifts within the food web: all of these complexities are lost by averaging across species and time, and more subtle individual-based models might provide greater insight (e.g. Claessen, De Roos & Persson, 2000). However, these marked changes in trophic interactions, whilst dramatically altering the occurrence of different feeding links between species, may still result in networks structured by size. If the life-history changes are reasonably synchronous (as is the case in many invertebrates) at any one time species can still be ordered by size, and the underlying size constraints on feeding still apply. If life-history changes are very asynchronous, such that many stages of each species are present at once, then size constraints still operate, but now at the level of life stages, or individuals. Thus, body size could provide an overarching set of rules that might generate relatively stable patterns of structure, even where links between particular species change markedly. Such structural constraints are suggested by static food-web models based on the hierarchical ordering of feeding niches (e.g. Cohen et al., 1986, Warren, 1996, Williams & Martinez, 2000, Cattin et al., 2004). The complex changes in feeding interactions associated with shifts in species’ size distributions are not inconsistent with these models if size rather than taxonomic identity is the constraint (e.g. Woodward & Hildrew, 2002b).

The other side of the equation: community-size distributions The ‘rules’ by which consumers are size selective might be considered to define the fundamental niche, whereas the realized niche is determined by the actions of individual consumers plus the size structure of the underlying community. The distribution of all possible body-size ratios in a food web (Fig. 6.7) is clearly a function of the size distribution of the different species. Size spectra have often been used to depict the distribution of body sizes within a community web in marine systems and, to a lesser but increasing extent, in freshwaters (Schmid,

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Tokeshi & Schmid-Araya, 2000, Stead et al., 2005). A commonly observed phenomenon within such distributions is the presence of distinct multiple modes within the size spectrum of a given food web: these separate peaks usually describe, respectively, the meiofauna (metazoans passing through a 500 mm sieve), the invertebrate macrofauna (e.g. stoneflies, shrimps), the vertebrate macrofauna (e.g. fishes) or the megafauna (e.g. cetaceans), if present (Warwick, this volume). There is often a degree of blurring between these boundaries, with some of the smaller macroinvertebrates passing temporarily through the meiofauna in their early life stages, but in general the peaks and their distributions are usually relatively discrete (Warwick, this volume). Unfortunately, very few studies of food webs have included all portions of the size spectrum, largely due to the difficulties in sampling the feeding links of such a vast array of organisms and in identifying many of the more cryptic, but highly speciose, groups of smaller taxa. Even in the few studies where the meiofauna has been included together with the macrofauna, the microbial fauna has been omitted, so even these highly resolved food webs are still incomplete (SchmidAraya et al., 2002a, b). Nonetheless, these limited data do suggest some form of dietary size partitioning is operating in response to the distribution of peaks and troughs in the underlying size spectrum. For example, within the ‘simple’ Broadstone Stream community, the meiofaunal component has been resolved to yield a summary food web that contains over 130 species and more than 800 links (Schmid-Araya et al., 2002a; Woodward et al., 2005c). Some intriguing results emerge from these data. For instance, the slope of the relationship between log number of links and log species richness of a set of these food webs (b ¼ 1.3) did not conform to the predictions of either the constant connectance hypothesis (b ¼ 2) or the link-scaling law (b ¼ 1); this intermediate slope suggests some form of size partitioning between the macrofaunal and meiofaunal webs (Schimd-Araya et al., 2002b; Woodward et al., 2005b, c). This

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partitioning can be seen clearly within the Broadstone Stream food web, where diet width increases with predator size when only macrofaunal prey are considered, but the opposite is true when links to both the macrofaunal and meiofaunal prey assemblage are included (Woodward et al., 2005c). In addition to ontogenetic and seasonal effects, population size structures can also be altered through extrinsic factors. For instance, strong size-selective predation, as occurs in commercial fisheries (e.g. Policansky & Magnuson, 1998), can extirpate prey species and change community structure (Brooks, 1968; Brooks & Dodson, 1965), but where predation falls on some parts of a population only, and is not so strong, the effect may be to alter the size structure, which could then have consequences for the feeding links from the affected population to others, and change the size structure of the wider food web (e.g. Blumenshine et al., 2000; Jennings, this volume).

Macroecological patterns: consequences of body-size shifts in response to environmental gradients Although body size affects feeding interactions at the individual level, the effects of such constraints also ramify through higher levels of organization, to the community and ecosystem (Persson & De Roos, this volume). The implicit suggestion is that, if individual interactions are determined largely by body size, then alterations in the distribution of body sizes within communities are also likely to have powerful effects at macroecological scales. Linked to this is the question of how size distributions change with species richness, and what the likely consequences are for food-web dynamics and ecosystem functioning across environmental gradients. The number of species and the distribution of body sizes within a food web are determined by a combination of biotic and environmental factors, and the relative importance of the two varies over different spatial scales. For instance, at biogeographical scales, species richness decreases and body mass increases with latitude (Ricklefs, 2004), whereas at finer spatial scales, anthropogenic stressors often play a key structuring role in many aquatic communities (Giller et al., 2004; Petchey et al., 2004). Predictable shifts in the taxonomic composition of a community in response to environmental gradients are well known, but much less attention has been paid to how the size spectrum changes across abiotic gradients, with the exception of some marine systems, where abundance-biomass curves have been used for some time to infer environmental stress (e.g. Warwick & Clarke, 1991; Warwick, this volume). Stressor-induced species loss is highly non-random with respect to body size: large, rare species, and particularly those at the higher trophic levels, are typically the first to be lost, and this can alter the size spectrum and distribution of interaction strengths within the food web (Petchey et al., 2004; Woodward et al., 2005b). The disproportionate loss of large species is likely to have particularly strong effects on the ‘functioning’ of

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stressed ecosystems, if such species are also keystones and/or strong interactors, as has been suggested (e.g. Scheffer & Carpenter, 2003; Solan et al., 2004). For instance, in freshwaters pH has strong effects on the distribution of body mass, biodiversity, ecosystem processes and food-web properties (Woodward & Hildrew, 2002a). At low pH fish populations are often replaced at the top of the food web by much smaller invertebrate predators, which benefit from mesopredator release (sensu Courchamp, Langlais & Sugihara, 1999). According to food-web theory, this should reduce average interaction strength, as the size disparity between consumers and resources shrinks and might account for the apparently high stability of the communities of acidified freshwaters, and their slow recovery following reversals of acidification (Woodward & Hildrew 2002a; Ledger & Hildrew, 2005).

Conclusions Recent advances in both theory and empirical data have led to a tighter coupling of the ecosystem and community approaches, and the implicit links between structure (e.g. the distribution of body size) and process (e.g. nutrient cycling; energy flux) are now starting to be addressed more rigorously. Metabolic theory has been proposed as a suitable framework within which to develop an integrated structural-functional approach, because basal metabolic rate, which is negatively correlated with body size, affects pattern and process across multiple levels of ecological organization, from individual organisms (e.g. growth and survival rates) to entire ecosystems (e.g. nutrient cycling and productivity (Woodward et al., 2005a, b). In the context of these large-scale problems, and the general theories proposed to address them, size seems likely to play a central role, linking as it does individual-level processes with ecosystem structure. Many of the component parts of this scaling process have been in place for some time: the challenging thing now is to develop an understanding of how to scale up to making the right connections. It is interesting that for such a basic question we still have rather patchy and heterogeneous information on the size relations of predators and their prey (Warren, 2005; Humphries, this volume). More systematic data collation from a wide range of ecosystems (see Brose et al., 2005) is obviously one key way forward, but new data are also needed to allow the effects of scaling from the individual to species to be examined. Size provides a way of building models that take individual-level processes and explore their consequences across populations and communities, but at present much of the information we have about how the mechanisms underpinning foraging and feeding dynamics of individuals comes from comparisons using intraspecific variation in body size. New, individual-based, food-web models may provide a means of testing how to generalize from individuals to species level aggregations and beyond. One potential way forward is to construct food-web models that employ size-based

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‘boxes’ through which individuals pass. Even static structural models such as the niche-based models (Warren, 1996; Williams & Martinez, 2000, Cattin et al., 2004) could be revisited (explicitly using using body size as the niche dimension), using size-specific rules for link allocation to examine the extent to which individual-level size-based trophic rules provide an envelope for food-web organization. Such models could potentially generate relative constancy of structure, even as the identities of the entities in the web change. Linking size distributions with trophic dynamics is also likely to be an area of increasing interest (Persson & De Roos, this volume), particularly because of the effects of stressors on size distributions and the implications for ecosystem functioning. Of course, going beyond aquatic systems also raises the considerable challenge of ascertaining whether the size-dominated view of aquatic food webs, that comes from looking through the contents of a pond net and using a plankton counter, applies to terrestrial systems.

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salmon Oncorynchus nerka in relation to size and temperature. Journal of the Fisheries Research Board of Canada, 30, 379–387. Brooks, J. L. (1968). The effects of prey size selection by lake planktivores. Systematic Zoology, 17, 273–291. Brooks, J. L. & Dodson, S. I. (1965). Predation, body size, and composition of plankton. Science, 150, 28–35. Brose, U., Berlow, E. L., Jonsson, T. et al. (2005). Body sizes of consumers and their resources. Ecology, 86, 2545–2546. Brown, J. H. (1995). Macroecology. Chicago: University of Chicago Press. Brown, J. H. & Gillooly, J. J. (2003). Ecological food webs: high-quality data facilitate theoretical unification. Proceedings of the National Academy of Sciences USA, 100, 1467–1468. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. (2004). Toward a metabolic theory of ecology. Ecology, 85, 1771–1789. Bystro¨m, P. (2006). Recruitment pulses induce cannibalistic giants in Arctic Char. Journal of Animal Ecology, 75, 434–444. Cattin, M.-F., Bersier, L.-F., Banasek-Richter, C., Baltensberger, R. & Gabriel, J.-P. (2004). Phylogenetic constraints and adaptation

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explain food-web structure. Nature, 427, 835–839. Chase, J. M. (1999). Food web effects of prey size refugia: variable interactions and alternative stable equilibria. American Naturalist, 154, 559–570. Claessen, D., de Roos, A. M. & Persson, L. (2000). Dwarfs and giants: cannibalism and competition in size-structured populations. American Naturalist, 155, 219–237. Cohen, J. E., Briand, F. & Newman, C. M. (1986). A stochastic theory of community food webs. III. Predicted and observed lengths of food chains. Proceedings of the Royal Society of London B, 228, 317–353. Cohen, J. E., Pimm, S. L., Yodzis, P. & Saldana, J. (1993). Body sizes of animal predators and animal prey in food webs. Journal of Animal Ecology, 62, 67–78. Cohen, J. E., Jonsson, T. & Carpenter, S. R. (2003). Ecological community description using the food web, species abundance, and body size. Proceedings of the National Academy of Sciences USA, 100, 1781–1786. Courchamp, F., Langlais, M. & Sugihara, G. (1999). Cats protecting birds: modelling the mesopredator release effect. Journal of Animal Ecology, 68, 292–293. Cousins, S. H. (1980). A trophic continuum derived from plant structure, animal size and a detritus cascade. Journal of Theoretical Biology, 82, 607–618. Cousins, S. H. (1985). The trophic continuum in marine ecosystems: structure and equations for a predictive model. Canadian Bulletin of Fisheries and Aquatic Sciences, 213, 76–93. De Roos, A. M. & Persson, L. (2002). Sizedependent life-history traits promote catastrophic collapses of top predators. Proceedings of the National Academy of Sciences USA, 99, 12907–12912. de Ruiter, P. C., Neutel, A. M. & Moore, J. C. (1995). Energetics, patterns of interaction strengths, and stability in real ecosystems. Science, 269, 1257–1260.

Dickie, L. M., Kerr, S. R. & Boudreau, P. R. (1987). Size-dependent processes underlying regularities in ecosystem structure. Ecological Monographs, 57, 233–250. Eggleston, D. B. (1990). Functional response of blue crabs Callinectes sapidus Rathburn feeding on juvenile oysters Crassostrea virginica (Gmelin): effects of predator sex and size, and prey size. Journal of Experimental Marine Biology and Ecology, 143, 73–90. Elton, C. S. (1927). Animal Ecology. London: Sidgwick & Jackson. Emmerson, M. C. & Raffaelli, D. G. (2004). Body size, patterns of interaction strength and the stability of a real food web. Journal of Animal Ecology, 73, 399–409. Fry, F. E. & Cox, E. T. (1970). A relation of size to swimming speed in rainbow trout. Journal of the Fisheries Research Board of Canada, 27, 976–978. Gaston, K. J. & Blackburn, T. M. (2000). Pattern and Process in Macroecology. Oxford: Blackwell Science. Giller, P. S., Hillebrand, H., Berninger, U.-G. et al. (2004). Biodiversity effects on ecosystem functioning: emerging issues and their experimental test in aquatic environments. Oikos, 104, 423. Hardy, A. (1924). The herring in relation to its animate environment, part 1. Fisheries Investigations, Series 27 (3). Hewett, S. W. (1980). The effect of prey size on the functional and numerical responses of a protozoan predator to its prey. Ecology, 61, 1075–1081. Hutchinson, G. E. (1959). Homage to Santa Rosalia or why are there so many kinds of animals? American Naturalist, 93, 145–159. Huxham, M., Beaney, S. & Raffaelli, D. (1996). Do parasites reduce the chances of triangulation in a real food web? Oikos, 76, 284–300. Kerr, S. R. (1974). Theory of size distribution in ecological communities. Journal of the Fisheries Research Board of Canada, 31, 1859–1862.

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Kislalioglu, M. & Gibson, R. N. (1976). Prey ‘handling time’ and its importance in food selection by the 15-spined stickleback, Spinachia spinachia (L). Journal of Experimental Marine Biology and Ecology, 25, 151–158. Ledger M. E. & Hildrew A. G. (2005). The ecology of acidification and recovery: changes in herbivore-algal food web linkages across a stream pH gradient. Environmental Pollution, 137, 103–118. Lehman, C. L. & Tilman, D. (2000). Biodiversity, stability, and productivity in competitive communities. American Naturalist, 156, 534–552. Lundberg, S. & Persson, L. (1993). Optimal body size and resource density. Journal of Theoretical Biology, 164, 163–180. Memmott, J., Martinez, N. D. & Cohen, J. E. (2000). Predators, parasitoids and pathogens: species richness, trophic generality and body size in a natural food web. Journal of Animal Ecology, 69, 1–15. Pastorok, R. A. (1981). Prey vulnerability and size selection by Chaoborus larvae. Ecology, 62, 1311–1324. Persson, L., Leonardsson, K., de Roos, A. M., Gyllenberg, M. & Christensen, B. (1998). Ontogenetic scaling of foraging rates and the dynamics of a size-structured consumerresource model. Theoretical Population Biology, 54, 270–293. Petchey, O. L., Downing, A. L., Mittelbach, G. G. et al. (2004). Species loss and the structure and functioning of multitrophic aquatic systems. Oikos, 104, 467–478. Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge, England: Cambridge University Press. Pitta, P., Giannakourou, A. & Christaki, U. (2001). Planktonic ciliates in the oligotrophic Mediterranean Sea: longitudinal trends of standing stocks, distributions and analysis of food vacuole contents. Aquatic Microbial Ecology, 24, 297–311.

Policansky, D. & Magnuson, J. J. (1998). Genetics, metapopulations and ecosystem management of fisheries. Ecological Applications, 8, 119–123. Polis, G. A. (1991). Complex trophic interactions in deserts: an empirical critique of food web theory. American Naturalist, 138, 123–155. Pyke, G. H. (1984). Optimal foraging theory: a critical review. Annual Review of Ecology and Systematics, 15, 523–575. Pyke, G. H., Pulliam, H. R. & Charnov, E. L. (1977). Optimal foraging: a selective review of theory and tests. Quarterly Review of Biology, 52, 137–154. Reuman, D. & Cohen, J. E. (2005). Estimating relative energy fluxes using the food web, species abundance, and body size. Advances in Ecological Research, 36, 136. Ricklefs, R. E. (2004). A comprehensive framework for global patterns in biodiversity. Ecology Letters, 7, 1. Scheffer, M. & Carpenter, S. R. (2003). Catastophic regime shifts in ecosystems: linking theory to observation. Trends in Ecology and Evolution, 18, 648–656. Schoener, T. W. (1969). Models of optimal size for solitary predators. American Naturalist, 103, 277–313. Schoener, T. W. (1971). Theory of feeding strategies. Annual Review of Ecology and Systematics, 11, 369–404. Schmid, P. E., Tokeshi, M. & Schmid-Araya, J. M. (2000). Relation between population density and body-size in stream communities. Science, 289, 1557–1560. Schmid-Araya, J. M., Hildrew, A. G., Robertson, A., Schmid, P. E. & Winterbottom, J. (2002a). The importance of meiofauna in food webs: evidence from an acid stream. Ecology, 83, 1271–1285. Schmid-Araya, J. M., Schmid, P. E., Robertson, A. et al. (2002b). Connectance in stream food webs. Journal of Animal Ecology, 71, 1056–1062.

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Scott, M. A. & Murdoch, W. W. (1983). Selective predation by the backswimmer, Notonecta. Limnology and Oceanography, 28, 352–366. Smyly, W. J. P. (1980). Food and feeding of aquatic larvae of the midge Chaoborus flavicans (Meigen) (Diptera: Chaoboridae) in the laboratory. Hydrobiologia, 70, 179–188. Solan, M., Cardinale, B. J., Downing, A. L. et al. (2004). Extinction and ecosystem function in the marine benthos. Science, 306, 1177–1180. Spitze, K. (1985). Functional response of an ambush predator: Chaoborus americanus predation on Daphnia pulex. Ecology, 66, 938–949. Stead, T. K., Schmid-Araya, J. M., Schmid, P. E. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487. Stephens, D. W. & Krebs, J. R. (1986). Foraging theory. Monographs in Behaviour and Ecology. Princeton, NJ, USA: Princeton University Press. Thompson, D. J. (1975). Towards a predator-prey model incorporating age structure: the effects of predator and prey size on the predation of Daphnia magna by Ischnura elegans. Journal of Animal Ecology, 44, 907–916. Tripet, F. & Perrin, N. (1994). Size-dependent predation by Dugesia lugubris (Turbellaria) on Physa acuta (Gastropoda): experiments and model. Functional Ecology, 8, 458–463. Turesson, H., Persson, A. & Bro¨nmark, C. (2002). Prey size selection in piscivorous pikeperch (Stizostedion lucioperca) includes active prey choice. Ecology of Freshwater Fish, 11, 223–233. Warren, P. H. (1989). Spatial and temporal variation in the structure of a freshwater food web. Oikos, 55, 299–311. Warren, P. H. (1996). Structural constraints on food web assembly. In Hochberg, M. E., Clobert, J. and Barbault, R. (eds.) Aspects of the Genesis and Maintenance of Biological Diversity, ed. M. E. Hochberg, J. Clobert and R. Barbault. Oxford, UK: Oxford University Press, pp. 143–161.

Warren, P. H. (2005). Wearing Elton’s wellingtons: why body size still matters in food webs. In Dynamic Food Webs: Multispecies Assemblages, Ecosystem Development, and Environmental Change, ed. P. C. de Ruiter, V. Wolters and J. C. Moore. San Diego: Academic Press. Warwick, R. M. & Clarke, K. R. (1991). A comparison of some methods for analysing changes in benthic community structure. Journal of the Marine Biological Association, UK, 71, 225–244. Williams, R. J. & Martinez, N. D. (2000). Simple rules yield complex food webs. Nature, 404, 180–183. Woodward, G. & Hildrew, A. G. (2001). Invasion of a stream food web by a new top predator. Journal of Animal Ecology, 70, 273–288. Woodward, G. & Hildrew, A. G. (2002a). Food web structure in riverine landscapes. Freshwater Biology, 47, 777–798. Woodward, G. & Hildrew, A. G. (2002b). Bodysize determinants of niche overlap and intraguild predation within a complex food web. Journal of Animal Ecology, 71, 1063–1074. Woodward, G. & Hildrew, A. G. (2002c). Differential vulnerability of prey to an invading top predator: integrating field surveys and laboratory experiments. Ecological Entomology, 27, 732–744. Woodward, G., Thompson, R., Townsend, C. R. & Hildrew, A. G. (2005a). Pattern and process in food webs: evidence from running waters. In Aquatic Food Webs: An Ecosystem Approach, ed. A. Belgrano, U. Scharler, J. Dunne and B. Ulanowicz.Oxford: Oxford University Press. Woodward G., Ebenman B., Emmerson M. et al. (2005b). Body size in ecological networks. Trends in Ecology and Evolution, 20, 402–409. Woodward, G., Speirs, D. C. & Hildrew, A. G. (2005c). Quantification and resolution of a complex, size-structured food web. Advances In Ecological Research, 36, 85–135. Yodzis, P. & Innes, S. (1992). Body size and consumer-resource dynamics. American Naturalist, 139, 1151–1175.

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Body size and trophic cascades in lakes J . IWAN JONES Centre for Ecology and Hydrology, UK

ERIK JEPPESEN National Environmental Research Institute, University of Aarhus, Denmark

Introduction Since its first appearance (Hairston, Smith & Slobodkin, 1960), the hypothesis that predation can structure communities has courted controversy (Shapiro, Lamarra & Lynch, 1975; Strong, 1992; McCann, Hastings & Strong, 1998). Nearly 50 years later there is still ongoing debate over the importance of predation relative to other factors limiting the growth of populations (Pace et al., 1999; Holt, 2000; Polis et al., 2000; Power, 2000), and the conditions that cause the effect of predation to cascade through the community (Polis & Strong, 1996; Schmitz, Krivan & Ovadia, 2004; Borer et al., 2005; Vander Zanden, Essington & Vadeboncoeur, 2005). With the discovery of predator impacts on the structure and dynamics of a diversity of real communities (Paine, 1980; Power, Matthews & Stewart, 1985; Carpenter & Kitchell, 1993), it became apparent that higher trophic levels could affect the biomass and dynamics of not only their prey, but of their prey’s prey and, hence, the whole community. Earlier it was assumed that communities were typically pyramidal in structure, with declining biomass in each successive trophic level, and the dynamics of each trophic level dependent upon those of their prey and ultimately the primary producers/basal resources (Whittaker, 1961). It is now clear from habitats as diverse as Californian islands (Roemer, Donlan & Courchamp, 2002), the forests of Yellowstone Park (Ripple & Beschta, 2004) and the cod banks of the North Atlantic (Worm & Myers, 2003; Frank et al., 2005) that this assumption is not correct, such that nowadays the predictions of the trophic cascade influence how we manage our natural environment (Scheffer, 1998). Nevertheless, despite numerous thoughtful arguments, and theoretical and empirical analyses, the subject still remains controversial. The trophic cascade is defined as the propagation of indirect mutualism between non-adjacent levels in a food chain, and manifests itself as a change in the biomass of primary producers in response to changes in the biomass of consumers separated by at least one trophic level. Hence, in the cascade described for lakes, increased biomass of planktivorous fish leads to decreased Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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zooplankton biomass and increased phytoplankton (Carpenter, Kitchell & Hodgson, 1985). The phrase trophic cascade has been variously applied, but it is generally accepted that it describes a community-wide response of species, including those near the base of the web, typically primary producers (Polis et al., 2000). There has been much discussion as to how widespread within trophic levels the response must be, but it has been argued that for a true community trophic cascade the impact of changes in predator biomass must result in a change in total primary producer biomass (Polis, 1999; Polis et al., 2000). Cascading interactions within compartments of the community are possible (e.g. Strong et al., 1996), but here there is limited change in primary producer biomass, typically resulting in a change in species composition rather than biomass change per se. It may be that the ‘runaway consumption’ (sensu Strong, 1992) required for a cascade is characterized by a substantial shift in community composition in circumstances where alternative primary producers may exploit the vacated niche, but there is no consensus on the extent of the compositional change required (Polis et al., 2000). In an attempt to define the conditions that give rise to trophic cascades, Polis et al. (2000) argued that trophic cascades are restricted to simple, trophically stratified systems in homogeneous habitats where strong interactions link uniformly susceptible prey to predators. In these relatively simple systems, energy (organic matter) passes through the community via a single direct route and there are few, if any, alternative routes to buffer changes in predator populations. As the variety of prey tends to be low, either as functional type or as species per se, there is little choice for predators and, as the system is homogeneous, there are few refugia for prey. It has been suggested further that these characteristics are typical of aquatic environments and that as a consequence, cascades are ‘all wet’ (Strong, 1992). Nevertheless, there is evidence to suggest that cascades can occur in the speciose communities of structured, complex environments, both aquatic and terrestrial (Pace et al., 1999; Moran & Scheidler, 2002; Jones & Sayer, 2003; Preisser, 2003, but see Gruner, 2004). Here we discuss whether a structured pattern of body size among predators and prey is involved in the occurrence of trophic cascades, and how such a pattern can arise in communities. We will examine other parameters and their relationship with body size, to determine if any patterns are the result of body size per se or some other correlated factor.

Body size Trophic cascades are dependent upon the presence of generalist herbivores (Jiang & Morin, 2005), which are often associated with large relative size at least at some stage in the life cycle where the primary producers are vulnerable (e.g. urchins feeding on macroalgae (Estes et al., 2004); large Cladocera feeding on phytoplankton (Carpenter & Kitchell, 1993); minnows feeding on algae

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(Power et al., 1985); lemmings and voles feeding on dwarf shrubs (Oksanen, 1983; Hamback et al., 2004)). A large size disparity between predators and prey tends to render prey uniformly susceptible to predation. This is because discrimination between prey types becomes more difficult with increasing size disparity and less worthwhile, unless there are considerable nutritional differences between prey species. If the size disparity is too large, visual selection of prey becomes impractical at anything other than a patch scale. In many cascades described from aquatic systems the herbivores are filter feeders or scrapers feeding on a mixed community of algae (Paine, 1980; Carpenter et al., 1985; Power et al., 1985; Jones & Sayer, 2003; Humphries, this volume). The strong effects in eutrophic lakes depend on the presence of large-bodied cladocerans (Jeppesen et al., 2003a; Jeppesen et al., 2004). Generalist herbivores are also typical of those terrestrial communities where community trophic cascades have been described (Hamback et al., 2004). Hence, predation has impacts across many trophically similar species, particularly at the lowest trophic level, and results in a community-wide response. It has been suggested, however, that the predominance of cascades in aquatic systems may be due to factors other than predation limiting the size of the primary producers (Strong, 1992). For phytoplankton, the constraints of remaining suspended within the water column are size dependent and it is possible that the restrictions imposed by sinking influence the pattern of body size among trophic levels. Nevertheless, planktonic algae can aggregate as colonies of relatively large ‘body size’, which makes them less vulnerable to grazing and several algal taxa that produce large colonies are positively buoyant (e.g. Microcystis). Even if sinking constraints on body size exist for phytoplankton, there does not seem to be any such constraint, either environmental or phylogenetic, on attached algae. Sinking does not affect attached algae, and several orders of algae contain large-bodied multicellular representatives, yet clear examples exist of cascades with attached algae at the base (Paine, 1980; Power et al., 1985; Jones & Sayer, 2003). Many algal species, both attached and planktonic, pass into a size refugium where grazers are no longer capable of consuming them effectively (Dodds, 1991); chemical defences to deter grazing occur among algal taxa (Turner & Tester, 1997). It appears that there are no constraints on the body size of aquatic organisms specific to their habitat that render them particularly susceptible to predation, and aquatic communities more susceptible to trophic cascades. As well as making prey more uniformly susceptible to predation, a large size difference between predators and prey means that predators must consume large numbers of prey to sustain their populations, as each individual prey item contributes little to the predators’ production. This is born out by estimates of interaction strength based on empirical data (Woodward, Speirs & Hildrew, 2005), and models estimating interaction strength from body size (Emmerson & Raffaelli, 2004). In a study of the flow of biomass and production through the community inhabiting

BODY SIZE AND TROPHIC CASCADES IN LAKES

Figure 7.1 Cascading trophic interactions within enclosures placed in the littoral zone of a shallow lake (Stigsholm). Data illustrate carbon flow between trophic levels in enclosures with and without submerged macrophytes. Boxes represent biomass (mg CL1) of different trophic components and arrows represent fluxes (mg CL1 d1). COP ¼ copepods, largely cyclopoids, ROT ¼ rotifers, CLA ¼ cladocerans, HNF ¼ heterotrophic nanoflagellates. PVI is the proportion of the volume inhabited by plants. Originally published in Jeppesen et al. (2002).

enclosures set up within vegetated and open water areas of a shallow lake, Jeppesen et al. (2002) showed that where macrophytes were present, and fish densities naturally low, zooplankton grazing was several-fold higher than phytoplankton biomass and production, reflecting an intense predation pressure (Fig. 7.1). The opposite was true of the open water enclosures, where high fish densities resulted in a substantially lower biomass of zooplankton (11% of that in the macrophyte stand), and a more than five-fold higher phytoplankton biomass. It is worth noting that in the macrophyte enclosures of Jeppesen et al. (2002) the production of zooplankton appeared to be supported by a source other than phytoplankton and bacterioplankton, possibly channelled through the microbial food web or from periphyton. If this is true then the cascade seen in this lake is merely an apparent one; zooplankton populations are maintained at higher densities than phytoplankton alone can support and can, therefore, exert a higher grazing pressure than would otherwise be expected. Similar suggestions

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have been made regarding fish, their populations being supported by zoobenthos thus allowing increased predation on zooplankton (Schindler & Scheuerell, 2002; Vander Zanden et al., 2005), and the communities of islands in the Sea of Cortez, where subsidies from the marine ecosystem support a cascade through the terrestrial community (Polis & Strong, 1996). If these suggestions of external subsidies fuelling increased predation are applicable to trophic cascades generally it is clear that the trophic cascade is nothing more than an indirect effect of alternative prey. It is clear also that longevity increases with body size (Brown, Allen & Gillooly, this volume) and, as a consequence, the populations of large-body-size predators high in the food web are damped in their response to fluctuations in the populations of small-body-size basal prey; dependent upon their susceptibility to resource depletion individuals may be able to survive periods of reduced food availability as they drive their prey’s populations to low levels, even in the absence of alternative prey. Such longevity is reflected in cohort dynamics and periodic release of prey populations when top predators pass through a reproductive cycle (Persson & De Roos, this volume); evidence of five- to six-year cyclicity has been found in fossil pigments in the sediments of lakes, suggesting that zooplankton, and thus phytoplankton, are released from predation as the dominant cohort of zooplanktivorous fish is replaced (Carpenter & Leavitt, 1991). In comparison, the generation time for phytoplankton may be as short as a few hours or days, with zooplankton taking several days to complete a generation cycle. As biomass abundance is the product of body size and numerical abundance, high densities of large individuals in the higher trophic levels lead to a deviation in the biomass distribution within the web from the typically assumed triangular trophic pyramid to a more square or inverted triangle pattern. The distribution of biomass within trophic levels has been linked to certain characteristics of food-web structure (Neutel, Heesterbeek & de Ruiter, 2002). Complex, highly connected webs where the majority of links are weak typically have a triangular distribution, and may be more stable than those that deviate from this pattern (Raffaelli, 2002). It is appealing to suggest that trophic cascades are a consequence of a certain pattern of biomass distribution (square or inverted triangle). However, whilst the slope of the trophic pyramid may help to identify communities where we would expect cascades to occur, this would not advance our understanding of the mechanism that leads to cascade dynamics. It merely leaves us with another question ‘Why does the distribution of biomass vary among communities?’

Productivity The Oksanen et al. (1981) hypothesis regarding trophic cascades, where topdown and bottom-up forces regulate community structure alternately dependent on the number of links in the food web, is an over-simplification due to

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assembling natural food webs into linear chains (Polis et al., 2000), but does illustrate that the rate of input of organic matter into the system appears to influence the structure of the web and the dynamics of the species within it. Unproductive systems appear to have highly connected food-web structures (Belgrano et al., 2005) that are resistant to changes in predation pressure, either natural (Woodward & Hildrew, 2001) or deliberate (Hildrew et al., 2004). Hence, it has been suggested that trophic cascades are restricted to productive systems (Polis et al., 2000). The strength of the cascade in lakes increases with total phosphorus concentrations (TP) (Jeppesen et al., 2003a). Furthermore, trophic cascades appear to be lacking in pelagic communities from unproductive environments such as the lakes of Greenland, even though food-chain length is as predicted by the Oksanen et al. (1981) model, body size well structured among trophic levels, and there are pronounced effects of predators on herbivores (Box 7.1). A similar pattern was found in oligotrophic alpine lakes where complete

Box 7.1 Greenland – a natural experiment on the effects of fish in lakes Greenland lakes are excellent for studying the cascading effects of fish on lake ecosystems as a large proportion of the lakes are naturally without fish. Lakes that have not been in contact with the sea at any stage since the last glaciation are nearly all fishless. However, many lakes that were previously connected to the sea, but are currently isolated, host land-locked populations of Arctic char (Salvelinus alpinus, up to three morphs) and/or three-spined sticklebacks (Gasterosteus aculeatus). Those lakes still connected to the sea also contain anadromous specimens of char. Eighty-two lakes in the high Arctic North-East Greenland (NEG) and near the Arctic circle in West Greenland (WG) have recently been subject to intensive studies (Lauridsen et al., 2001; Jeppesen et al., 2001, 2003a, b; Christoffersen, 2001; Brodersen & Anderson, 2002). In NEG, Arctic char is the only fish species present, while the stickleback is present in some of the lakes in WG. Neo- and palaeolimnological analyses of these lakes have shown clear differences in cladoceran community structure among lakes with and without fish, large pelagic and benthic forms being dominant in fishless lakes (Lauridsen et al., 2001; Jeppesen et al., 2003a, b). Accordingly, the body size varies substantially among the two lake types (Fig. 7.2). The body mass of all zooplankton, cladocerans and cyclopoid copepods was much larger in the fishless lakes in both regions, while no differences were found for calanoid copepods (present only in WG), rotifers and ciliates. The ratio of zooplankton to phytoplankton biomass (calculated from chlorophyll a) is much higher overall in fishless lakes. Nevertheless, no differences were seen in chlorophyll a (Fig. 7.2) or in

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the yield; chlorophyll:TP was similar in lakes with and without fish (E. Jeppesen et al., unpublished data). Canonical correspondence analysis indicates changes in community structure of phytoplankton (K. Christoffersen et al., unpublished data) along the fish gradient. These results suggest that the strong impact of fish on zooplankton abundance and body size in these oligotrophic lakes is not translated to total phytoplankton biomass, which is likely to be determined mainly by nutrient availability (Jeppesen et al., 2003a).

removal of fish had no effect on chlorophyll in two experimental lakes (though the colonization of a fishless lake by Daphnia did result in reduced algal biomass (Sarnelle & Knapp, 2005)). This is in contrast to the situation in more productive environments, where cascading effects can be seen in lakes of varying (high)

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nutrient status and are sufficiently predictable to be used as a management tool (Box 7.2). Certain patterns in food-chain length and body-size distribution are insufficient alone to predict trophic cascades; other factors must be involved.

Box 7.2

Trophic cascades, biomanipulation and body size

Mass removal of planktivorous fish (biomanipulation) is a method regularly used in shallow lakes to reinforce improvements in lake water quality after a nutrient loading reduction (Perrow et al., 1997; Hansson et al., 1998; Jeppesen & Sammalkorpi, 2002). The idea is that removal of zooplanktivorous fish induces increased grazing by zooplankton and higher water clarity, which, in turn, stimulates the growth of submerged macrophytes. Via a number of positive feedback mechanisms this will contribute to maintaining the clearwater state (Moss, 1990; Scheffer et al., 1993). Analyses of data from before and after the biomanipulation may provide evidence for the cascading effects of fish in eutrophic lakes. Here, we present data from three Danish long-term studies of the effects of reduction on zooplanktivorous fish. The lakes are all eutrophic and relatively shallow (Table 7.1). In Lake Engelsholm, 19 t cyprinids were removed by netting from April to September 1992, reducing the calculated biomass of cyprinids from 675 to 150–300 kg ha1 (Møller, 1998). In Lake Arreskov, a major fish kill occurred during autumn and winter (1991). An additional 4 t cyprinids were removed in 1995, and during 1993 and 1995 the lake was stocked with under-yearling pike (Esox lucius) to a density of 141 ind. ha1. Cyprinid biomass was calculated as 172 kg ha1 in 1987 and 71 kg ha1 in 1995 (Sandby, 1998). In Lake Bastrup, 7 t cyprinids were removed during 1995–1997. The cyprinid biomass was calculated to 300–400 kg ha1 before biomanipulation and to 150 kg ha 1 afterwards (Frederiksborg County, 2000). The fish removals resulted in a major increase in cladoceran body weight and the zooplankton:phytoplankton biomass ratio, a major reduction in phytoplankton biomass expressed as chlorophyll a, and marked reductions in both total phosphorus and total nitrogen (Fig. 7.3, see also Jeppesen et al., 1998, 2004). These changes occurred in all three lakes despite different nutrient levels. In contrast, no uniform response could be traced in the body weight of copepods, rotifers or total zooplankton. When comparing these results with those from oligotrophic Greenland lakes with and without fish (Box 7.1), we find a strong effect of fish on cladoceran body weight and the zooplankton:phytoplankton ratio in both sets of lakes. However, in contrast to the oligotrophic Greenland lakes the fish reduction in the eutrophic Danish lakes has major cascading effects on the phytoplankton and even on the nutrient concentrations. This holds true even though far from

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Table 7.1 Morphometric data and annual mean hydraulic retention time in the epilimnion of the three lakes in which the fish stock was reduced.

Lake Engelsholm Lake Arreskov Lake Bastrup

Surface area (km2)

Mean depth (m)

Maximum depth (m)

Retention time (days)

0.44 3.17 0.32

2.6 1.9 3.5

6.1 3.7 7.0

65–88 510–770 600–2200

Figure 7.3 Average of summer means (1 May–1 Oct) of selected variables for the period before (2–6 years) and after (9–13 years) a mass removal of planktibenthivorous fish by biomanipulation (Lake Bastrup, BAS, and Lake Engelsholm, ENG), and in Lake Arreskov (ARS) in addition by mass fish kill. The three lakes are all eutrophic.

all fish were removed from the Danish lakes. Presence of fish may explain why the body weight of total zooplankton and cladocerans, as well as the zooplankton:phytoplankton ratio, are higher overall in the fish-free Greenland lakes than in the Danish lakes after the fish removal. It is noteworthy that the reduction in chlorophyll a, total phosphorus and total nitrogen occurred in Lake Engelsholm despite the absence of submerged macrophytes (Jeppesen et al., 1998), indicating that it is largely the effect of the fish removal that triggers the abrupt changes observed.

BODY SIZE AND TROPHIC CASCADES IN LAKES

Meta-analyses of the role of eutrophication in marine pelagic cascades (Micheli, 1999) and in experimental systems (Borer et al., 2005) indicate that productivity does not explain the strength of cascading interactions. Productivity is intertwined with the turnover rate (rate of replacement of biomass) and susceptibility to herbivory (a combination of palatability and size refugia; Polis, 1999) of primary producers. In fact these three can be summarized solely as the turnover rate, as large or heavily defended primary producers do not replace biomass rapidly, akin to a situation of low productivity. Where production is sufficient, high losses to herbivory can select for either k (resistant, large or welldefended, slow-turnover species) or r (resilient, small, rapid re-growth, fastturnover species) strategists. If the community is dominated by primary producers of the latter type there is great potential for a change in herbivory to produce a significant change in standing crop. Increased herbivory often leads to increased specific primary production as nutrients are recycled more rapidly and competitors suppressed. Hence, in communities where herbivores are abundant, primary production may be high even though standing stock is low (Liboriussen & Jeppesen, 2003). Thus, the turnover rate of individuals, biomass and nutrients is higher where the rate of predation is high relative to herbivory. Under such conditions it is likely that small body size of primary producers is an advantage, as reproduction is achieved early and less investment of production made in each individual. In biomanipulated lakes where zooplanktivorous fish have been removed, the resultant cascade leads to a shift away from slow-growing, large cyanophytes to fast-growing small algae (Hansson et al., 1998) as rapid growth is required to compensate (partially) for losses to grazers. Large primary producers gain competitive advantage only if they can achieve a size refugium (e.g. Aphanizomenon flos-aquae), a condition more easily achievable where herbivores are small and infrequent or when grazing is low. We should, therefore, reconsider the well-described relationship between productivity (though standing stock is often used as a proxy (Keddy, 2000)) and the size of primary producers that has been described for higher plants, both terrestrial (Grime, 1979) and aquatic (Willby, Pygott & Eaton, 2001). Although small body size is an advantage in unproductive environments, increasing productivity does not always lead to increased body size and a competitive advantage. Where grazing is intense, small size and rapid turnover are an advantage, with large size only conferring an advantage where production is potentially high and losses to higher trophic levels are low (either because herbivores are scarce or because a size refugium exists). Thus, we would expect mean body size of primary producers to peak at intermediate productivity. Again, rather than body size per se, the turnover rate of primary producers may provide a more integrated measure of the potential for strong cascading interactions, with cascades occurring where the community is structured such

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that there is a decreasing turnover rate with trophic level. To enable comparison across habitats we suggest that differences in predators need to be taken into account, and that any measure of turnover rate of primary producers is relative to that of predators.

Turnover rate The turnover rate of primary producers has important consequences for the rest of the community, as it influences the potential rate of supply of energy (biomass) to the upper trophic levels. The biomass contained within upper trophic levels is governed by the rates of supply and loss (from the system and to further trophic levels) of production; if the supply is low (relative to the biomass of primary producers) biomass cannot be sustained at more than the trophic level below, a characteristic of the trophic cascade. In other words, if primary producers turn over at a slow rate, then a large amount of biomass will be retained within the lowest trophic level. If this is repeated at every trophic level the trophic pyramid will tend towards a triangle. If the turnover of primary producers is fast, there is the potential for herbivores to be maintained at a higher biomass than primary producers, and a square or inverted triangle trophic pyramid is possible. However, it has been suggested that such a structure is unstable (Raffaelli, 2002), with the upper trophic levels prone to oscillation unless supported by external subsidies or via two routes, one slow and one fast with top predators receiving 20–60% of their energy from either pathway rather than 100% from a single pathway (Moore et al., 2004). To investigate whether the turnover rate of primary producers influences the shape of the trophic pyramid and the potential for a trophic cascade we constructed trophic pyramids for a number of shallow lakes spanning a gradient of top-down effects of fish (Box 7.3). There was a significant relationship between the shape of the trophic pyramid and the ratio of slow- to fast-turnover primary producers. The distribution of biomass among trophic levels became more triangular with an increasing proportion of slow-turnover primary producers (macrophytes and macroalgae). A similar shift in biomass distribution has been seen in cave communities with differences in the turnover among the basal species (Moore, Deruiter & Hunt, 1993); bacteria (small, fast-turnover) are associated with a square trophic pyramid, fungi (large, slow-turnover) with a triangular pattern. As a note of caution, however, it might be that long time scales are required to detect change in communities with long-lived primary producers, far in excess of those typical of experimental methods (but see Sinclair et al., 2000), and that our opinion is constrained by the practicalities of experimental design. Few experiments are undertaken at a temporal scale that incorporates multiple generations of predators (though some biomanipulation experiments have

BODY SIZE AND TROPHIC CASCADES IN LAKES

Box 7.3 Trophic pyramids and turnover rate in primary producers A cascade appears to explain the loss of aquatic plants in shallow lakes. Across a range of eutrophic to hypertrophic lakes, increased fish biomass leads to a reduction in the density of grazing invertebrates on the surfaces of submerged plants, an increase in periphyton on the plant surfaces and, due to competition with periphyton, a reduction in plant biomass (Jones & Sayer, 2003). Data from 17 shallow lakes across this gradient were used to determine the distribution of biomass by trophic height. All lakes are of similar depth (circa 1 m). Total biomass per m2 was measured, calculated from size measurements, or estimated from mean annual chlorophyll concentrations (Jones & Sayer 2003; Beresford, Davidson, Jones, Sayer & Perrow, unpublished data). Species were allocated to discrete trophic levels according to known or published descriptions of diet, such that 1 ¼ primary producers, 2 ¼ herbivorous/detritivorous invertebrates, 3 ¼ predatory invertebrates, 4 ¼ invertivorous fish, 5 ¼ piscivorous fish (both invertivorous and piscivorous fish feed omnivorously in these systems (Jones & Waldron, 2003) but were allocated to higher trophic levels than predatory invertebrates following Jonsson et al. (2005). Inclusion of predatory invertebrates in the same trophic level as fish had no significant effect on the analysis). Primary producers were classified according to slow or fast turnover of biomass (macrophytes and macroalgae versus microalgae (periphyton and phytoplankton)) and the proportion of the biomass of these two groups determined. By ranking the lakes by the proportion of slow to fast turnover of primary producers it is possible to see a change in the trophic pyramid across this gradient, such that relatively more biomass appears to be present within the upper trophic levels where the turnover of primary producers is high (Fig. 7.4). A triangular distribution of biomass within the trophic pyramid is indicative of the presence of long loops with weak links, inferring stability (Neutel et al., 2002), and a square or inverted pyramid of biomass is indicative of a trophic cascade. The slope of the side of the biomass pyramid has been suggested as a possible indication of the stability of the system (Raffaelli, 2002). The slope of biomass within the trophic pyramid (determined by regression) indicates that this change in food-web structure with the rate of turnover of primary producer biomass is significant (Fig. 7.5), suggesting that the occurrence of a trophic cascade is related to high biomass turnover in primary producers. In such circumstances there is considerable passage of organic matter through the web, to the upper trophic levels where it becomes bound in relatively long-lived individuals. In the lakes with slow turnover of primary producers the biomass is bound at the bottom of the web

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5 4 3 2 1 0 0

1

2

30

1

2

3 0

1

2

30

1

2

3 0

1

2

3

2 1

Trophic level

5 4 3

0 0

1

2

30

1

2

3 0

1

2

30

1

2

3 0

1

2

3

Log10 Biomass (g m–2)

Figure 7.4 Trophic pyramids from the five lakes with the fastest (upper) and slowest (lower) turnover of primary producers (estimated as the proportion of the biomass that was slow relative to fast turnover primary producers) across a gradient of increasing intensity of top-down effects of fish (fish–invertebrates–periphyton–plants; Jones & Sayer, 2003).

Square–Inverted

0.2 

0.1

 

0 

–0.1





–0.2

 



  



Triangular

Slope of Trophic Pyramid

130



–0.3



–0.4 

–0.5 0

0.2

0.4

Phytoplankton

0.6

0.8

1 Macrophytes

Proportion of Biomass of Slow to Fast Turnover Primary Producers

1.2

Figure 7.5 Relationship between slope of the trophic pyramids in 17 lakes across a gradient of increasing intensity of top-down effects of fish and the proportion of biomass of slow to fast turnover primary producers. y ¼  0.5104x þ 0.196, R2 ¼ 0.387, p ¼ 0.004.

BODY SIZE AND TROPHIC CASCADES IN LAKES

in large body-sized primary producers, to which the consumers have little access, the passage of organic matter through the web is relatively small and a triangular trophic pyramid produced. Furthermore, the presence of large body-sized primary producers adds structural complexity to the habitat, which results in increased species richness and reduced interaction strength.

lasted for more than ten years). It is unclear whether experiments of the type ‘a wolf in the sheep field and the grass grows longer’ tell us anything about community assembly other than that wolves eat sheep.

Complexity Although habitat architecture is likely to influence species interactions, its effects are confounded by species richness. Architecturally complex environments offer a wider variety of niches for species to exploit (Jeffries, 1993). Species-poor communities present few opportunities for prey specialization and an increased likelihood of strong interactions between predators and prey, with both of these conditions thought to favour trophic cascades (Polis & Strong, 1996). The physical complexity of a habitat also affects how the organisms within it interact, particularly by providing refugia. This, coupled with a wider array of prey, increases the number of pathways through the web, increasing compartmentalization and imparting stability to the system (Neutel et al., 2002). However, many types of spatial structure do not provide complete refugia for prey but merely restrict movement, thereby reducing the encounter rate. Models indicate that encounter rate is a function of the fractal dimension of the environment, with movement and predation being constrained in more complex environments (Johnson, Hatfield & Milne, 1995; Cuddington & Yodzis, 2002). Due to reduced encounter rate, the foraging success of predatory insects (Heck & Thoman, 1981; Grevstad & Klepetka, 1992) and fish (Crowder & Cooper, 1982; Winfield, 1986; Diehl, 1988; Nelson & Bensdorff, 1990) depends upon the structural complexity of the environment (e.g. plant density). In lakes, zooplankton (Timms & Moss, 1984) and fish (Persson & Eklo¨v, 1995) use the complex structure of plant stands as refugia from predators, even though these refugia do not absolutely exclude predators, presumably because encounter rate and predation risk is reduced (Nelson & Bensdorff, 1990). The behaviour of both predators and prey may change as a consequence of structural complexity, such that foraging, and hence encounter and predation rates, are affected (Romare et al., 2003). In oyster beds, even though complexity both reduces predation on mud crabs and enhances their activity, the presence of toadfish affects their behaviour more, such that a cascade is still apparent in the presence of complexity (Grabowski, 2004). The cascade described in New

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Zealand streams invaded by trout is a consequence of the behaviour of the invertebrate prey, which seek refuge under stones and release benthic algae from grazing pressure (McIntosh & Townsend, 1996). Structural complexity also affects the extent to which predators feed omnivorously (Diehl, 1992), and omnivory has potentially a stabilizing influence on species’ dynamics (Polis & Strong, 1996). The wider array of potential prey in complex habitats enables species to undergo ontogenetic shifts in their diet (Diehl & Kornijo´w, 1998; Svanba¨ck & Eklo¨v, 2002) and introduces life-history omnivory into the web (Persson, 1999). Even within a single life stage, the diversity of prey, coupled with an increased proximity before a prey item is encountered and the reduced apparent density (encounter rate), will result in an increased probability that non-preferred prey are taken, a wider diet width and an increased likelihood of omnivory. Fish that feed in structurally complex vegetated lakes are frequently generalist and omnivorous (Diehl, 1992; Diehl & Kornijo´w, 1998; Jones & Waldron, 2003; Okun & Mehner, 2005). However, the extent to which habitat complexity, food-web complexity and biomass turnover interplay with each other and with other factors is as yet unresolved. Habitats with a high proportion of primary producers with large body size and a slow rate of turnover are physically the most complex, the most species rich, and have the most complex food webs (Box 7.3). Whilst separating the influence of these effects on cascade dynamics will require careful experimentation, this area is ripe for investigation and liable to lead to greater insight into the mechanisms that cause trophic cascades.

Alternative equilibria Anybody working in the field of shallow-lake ecology cannot ignore two hypotheses, namely trophic cascades and alternative equilibria (the presence of two alternative community structures in lakes dominated by either phytoplankton or macrophytes; Scheffer et al., 1993). These are intrinsically linked. Alternative equilibria are the manifestation of the presence or absence of a trophic cascade (Pace et al., 1999) and are characterized by many of the features we have discussed so far. In shallow lakes the primary producers can be of small or large body size, with corresponding fast or slow turnover (phytoplankton or macrophytes). As a consequence of their large body size, macrophytes achieve a grazing refugium and, although consumed by numerous species, do not suffer losses at the same rate as phytoplankton (Lodge et al., 1998). Macrophyte dominated lakes typically have a large standing crop of primary producers (Liboriussen & Jeppesen, 2003), and the majority of the production passes through a detrital stage before passing to primary consumers (Carpenter & Lodge, 1986). A grazing refugium is also possible for phytoplankton, but is usually only achieved when zooplankton grazing is low to moderate (Jeppesen et al., 1997, Hansson et al., 1998). Due to the presence of large-bodied

BODY SIZE AND TROPHIC CASCADES IN LAKES

Table 7.2 Habitats where alternative equilibria have been suggested and the dominant primary producers characteristic of the two states. The primary producers typical of the two states are either rapid turnover, relatively small body size, low standing stock (State 1) or slow turnover, relatively large body size, high standing stock (State 2). Habitat

State 1

State 2

Lakes Coral reefs Rocky shores Woodlands Burnt heathland Deserts

Phytoplankton Microalgae Microalgae Grass Heath Ephemeral plants

Macrophytes Fleshy brown algae Fucoid algae Woodland Woodland Perennial vegetation

macrophytes, the plant-dominated state is more structurally complex than the phytoplankton-dominated state and has greater species richness (Declerck et al., 2005), with both these factors feeding back to produce a complex food web with weak links and frequent omnivory (Diehl, 1992; Jones & Waldron, 2003). Phytoplankton-dominated lakes tend to be characterized by simple, well-structured food webs, with strong interactions between predators and prey and their populations closely tracking one another (Townsend, 1988). The shift between these two states involves considerable change in community structure and biomass of primary producers, a characteristic that is taken as the definition of a community trophic cascade (Polis et al., 2000). A similar pattern occurs in many of the communities where well-described alternative equilibria are found (Table 7.2). Primary producers can be either small or large relative to consumers, with energy passing along a fast or a slow cycle, respectively. Where primary producers have a large body size relative to consumers the community has a complex, stable food web, in contrast to the simple, linear structure of the cascade food web where the primary producers are small (relative to consumers). In each case there are two alternative groups of primary producers that exhibit intense size-based competition, with one group having access to a sized-based grazing refugium. Whilst these patterns are of relevance in understanding the occurrence of alternative equilibria, they should also be used to guide future search for cascades. We suggest that any such directed search will prove fruitful in any habitat, terrestrial or aquatic.

Conclusions It appears that the pattern of body sizes of the organisms in the community is related to the occurrence of a trophic cascade. However, it is not body size per se,

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but the rate of turnover of primary producer biomass that influences their occurrence. Body size plays various roles which can be summarized thus: (i)

A large size disparity between predators and prey leads to strong interaction strengths and less discrimination between prey types. (ii) The trophic pyramid assumes a square or inverted triangle shape, associated with a trophic cascade, where the turnover of primary producer biomass is high. High-turnover primary producers typically have small body size, but the opposite is not true. (iii) Large body size of primary producers leads to increased complexity of habitat architecture, which in turn stabilizes the food web. (iv) Facilitation can be of importance for trophic cascades and may affect body size – trophic cascade relationships. The often repeated dearth of cascades in terrestrial habitats, if true, may be a consequence of a relatively large size and slow turnover of primary producers in terrestrial environments. However, it is more likely to be a consequence of less effort to demonstrate their presence. A directed search for cascades in communities where there is a large predator:prey body size and rapid turnover of primary-producer biomass is likely to be fruitful. Nevertheless, we suggest that effort is put into linking body size, biomass turnover, productivity and trophic cascades, as by bringing these together we may be able to take our understanding of this subject forward into new and exciting areas.

Acknowledgements We thank the British Ecological Society and Freshwater Biological Association for their support, and the other contributors for stimulating discussions. EJ was supported by Euro-limpacs (GOCE-CT-2003-505540), the Danish Natural Science Research Council (CONWOY project), CLEAR and NORLAKE. JIJ was supported by a NERC Fellowship, GT5/98/21/CB, and by NERC CEH. We are also indebted to the Greenland team at NERI and the Freshwater Biological Laboratory, Hillerød and to those who allowed us to use their data, particularly the Danish Counties, Angela Beresford, Tom Davidson, Carl Sayer and Martin Perrow.

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CHAPTER EIGHT

Body size and scale invariance: multifractals in invertebrate communities PETER E . SCHMID Queen Mary, University of London University of Vienna

JENNY M . SCHMID - ARAYA Queen Mary, University of London

Introduction As ecologists seek conceptual syntheses to understand the mechanistic and functional processes that underlie empirical community patterns in different ecosystems, they are developing concepts that depict complexity on a number of universal themes. General patterns in the statistical distributions of species and individuals within and across ecosystems provide information about the organizing principles underlying ecosystem structure. Interrelations between species richness, population density, body-size and distribution ranges are of central concern in ecology and have been widely debated (Brown, 1995; Brown, Allen & Gillooly, this volume). To represent the structure of ecosystems adequately, species composition and population size are the most appropriate attributes containing information that is closely correlated with the organism’s size. Attributes of body size may affect many ecological characteristics, such as resource use and allocation in communities, reflecting their complex internal structure. Feeding patterns that result in resource partitioning among species of a benthic species assemblage demonstrate strong body-size dependence (Schmid & Schmid-Araya, 1997; Woodward & Warren, this volume). Information on species population and body-size distribution (BSD) of communities is frequently given for the larger or is toxonomically not well resolved, organisms inhabiting an ecosystem, therefore resulting in veiled, often highly scattered and incomplete, distributions. In contrast, the size distribution of well-resolved species communities may reflect the different evolutionary traits underlying diverse scaling domains. Therefore, more realistic expectations for real-world species and abundance distributions are obtained using scale-dependent definitions of individual species’ spatial and/or size structure within communities. Empirical evidence has been mounting that a number of dynamic systems in disciplines as diverse as physics, economics and ecology have certain Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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quantitative features that are intriguingly similar. These properties can be conveniently grouped under the heading of scale invariance. By scale invariance is meant a hierarchical organization that often results in power-law behaviour over a wide range of values of some control parameters such as species size (Stanley et al., 2000). These empirical scaling relations often exhibit power-law behaviour and are essential to describe and understand the distribution of species populations and, consequently, the emergent properties of communities. Particularly, non-integer power laws have become an intensively studied area covering all fields of the biological sciences with large overlap into the field of statistical physics. The latent causes of power-law behaviour often relate to fractal structures or the recursive dynamics of systems (Gisiger, 2001). The recognition of fractal properties as a framework from which non-integer power laws derive, and their implications for other ecological characteristics, have intensified in ecology (Margalef, 1996, 1997; Kunin, 1998; Harte, Kinzig & Green, 1999; Schmid, 2000). If the same scaling law applies to an object or measure at any arbitrary positions, we can define a homogeneous fractal (statistically self-similar), while different scaling laws found at different positions of the object yield inhomogeneous, statistically self-affine fractals (Schmid, 2000). Fractal geometry serves as a mathematical framework that can quantify the relationships between the many physical and biological phenomena in ecological systems, including patterns of habitat, behavioural patterns of individuals and size-frequency spectra (Schmid, 2000; Schmid, Tokeshi & Schmid-Araya, 2002). More intensively studied ecological patterns, which can display scale-invariance and fractal properties, include species-abundance distributions (SADs) and species-area relationships (SARs). SADs of taxonomic assemblages have been fitted to statistical, niche-assembly and dispersal-assembly models (e.g. Tokeshi, 1999; Hubbell, 2001), while SARs have been described by many statistical models, with no consensus whether individual mechanisms contribute to the generation of different types of SARs observed in nature (e.g. Rosenzweig, 1995; Lennon, Kunin & Hartley, 2002). The shapes of species-area curves have been discussed extensively and are most commonly fitted to either a power law or a double-logarithmic transformed data set (Tokeshi, 1999). The power function is given as S ¼ cAz, where S is the species richness within area A, c is a constant dependent on spatial scale and z is the scale-free regression exponent. The loglog transformation that follows a power-law relationship may imply statistical self-similarity, and fractal models have been proposed to predict SARs for plants at the level of assemblages (Harte et al.,1999) and species (Lennon et al., 2002). However, single fractal dimensions (monofractals) for size-related distributions or SARs do not provide comprehensive quantitative information on the species and the inherent population-size structure of communities (Schmid, Tokeshi & Schmid-Araya, 2002; Borda-de-A´gua, Hubbell & McAllister, 2002).

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The fractal dimension calculated from a power-law fit of SAR data and the fractal dimension(s) of species that make up that distribution are different quantities. Species and their population-density distributions are measures that are allocated over a size range (e.g. body size, area) that are in turn embedded in a surface or volume of habitat. This habitat structure may have a spatial distribution, which itself displays fractal characteristics (Schmid, 2000; Schmid et al., 2002), potentially influencing the spatial distribution of populations in a scaleinvariant manner. The particle-size distribution (PSD) is one of the fundamental properties characterizing benthic habitats. Most functions that fit the PSD are based on a power-law dependence of particle number or mass on particle diameter (Turcotte, 1986). Such power-law dependence has been interpreted as the result of a fractal distribution often characterized by several scaling domains (Bittelli, Campbell & Flury, 1999). However, because BSDs (body-size distributions), PSDs and SARs, are measures rather than geometric objects, the measure itself may display self-similarity. To understand this concept, we can envisage benthic invertebrates occurring in two similar-sized areas of a streambed with different species richness and different densities. We can then equally subdivide the areas and find that the number of species and their densities are again different. Consequently, this process reflects an ‘irregular pattern’. These subdivisions could be carried through to small interstitial pore sizes and more species and individuals will still be found in one site rather than another. This ‘scaling-down’ process reflects the distribution and patchiness both of benthic organisms and particles, and is an example of a measure that is irregular at all scales. When the irregularity is statistically the same at all scales, then the measure is a multifractal. This phenomenon was first described by Mandelbrot (1974) for turbulences, later elaborated as a mathematical tool in an ecological context by several studies. Empirical applications have been the spatial variability in bioactive marine sediments (Kropp et al., 1994), chemical soil properties (Kravchenko, Boast & Bulloc, 1999), soil PSDs (Posadas et al., 2001), river networks, stream order and water discharge (Rodriguez-Iturbe & Rinaldo, 2001), canopy structure (Drake & Weishampel, 2000), self-organization and species abundance in a tropical forest (Manrubia & Sole´, 1996; Borda-de-A´gua et al., 2002), zooplankton biomass distribution (Pascual, Ascioti & Caswell, 1995) and copepod behaviour (Schmitt & Seuront, 2001). Multifractals are then a refinement and a generalization of the fractal properties that arise naturally from statistically self-similar distributions. Multifractals describe a local singularity in behaviour of those measures or functions that display high irregularities. Many physical quantities exhibit a non-trivial scaling behaviour where multiplicative iterative random processes generate multifractal structures, while additive processes generally produce single fractals.

BODY SIZE AND SCALE INVARIANCE

Multifractal distributions are best suited for representing the multiplicative action of the various biotic and physical processes acting on, for instance, the parent particle material that results in a given distribution of particle sizes. Consequently, similarities in the irregularities of a measure over several scales give rise to a multifractal distribution of that measure (Feder, 1988; Schmid, 2000). The conditions leading to observed size distributions and SARs in nature could lead us to anticipate that these measures should generally display multifractal behaviour (Posadas et al., 2001; Schmid et al., 2002). This chapter is concerned with scale-related patterns within river ecosystems and it demonstrates that body-size scale invariance observed in benthic invertebrate communities and their habitat should conform to multifractal relationships. In addition, the body size of benthic invertebrates may relate to habitat size-structure and, therefore, species-abundances patterns, in turn, may be governed by habitat heterogeneity. Using empirical, quantitative data on benthic invertebrate species from three geographically separate stream systems, we illustrate the inappropriateness of the homogeneous power-law interpretations and we demonstrate that multifractal behaviour often governs species-rich communities. Data collection The data sets were drawn from three geographically separate stream ecosystems, the second-order streams Oberer Seebach (SB) in Austria and the Afon Mynach (MY) in North Wales and a first-order stream of the Nant Cwm Llwch (LL) catchment in South Wales, UK. Quantitative benthic samples (n ¼ 867) were collected to obtain data on invertebrates and interstitial habitat between 1991 and 2004. In each stream, stratified random sampling was conducted at variable time intervals, mainly bimonthly in SB and MY and seasonally in LL. Samples were collected within 100 m reaches with modified Hess samplers (mesh-size for LL: 20 mm and for SB and MY: 50 mm) to a sediment depth of 10 cm. The data sets for these stream communities included a total of 1040 species ranging from testate amoebae and benthic rotifers to insect larvae, including more than 106 measured individuals. Gut contents analyses of these species revealed that they represented mostly detritivores and to a lesser extent omnivores. In headwater streams, detritus, or particulate organic matter, contributes substantially to the total food consumed by individuals of all trophic groups (Schmid & SchmidAraya, 1997, 2002). The data were standardized to a common sample size of 1 m2, while data on larger areas were obtained by amalgamating randomly aggregated samples taken at different sites during the sampling period. To analyze relationships between the habitats and their organisms, the organic and inorganic particles from the interstitial streambed were collected simultaneously at each sample site in each stream. Because invertebrates use particles both as habitat and food

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often proportional to their body size (Schmid & Schmid-Araya, 1997, 2002), particles were analyzed within the size range of organisms at 5 mm increments using the Galai CIS100L laser analyzer with in situ video analysis (Ankersmid, 2002). Because the organic fraction (FPOM) constituted the majority of particles (>95%) in that size range, samples were softly stirred and sonicated in the liquid flow controller of the CIS for 10 s to break up possible flocs (aggregates) of particles before each measurement in the CIS100L. Power-law and scaling relationships Power-law scaling characterizes many patterns observed in ecology, ranging from individuals to the level of ecosystems (Margalef, 1996; Calder, 1996; Brown & West, 2000). Many fundamental allometric characteristics of organisms scale with body size as power laws (Peters, 1983), with exponents often being simple multiples of 1/4 (Brown et al., 2002; Brown, Allen & Gillooly, this volume). These power laws often hold for scales ranging over several orders of magnitude, sufficiently large to justify a unifying theoretical framework. Power laws are scale-invariant (Schmid, 2000; Marquet et al., 2005), where a change in scale of the independent variable l preserves the functional form of the original relationship. This can be demonstrated with the function: gðlÞ ¼ alb

(8:1)

by considering a scale transformation in l so that l! l, gðLÞ ¼ ðaLb Þlb

(8:2)

Therefore, even with a change in scale, the functional form of the original relationship with the scaling exponent b remains unchanged. Only the proportionality constant changes from a to ab allowing for changes of resolution by altering the value of . A scale-invariant (¼ scale-free) pattern denotes that a characteristic property will look the same no matter which scale is chosen (sensu Gisiger, 2001). Therefore, scale-free patterns arise where the same principles or processes are at work no matter what is the scale of analysis (Milne, 1998). Scaling relationships often emerge from non-experimental approaches emphasizing the existence of statistical patterns in the structure of assemblages or communities that seemingly reflect the operation of universal principles (Brown et al., 2004). A potentially universal rule for the scaling of energy metabolism across species could be based on the assumption that an optimal design of fractal-like structure and function operates across all species (West, Brown & Enquist, 1999; Brown et al., 2004). However, this view of a 3/4 scaling rule, has also been questioned by several authors (e.g. Dodds, Rothman & Weitz, 2001). One intriguing scaling relationship found in nature is the population density – body-mass relationship, with body mass (M) explaining often more than 50% of the variation in species density (N). The slope of the relationship often

BODY SIZE AND SCALE INVARIANCE

approximated to 3/4 within trophic groups, commonly using ordinary least squares model I regression (OLS). Since body mass scales with metabolic rate to the 0.75 power, the 0.75 exponent between N-M was taken as evidence that species abundance is limited by energetic requirements (e.g. Nee et al., 1991). This ‘energetic equivalence rule’ is expected in situations where all species use the same source of energy from a limited resource. Using model I regressions, this inverse proportionality with a 3/4 exponent was also evident between mean population density and mean body mass in two geographically separate stream communities and between different trophic groups of these invertebrate communities (Schmid, Tokeshi & Schmid-Araya, 2000). Although the scaling relationship with exponents close to 0.75 also holds seasonally for the same streams (Schmid et al., 2002), wide variations in regression slopes among different taxonomic assemblages makes it unlikely that these assemblages are governed by a single energetic rule (Schmid et al., 2000).

Density – body-mass scaling with sample area The area sampled has a distinct influence on a scaling relationship, as the species number and their densities tend to increase as a power function of the area (see Multifractal species–area relationships, below). Consequently, N-M relationships must change with area until the area sampled is large enough not to be dominated by populations with transient individuals. Scale invariance in space can be expected if the scaling exponents collapse into a single value at a specific sample area. To test this assumption, the N-M scaling relationships of the benthic invertebrate communities of the three streams (SB, LL and MY) were analyzed from a single sample scale (1 m2) to the scale of a whole river section (240 m2). By including and amalgamating samples taken at any sampling position or occasion, it was possible to obtain spatially independent samples incorporating invertebrate species over different developmental stages, bodysize and density ranges. Preliminary test results showed that the observed trend in the relationship between the regression slopes of the log density – log bodymass and area size stabilized after 1000 randomizations. Therefore, 104 random amalgamations of the observed data were conducted (Fig. 8.1) as an estimate for all possible >1095 sample combinations (e.g. j!/(j  i)!i!, where j is the possible number of samples of size i, and i ¼ 2, 3, 4, . . . , n m2). The insets of Fig. 8.1 show the linear regressions of log mean population density on log mean body-mass for each of the three stream communities over the total sampled area. In contrast to the communities of the SB and MY, the community of the LL departed significantly from a 3/4 assumption when considering OLS model I slopes (t ¼ 9.57; df ¼ 330; P < 0.001). However, using the bisector model II regression approach, which accounts for the error scatter in the data (Schmid et al., 2000) results in a slope bBIS ¼ 0.727(1 SE: 0.025) not significantly different from the 3/4 assumption (t ¼ 0.92; df ¼ 330; P ¼ 0.357).

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7 6 5 4 3 2 1 0 –1 –2 –5 –4 –3 –2 –1 0 1 2 3 4 5 log Body-mass (µg DM)

bOLS = –0.702 ± 0.071

LL

log Density (ind m–2)

0.4

log Density (ind m–2)

0.4 SB 0.2 0.0 –0.2 –0.4 –0.6 –0.8 –1.0 0.2 0.0 –0.2

6 5 4 3 2 1 0 –1 –2 –5 –4 –3 –2 –1 0 1 2 3 4 5 log Body-mass (µg DM)

–0.4 –0.6

bOLS = –0.496 ± 0.028

–0.8 0.4 MY 0.2 0.0 –0.2 –0.4 –0.6 –0.8 –1.0 0 50

log Density (ind m–2)

Slopes of log density – log body-mass relationships for different areas, bA – OLS

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6 5 4 3 2 1 0 –1 –2 –5 –4 –3 –2 –1 0 1 2 3 4 5 log Body-mass (µg DM)

bOLS = –0.733 ± 0.088

100

150

200

Area, A (m2)

250

300

350

Figure 8.1 Ordinary least-square slopes (bA  OLS) of the linear regressions between log density and log body-mass for increasing sampling areas of the benthic invertebrate communities of three streams (Seebach (SB), Llwch (LL) and Mynach (MY)). Curves are exponential decay functions with details given in Table 8.1. The insets show the linear regressions of log mean population density on log mean bodymass obtained for the total sampled area of the three streams. bOLS values are the slopes for these ordinary least-square model I regressions with 1 SE. Insets for the SB and MY are modified after Schmid et al., 2000.

When changing spatial scales (Fig. 8.1), the range of N-M slopes obtained was wider over smaller sampling areas (<20 m2) reflecting the small-scale patchiness of individuals and species in the stream communities. The slope values decreased exponentially with increasing area and an asymptote is reached at sampling areas > 200 m2 in the three streams (Fig. 8.1; Table 8.1). The fitted exponential decay function predicts well the scaling exponents of the N-M bOLS (Table 8.1; Fig. 8.1). Thus, the N-M scaling appears to be roughly constant across communities of different stream orders. However, a sufficiently large area has to be sampled in order to detect an invariant pattern of scaling exponents.

Density and biomass scaling The data based on all 867 samples from the three stream communities illustrate that density rapidly reaches an asymptote with increasing species richness, following a power function (Fig. 8.2). In contrast, total biomass or standing stock (g DW m2) remains roughly constant across sites of different number of species (Fig. 8.2). However, higher variability of biomass occurring in samples with a low number of species in the first-order LL (Fig. 8.1) may reflect early

BODY SIZE AND SCALE INVARIANCE

Table 8.1 Estimated predictions of the relationship between sampled area size (A) and the ordinary least-square slope (bA – OLS) of linear regressions of log population density on log body-mass based on the exponential decay function: bA – OLS ¼ a þ b e( A/c) for stream communities (Seebach (SB), Llwch (LL), Mynach (MY)). a, b, c are the regression coefficients; confidence limits (95%) are given in parentheses; r2 is the variance explained; n is the number of random amalgamations of the data (see details in text). ***P < 0.001. Streams

a

b

c

r2

n

SB

0.684 (0.685, 0.683) 0.496 (0.500, 0.493) 0.723 (0.724, 0.722)

0.197 (0.195, 0.198) 0.062 (0.059, 0.065) 0.363 (0.350, 0.356)

48.180 (47.098, 49.261) 78.348 (68.350, 88.346) 22.684 (22.313, 23.056)

0.850***

104

0.255***

104

0.890***

104

LL MY

109 108 107 106 105 104 103 102 101 100 10–1 10–2 10–3 10–4 10–5 10–6

109 108 107 106 105 104 103 Btot = 0.501 + 0.003Stot 102 101 100 10–1 10–2 SB 10–3 LL 10–4 MY 10–5 10–6 50 200 100 150 Total number of species,Stot 1.064

Ntot = 8.892 × 103 Stot

0

Total density, Ntot (ind m–2)

Total biomass, Btot (g DM m–2)

stages of species colonization within that system. This biomass invariance denotes that, in species-rich communities, a finer division of biomass and, therefore, resource partitioning must occur rather than an increase in community biomass. These results are similar to those obtained in tree-dominated communities, where biomass and energy use was constant across species of a single trophic level (Enquist & Niklas, 2001).

Figure 8.2 Total densities and biomass per 1 m2 as a function of the number of species per 1 m2 across stream communities (Seebach (SB), Llwch (LL) and Mynach (MY)). Regression of log-transformed density on log-transformed number of species gives r2 ¼ 0.254, F1,866 ¼ 294.91, P < 0.001. Regression of untransformed data for total biomass per 1 m2 against number of species gives r2 ¼ 0.015, F1,866 ¼ 13.53, P ¼ 0.001. Regression equations are given in Table 8.2.

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If an ecosystem is to maintain a constant biomass, energy degradation through respiration is balanced by the rate of energy supply by the system (Peters, 1983). This also implies in principle that variations in species composition are associated with concomitant variations in the degree of resource partitioning, which are usually constrained by the environment.

Linking scaling relationships to niche and dispersal-mediated species-abundance patterns Because total biomass is invariant across species communities and, thus, trophic groups, it is expected that species-abundance distributions (SADs) based on biomass should reflect a similarity of resource partitioning irrespective of trophic guild. The SAD describes the relative abundance in terms of biomass or density of species ranked within an assemblage and usually displays many rare and a few highly-abundant species. More than 25 different probability distributions have been suggested as fitting SADs best, ranging from statistical, niche- to dispersalassembly SAD models (e.g. Tokeshi, 1993; Hubbell, 2001). To explore which mechanisms may be responsible for observed biomass invariance in stream communities, the SADs of all species in the invertebrate community were fitted to niche- and dispersal-assembly models. Few niche-assembly models are based on ecological assumptions that allow the modelling of community-wide SAD patterns. Two of these models, the Sugihara Fraction (SF) and the Power Fraction (PF) model were fitted to the observed SADs, both on biomass and density, using the speciesoriented approach (sensu Tokeshi, 1993). For comparative purposes a dispersalassembly model, the zero-sum multinomial distribution (ZSM; Hubbell, 2001) was also fitted to the observed SADs. However, this model involves a different approach, because it is fitted to the total number of individuals in an assemblage. SF model: Sugihara (1980) assumed a sequential niche apportionment process governing species assemblages with niche division ratios k (0.5  k < 1) centred around 0.75:0.25 producing a triangular probability distribution. Here, the SF was fitted to the species community data, allowing for normally distributed division ratios with a mean of k. PF model: among random niche-apportionment models, the PF follows the concept that the resource volume is multidimensional and is sequentially and randomly divided. In the PF model, the probability (p) of selecting a subsequent resource partition is proportional to the resource use (x) of species following a power function as p ¼ xk (Tokeshi, 1996), where 1  k  þ1 and  is a proportionality constant common to all species in the community. PF extends over a range of other species-abundance curves including Tokeshi’s Random Fraction (k ¼ 0) and the MacArthur Fraction model (k ¼ 1). Because SADs are expected to shift from stages of incompletely filled resource space to even distributions, it is appropriate to use PF to assess the potential convergence of k-values among communities.

BODY SIZE AND SCALE INVARIANCE

ZSM-neutral model: in contrast to niche-assembly theory, the unified theory of biodiversity (UTB) predicts that species diversity and relative abundances can be explained by neutral drift of abundances of different species (Hubbell, 2001). Neutral or dispersal-assembly concepts neglect functional and ecological differences between individuals and species, implicitly assuming that they have identical probabilities of birth, death, dispersal and speciation (Hubbell, 2001). The compounded effects of dispersal limitation, speciation and the role of chance through time would influence the way species form patterns of SAD similar to those found in nature. The model assumes that SADs are dynamic and reflect the spatial diversity-equilibrium among ongoing processes of speciation, dispersal and extinction. The UTB predicts that SADs should generally follow the zero-sum multinomial distribution (ZSM). This model has three main parameters, the number of individuals in a community, JM, the fundamental biodiversity number, , and the dispersal probability, m. Hubbell’s  is a linear function of the area occupied by the assemblage and it controls the shape of SADs. The ZSM was implemented using a log-likelihood approach to loop over all possible values of  and m maximizing the fit of ZSM to the data (Hubbell, 2001; McGill, 2003; Etienne, 2005). To obtain a reasonable estimate of the ZSM, 500 samples were generated for each set of parameters. For each stream community 105 model communities were generated and the mean model SAD compared to the observed SADs. To test departures of the observed SADs from the model predictions, conventional goodness-of-fit statistics, such as the Kolmogorov-Smirnov (KS) test and the coefficient of variation were applied. In addition, another test was used, based on the probability of deviations from the model using the sum of deviations of those species lying outside the 95% confidence limit of the modelled community (PCL). The observed SADs of biomass and density data followed closely both sequential resource apportionment models (SF and PF) as shown by KS statistics and the coefficient of variation (Fig. 8.3; Table 8.2). However, the KS test and the coefficient of variation are not reliable enough to differentiate minor departures from the model predictions (Table 8.2). In contrast, using the deviation probability (PCL), it can be shown that, among these two models, the observed SADs fitted significantly to the predictions of the PF model with k  0.0–0.16 (PCL < 0.05: Table 8.2; Fig. 8.3), while the density distribution of the Afon Mynach (MY) departed from any model prediction. More species departed from the SF model, although it correlated well with the overall shape of the distribution (r2 values in Table 8.2). These results would suggest that stream communities are formed by resource apportionment processes where the probability of successive resource divisions tends to be slightly higher (k > 0) for species with higher abundances. In general, smaller species are more common (see inset Fig. 8.1) because they are more likely to subdivide food and habitat space available for other species.

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(a) 100 PFk = 0.125 10–1 10–2 10–3 10–4 10–5 10–6 10–7 SB 10–8 0 200 100 PFk = 0.086 10–1 10–2 10–3 10–4 10–5 10–6 10–7 LL 10–8 0 100 100 10–1

PFk = 0.159

10–2 10–3 10–4 10–5 10–6 10–7 MY 10–8 0

100

(b) PFk = 0.024

400 0

200

PFk = 0.108

200

300 0

100

JM = 4.43 × 107 10–1 θ = 40.76 10–2 m = 0.99 10–3

400

600

101

JM = 2.45 × 106 100 θ = 48.50 10–1 m = 0.99 –2

100 200 300 400 500

PFk = 0.052

0 200 100 Species rank

10–4 10–5 10–6 10–7 10–8 10–9 10–10

10 10–3 10–4 10–5 10–6 10–7 10–8 10–9

Relative abundance (density)

Relative abundance (biomass)

150

101

JM = 6.69 × 106 100 θ = 33.33 10–1 10–2 m = 1.00

200

300

10–3 10–4 10–5 10–6 10–7 10–8 10–9 10–10 400

Figure 8.3 Species-abundance distributions (SADs) shown with fits to the power-fraction (PF) model and to the zero-sum multinomial (ZSM) neutral model in the three streams Seebach (SB), Llwch (LL) and Mynach (MY). (a) Observed SADs based on biomass (symbols) with fitted PF model (line and dotted line) superimposed. (b) Observed SADs based on densities (symbols) with fitted PF and ZSM model (line and dashed lines) superimposed. PFk is the estimated k-value of the PF model;  and m are the fundamental biodiversity number and dispersal probability, respectively, and JM is the total number of individuals for the ZSM model. Dotted and dashed lines are the 95% confidence limits of the PF and ZSM model, respectively. Details of estimated parameter values are given in Table 8.2.

Among the streams, invertebrate species of the Oberer Seebach (SB) followed the maximum-likelihood predictions of the ZSM most closely, although the majority of smaller and larger species departed from the model (Fig. 8.3; Table 8.2, PCL ¼ 0.496). There is a tailing-off of rare, large-sized species, indicating that, in contrast to the ZSM prediction, there is dispersal limitation (m < 1) in the SB. The other two stream communities are not defined by this neutral assemblage concept, as evident by high departures from ZSM predictions (Fig. 8.3; Table 8.2,

BODY SIZE AND SCALE INVARIANCE

Table 8.2 Estimated parameters and goodness-of-fit statistics for the Sugihara Fraction (SF), Power Fraction (PF) model and the zero-sum multinomial distribution (ZSM) fitted to observed SADs of three invertebrate stream communities. Niche-assembly models are tested for observed SADs based on biomass (e.g. SFB) and density (e.g. SFD), while ZSM is tested on SADs of density. Param gives the estimated parameter values of the SAD models with the best fit to the observed SAD; q is the estimated fundamental biodiversity number and m is the dispersal probability of ZSM; Kolmogorov-Smirnov (KS) test statistics for the goodness-of-fit between observed and expected distributions. PKS gives the probability of departure of a model from observed SADs; r2 is the coefficient of variation between two distributions; PCL gives the probability of deviation from the model. *PCL  0.05. Further details in text. Seebach Model

Param

KS

PKS

r2

PCL

SFB SFD PFB PFD ZSM  m

0.663 0.772 0.125 0.024 – 40.756 0.990

0.042 0.069 0.027 0.031 0.154

0.816 0.234 0.997 0.981 <0.001

0.944 0.974 0.967 0.987 0.574

0.054 0.076 0.010* 0.036* 0.496

Llwch Model

Param

KS

PKS

r2

PCL

SFB SFD PFB PFD ZSM  m

0.717 0.678 0.086 0.108 – 48.500 0.990

0.051 0.042 0.054 0.039 0.280

0.778 0.930 0.715 0.961 <0.001

0.975 0.960 0.968 0.983 0.463

0.056 0.090 0.043* 0.006* 0.943

Model

Param

KS

PKS

r2

PCL

SFB SFD PFB PFD ZSM  m

0.670 0.760 0.159 0.052 – 33.333 0.999

0.073 0.092 0.054 0.092 0.338

0.492 0.218 0.846 0.218 <0.001

0.939 0.952 0.870 0.946 0.741

0.144 0.245 0.026* 0.153 0.900

Mynach

151

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P. E. SCHMID AND J. M. SCHMID-ARAYA

PCL  0.9). Predicted m-values close to 1 would imply that local communities are continuously reassembled by metacommunities similar to results shown for pelagic copepod assemblages (Hubbell, 2001). However, the highly insignificant fits of the ZSM to the observed stream community data demonstrate that the ZSM does not predict patterns in benthic systems dominated by environmental and speciesmediated resource heterogeneity. Differences between species in response to resource supply and discharge variations refutes the central assumption of Hubbell’s UTB that species are demographically similar (Schmid, SchmidAraya & Tokeshi, unpublished; Dornelas, Connolly & Hughes, 2006). Thus, at the community level aspects of resource apportionment and their interspecific variations play a much more prominent role in streams than the dispersalmediated processes predicted by the ZSM. It remains to be tested if and under what circumstances, particular taxonomic assemblages are more likely to follow neutral rather than niche-apportionment assumptions in benthic systems. Evidence to date supports the notion that species-rich and abundant assemblages, such as larval chironomids, assemble and reassemble stochastically in stream environments, significantly fitting to random niche-assortment and apportionment models (Tokeshi, 1993; Schmid, 1997; Fesl, 2002).

Fractal properties of size-structured communities Power-law scaling can help to reveal if fractal characteristics govern size- and scale-related distribution patterns. Fractals are particularly useful models to help to understand the multiscale nature of natural phenomena. The fractal dimension, D, is the basic parameter for describing structures that display self-similarity or scale invariance over a wide range of resolutions. Scale invariance can be the result of iterative diffusion processes of mass in the habitat, which repeat themselves at different scales of observation (Johnson, Tempelman & Patil, 1995). A method often applied to estimate self-similarity is the capacity dimension, introduced by Kolmogorov (1959). Thus, this fractal dimension (Dk) defines a partition of the fractal into equally sized lattice cells with edge size l as: log NðlÞ l!0 logð1=lÞ

Dk ¼ lim

(8:3)

where N(l) denotes the minimum number of cells required for covering the mathematical set. In nature, however, the limit cannot be obtained and, instead, a scaling region of a specified size range l must be used as: NðlÞ / clD

l!0

(8:4)

where N(l) are the number of cells of size l needed to enclose the object, c is a proportionality constant of d-dimensional length of l, and D is the HausdorffBesicovitch dimension. Random (natural) fractals define these real distributions, which have natural upper- and lower-scale limits, and separate them from infinite,

BODY SIZE AND SCALE INVARIANCE

purely mathematical fractals (Schmid, 2000). Scale-dependent analysis of this type has been applied to describe the species-size distribution in ecological communities by assuming proportionality between the physical scale and body size following: SðL > lÞ / lD

(8:5)

where S is the cumulative size distribution of species at scale l larger than a characteristic size , and D is the fragmentation dimension (Schmid et al., 2002). Thus, in a homogeneous system, the probability (p) of a measure varies with l as p(l) / lD. However, not all cells of scale l contain equal measures or mass and, consequently, averaging these subsets eliminates information that may elucidate the processes that generate community patterns. Species size-frequency distributions can be considered mathematically as measures that themselves may display statistical self-similarity. This self-similar pattern could arise through stochastic resource partitioning among different sized species together with an inherent resource space, which itself displays fractal characteristics. Consequently, finer resolutions of body-size patterns would reveal that each subinterval of size has different scaling exponents, which should not be confused with the concept of ‘multiscaling or mixed fractals’ in which the slope of a log-log plot changes abruptly at some particular scale (Schmid, 2000). If different subintervals of body-size and their corresponding measures are considered, a heterogeneous distribution of fractal exponents for such intervals would be expected. These heterogeneous features are present in many benthic distributions (Schmid, 2000), displaying a multifractal behaviour, and the probability within each ith subinterval, pi scales as: pi ðlÞ / li

(8:6)

where i is the Lipschitz-Ho¨lder exponent (see Eq. (8.12)), characterizing scaling in the ith subinterval (Feder, 1988). This multifractal type of a distribution can be analyzed directly when many data are available, and involves a spectrum of scaling indices, where the mass around different points is characterized by different single fractal dimensions. Various formalisms have been developed to describe the statistical properties of these measures in terms of their generalized dimensions Dq or the singularity spectrum f() (Mandelbrot, 1974, 1989; Hentschel & Procaccia, 1983; Halsey et al., 1986). A set of different lattices with cells or subintervals of equal length is required to implement the scaling analysis of a general size distribution  on an interval  ¼ [a, a þ L]. For the size spectra in each stream, a measure  is considered, and the interval determined by the extreme values of all body and particle sizes. A common choice is to consider dyadic scaling with successive partitions of  of size Ll ¼ L2 f, where L is the length of , l is the size scale and f ¼ 1, 2, 3, . . . , L. For every l a number of cells, N(l) ¼ 2f, are calculated and their measures i(l) are supplied from the size spectra.

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The probability of finding the ith species and particle at the scale l is defined as pi ¼ Ni / N, where N is the total number of species or particles and Ni is the ith species and particle at scale l. This probability, pi, is used to compute the partition function (Evertsz & Mandelbrot, 1992) as: q ðlÞ ¼

NðlÞ X

pqi  lðqÞ

(8:7)

i¼1

where (q) is the Re´nyi or mass exponent of q-moments, which is given as: ðqÞ ¼ lim

log q ðlÞ log l

(8:8)

Moments of order q act as a scanning tool scrutinizing the denser and sparser regions of the measure  (Chhabra & Jensen, 1989). When q > 0,  emphasizes regions in the distribution with higher proportions (concentrations) of the measure, whereas the opposite is true for q < 0. More generally, the q-moments are linked to the dynamics of the scale-related distributions and measure the amount of non-additivity in the system (Keylock, 2005). It follows that Re´nyi’s generalized dimension, Dq, which is based on the concept of generalized entropies (Re´nyi, 1955), is given as: Dq ðlÞ ¼

log q ðlÞ 1 ðqÞ lim ¼ 1  q l!1 log l ð1  qÞ

for q 6¼ 1

(8:9)

for q ¼ 1, 

NðlÞ P

pi log pi

i¼1

D1 ðlÞ ¼ lim

log l

l!1

¼

dðqÞ dq

(8:10)

and for q ¼ 0 D0 ðlÞ ¼ lim

l!1

log NðlÞ log l

(8:11)

where D0 is the capacity, D1 the entropy and D2 the correlation dimension. D0 is equivalent to the single fractal dimension of the measure, D1 is the entropy dimension and quantifies the degree of disorder present in the distribution, and D2 is mathematically linked to the correlation function, estimating the correlation of measures contained in intervals of size l. As q varies from 1 to þ1, the function Dq describes the spectrum of generalized fractal dimensions. One can theoretically encounter difficulties in establishing reliable estimates of Dq for q > 0, because positive q-moments diminish the terms with smaller pi and the limit converges very slowly (Schroeder, 1991). To overcome this potential drawback, the numerator in Eq. (8.9) was calculated for both l and 2l following the procedure outlined in Halsey et al. (1986).

BODY SIZE AND SCALE INVARIANCE

The Ho¨lder exponent or singularity strength (i) of the ith cell is defined as: i ¼

log i ðlÞ log l

(8:12)

A greater value of i is related to smaller pi values (concentrations of ) and vice versa. The function (q) is the Ho¨lder spectrum and is computed as a function of q-moments following Chhabra & Jensen (1989) as: NðlÞ P

ðqÞ ¼ lim

q ðlÞ log pi ðlÞ

i¼1

log l

l!0

where

NðlÞ P

(8:13)

q ðlÞ is the partition function (Halsey et al., 1986).

i¼1

For the purpose of a direct and mathematically precise evaluation of the singularity spectrum, f(), is defined as: NðlÞ P

f ððqÞÞ ¼ lim i¼1 l!0

q ðlÞ log q ðlÞ log l

(8:14)

and takes its maximum value for q ¼ 0, displaying a parabolic shape around this point. The Ho¨lder and singularity spectrum for each size-frequency distribution was calculated following Equations 8.12 to 8.14, respectively, for values 10  q  10 and 0.1 lag increments using least squares linear regressions. As a test criterion for multifractality, the linearity between the log-partition function (Eq. (8.7)) and the q-moments must be fulfilled for a range of q-moments. Besides visual inspection of these relationships (suggested by Evertsz & Mandelbrot, 1992), coefficients of determination (r2) of log-linear regression fits were obtained to characterize their scaling quality. Moments with r2 values  0.95 were considered to be significant, and, thus, attributing to multifractal patterns. In addition, the validity of the results was tested by verifying that the tangent of the graph f() versus  at  ¼ 1 is the bisector defined by df()/d ¼ q with the intersection point corresponding to f((1)) ¼ (1) ¼ D1 (Evertsz & Mandelbrot, 1992). In Fig. 8.4, the BSD is given over 300 size classes in increments of 100 mm (total size range  30 mm), while the BSD represented in the insets encompasses the same number of size classes over 10 mm increments (size range 3 mm). Thus, similar patterns of irregularity can be observed across different scales of resolution illustrating inherent self-similar size-frequency distributions. In the three streams, the mean number of species found per unit area declined with increasing body size with marked irregularities at both resolution scales particularly evident in the Cwm Llwch (LL) (Fig. 8.4). The BSD displayed a multifractal pattern in all communities ranging over a wide range of scales (all q-moments, r2 > 0.99; Fig. 8.5; Table 8.3). The wide range of Ho¨lder exponents covered by the f()-spectrum

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P. E. SCHMID AND J. M. SCHMID-ARAYA

n = 448

10

40

SB

8 6

30

4

20

2 0

10

0

1

2

3

107 106 105 104 103 102 101 100

Particles,

(λ) ml–1

50

25

107

10

n = 332

LL 106

8

20

6

15

4 2

10

0 0

5

1

2

3

105 104 103 102 101 100

Particles,

(λ) ml–1

0

0 25

n = 260

10

20

MY

8

107 106 105 104 103 102 101 100

6

15

4

10

2 0

5

0

1

2

Particles,

(λ) ml–1

Mean number of species, <S > (λ) m–2

156

3

0 0

5

10 15 20 Mean body-length, λ (mm)

25

30

Figure 8.4 Species- and particle-size frequency distribution in three stream ecosystems (Seebach (SB), Llwch (LL) and Mynach (MY)). Mean number of species per 1 m2 given over 300 sizeclasses in increments of 100 mm for the total size range 30 mm. The figure insets show the most abundant species over 300 size classes in increments of 10 mm for body sizes 3 mm. Mean particle density per 1 ml over 600 size classes in increments of 5 mm is shown superimposed in the inset as open circles (SB), triangles (LL) and squares (MY). n is the number of species in each stream community.

emphasizes the distinctness for multifractality of the BSDs in all streams (Fig. 8.6a). This result strongly contrasts to spectra, which would collapse into a narrow range of  or even into a single value for a strictly monofractal, homogeneous size distribution with a single scaling exponent. In the three streams, the multifractal spectra were characterized by similar entropy dimensions, (1) ¼ D1 with values close to 1, which predicts that the irregularities of the species-frequency distribution are even across body sizes (Figs. 8.4 & 8.6a; Table 8.3). The fraction of small-sized particles from interstitial sediments may serve as a potential food and habitat source for the benthic communities. The particle-size distribution displayed a decline in the mean number of particles with increasing particle size (inset Fig. 8.4). Scaling irregularities increased with particle size and were particularly pronounced in the SB (inset Fig. 8.4). The interstitial particle

BODY SIZE AND SCALE INVARIANCE

Table 8.3 Summary of parameters obtained by multifractal analysis of body- and particle-size distributions in the streams Seebach (SB), Llwch (LL) and Mynach (MY). a(1), a(0) and a(1) are the Lipschitz-Ho¨lder exponents with 1 SE for q ¼ 1, q ¼ 0 and q ¼ 1 respectively. r2 are the coefficients of variation of the linear regression of log partition function on log size for each a(q). Stream

SB LL MY

Body-size distribution ( 1)

r2

(0)

r2

(1)

r2

1.039  0.078 1.131  0.024 1.075  0.011

0.998 0.999 0.999

1.012  0.027 1.044  0.003 1.030  0.001

0.997 0.999 0.999

0.882  0.002 0.949  0.001 0.968  0.001

0.998 0.999 0.999

Stream

SB LL MY

Particle-size distribution 2

( 1)

r

1.389  0.096 1.244  0.047 1.289  0.033

0.995 0.996 0.999

40

(0)

r2

(1)

r2

1.138  0.004 1.087  0.002 1.098  0.002

0.999 0.999 0.999

0.792  0.003 0.842  0.003 0.767  0.002

0.996 0.996 0.997

SB

30 20 10 0

Log partition function, log µq(λ)

–10 –20 40 30

LL

q = –10

20 10 0 –10 –20

q = 10

40 MY

30 20 10 0 –10 –20

–1.0 –0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6 0.8 Log body-size, λ (mm)

Figure 8.5 Log partition function, log q(l), as a function of log body-size (l) for q-moments in the range between 10 and 10 at 0.5 lag increments for the streams SB, LL and MY. Linear regressions are superimposed for each q-moment (for all r2  0.95; P < 0.001). Significant linear relationships are similar for particle-size distributions not shown here.

157

Multifractal spectrum, f (α)

P. E. SCHMID AND J. M. SCHMID-ARAYA

(a)

(b)

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

SB LL MY

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Lipschitz-Hölder exponent, α

Figure 8.6 Multifractal spectra for the (a) species- and (b) particle-size distributions in the streams SB, LL and MY.

distribution displayed multifractal properties (over all 10  q  10; r2 > 0.99), with wider f()-spectra than those for the species-size distributions (Fig. 8.6b). The values of the entropy dimension, (1) ¼ D1, differed from 1 (Table 8.3), which implies that particle-size irregularities are unevenly distributed and concentrate in several subintervals, which was particularly evident for the SB and MY (Figs. 8.4 & 8.6b). The various scaling domains of interstitial particles are similar to those from different soil PSDs (Posadas et al., 2001). To test the similarity of the multifractal patterns between organisms and particles the Re´nyi exponents,  q, of the BSD were plotted against the  q of the PSD for each stream (Fig. 8.7). All stream ecosystems were characterized by two linear sections of the  q relationships, where the larger section defined trends for q < 0 and the shorter, steeper section of the curve defined trends for q > 0. The well-defined difference between the two curve sections strengthens the finding of multifractal patterns governing both BSD and PSDs in streams. Particularly striking is the similarity between BSD and PSDs scaling exponents in the first-order LL as shown by the closeness of the curve to a slope of unity (Fig. 8.7). Moreover, the relationship between the Re´nyi exponents of the BSD 10

Rényi exponent of body-size distribution, τq

158

5 0 –5 –10 –15

SB LL MY

–20 –20 –15 –10 –5 0 5 Rényi exponent of particle-size distribution, τq

Figure 8.7 The Re´nyi exponents, (q), of the body-size versus (q) of particle-size distribution in the streams SB, LL and MY. The dotted line gives a slope of unity.

BODY SIZE AND SCALE INVARIANCE

and PSD are similar between the Oberer Seebach (SB) and Afon Mynach (MY) for larger species and particle sizes. A distinct departure occurred between the two streams for smaller, more common species and particles. Further evidence for a close link between habitat- and body-size is given by recent experiments conducted in a Japanese mountain stream. This study revealed that body sizes of invertebrates tended to decline with decreasing crevice size, thus, strongly underlining the effect of fractal habitat complexity on body-size distribution (Taniguchi & Tokeshi, 2004; see also Townsend & Thompson, this volume).

Multifractal species-area relationships The species-area relationship (SAR) is one of the most widely studied patterns in community ecology and is often expressed as a single power-law curve. However, the SAR should not be characterized by a single curve that assigns one species richness value to each sampled area, as different samples of equal area differ in species number. Therefore, the SAR should be given as the relationship between area and its mean number of species, <S>. <S> was calculated for non-overlapping but equally shaped sampling areas taken over the sampling period. In order to estimate the mean number of species in an increasing area of size l ¼ k2 (where k ¼ 1, 2, 3, . . . ! l  maximum area), 106 Monte-Carlo randomizations without replications of the data matrix were conducted for each k-set. By randomly pooling samples of the observed data sets taken at arbitrary sampling positions and/or occasions, it was possible to obtain samples incorporating invertebrate species over different developmental stages, body-size ranges and densities. The species-area curves were obtained by averaging species richness of those randomly pooled sample sites for each area of size l. Some authors have suggested that the SAR following a power-law curve holds at all spatial scales and implies self-similarity in the distribution and abundance of species (e.g. Harte et al., 1999). A problem with this monofractal assumption is that scale invariance of SARs is not maintained over all spatial scales, but that there are different scaling domains underlying SARs over different spatial scales. Thus, irregularities in the species-abundance distribution may be statistically the same across areas resulting in a spectrum of fractal subsets. To test for different scaling domains underlying the SARs of the stream communities, the method of Re´nyi’s generalized dimension (Dq) was used for the speciesabundance data. This method follows Eqs. (8.7) to (8.11) outlined in Fractal properties of size-structured communities (see above), where in the current context, pi is defined as the relative abundance of species i in an area l. The relationships between mean species richness and sampled area is displayed as a power-law function for each of the three streams (Fig. 8.8; Table 8.4). The mean values for the parameter z (Table 8.4) differed significantly between stream communities (ANCOVA: F2,41 ¼ 54.82, P < 0.001) due to a higher z-value in the LL. No differences in slopes were found between the SB and MY

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Table 8.4 Regression parameters of the power-law relationship between the mean number of species and sampled areas of size l ¼ k2 in the streams Seebach (SB), Llwch (LL) and Mynach (MY). c gives the intercept, z the slope, r2 is the variance explained by the correlation of area with mean number of species per area, F is the value of the variance ratio test, df are the degrees of freedom, P-values are given for the F-test. Bootstrap confidence limits (95%) are given in parentheses for c and z values. Stream

c (95% CL)

z (95% CL)

r2

SB

134.50 (107.90, 205.12) 34.36 (28.64, 56.89) 92.05 (87.30, 96.16)

0.233 (0.140, 0.282) 0.448 (0.338, 0.498) 0.200 (0.190, 0.214)

0.903

LL MY

Mean number of species, <S > (λ)

160

F

df

P

139.46

1,15

<0.001

0.968

395.06

1,13

<0.001

0.992

1694.93

1,13

<0.001

1000

100

10

SB LL MY 1 1

10 100 Area, λ (m–2)

1000

Figure 8.8 Species-area relationship (SAR) of all benthic invertebrate species for three geographically separate stream ecosystem, the SB, LL and MY. The plot shows the linear regression of log mean number of species on log area, in l ¼ k2 intervals (see details in text). The regression equations are given in Table 8.4.

community (ANCOVA: F1,28 ¼ 2.49, P ¼ 0.126). A higher value of z for the SAR of the LL is attributed to a rapid increase in species richness with increasing area, with a ten-fold increase in species number over a spatial scale encompassing an order of magnitude (Fig. 8.8). In contrast, over the same spatial scale species richness increased four-fold in the SB but only two-fold in the MY. Moreover, a wider range of the scale-dependent coefficient c for the SB and LL invertebrate communities implies higher sample-to-sample variations in species richness at small spatial scales compared to the MY. Empirical observations suggested that the parameter z of the SAR is about 1/4 for many ecosystems (Rosenzweig, 1995). The z-values of the SAR differed from a 1/4 assumption for the LL (t ¼ 13.45; df ¼ 13, P < 0.001) and MY (t ¼ 9.46, df ¼ 13, P < 0.001) but were close to 1/4 for the SB community (t ¼ 0.49, df ¼ 15, P ¼ 0.628). The results indicate that z-values, and therefore SARs, do not display a common scale-invariant behaviour across stream systems.

BODY SIZE AND SCALE INVARIANCE

80 60 40 20 0

SB

log Partition function, log μ q(λ)

–4 –8 1

10

100

80 60 40 20 0

1000 LL

–4 –8 1

10

100

100 80 60 40 20 0

1000 MY

–4 –8 1

10 100 Area, λ (m2)

1000

Figure 8.9 Log partition function, log q (l), as a function of log area (l) for q-moments in the range between 10 and 10 at 0.5 lag increments given for the streams Seebach (SB), Llwch (LL) and Mynach (LL). For each stream the upper panel gives the partition function for q < 0 and the lower panel for q > 0. Linear regressions are superimposed for each q-moment (all q < 1 and q > 2 with r2 > 0.95; P < 0.001).

Rényi’s generalised dimension, Dq

All streams are characterized by a class of multifractal distributions, as the test criterion of linearity between the log-partition function and log area is fulfilled, particularly for all q-moment <2 (Fig. 8.9). The spectra of the generalized Re´nyi dimensions for q-moments are a monotonically decreasing function for all q-moments < 2 in each stream community (Fig. 8.10). With q-moments >2, Dq increases slightly in all ecosystems (Fig. 8.10) while the linearity criterion 1.0

SB LL MY

0.8 0.6 0.4 0.2 0.0 –10

–5

0

Moment, q

5

10

Figure 8.10 Re´nyi’s generalized dimensions (Dq) versus q-moments for the SAR of all benthic invertebrate species in three streams, the Seebach (SB), Llwch (LL) and Mynach (MY). Parameters are given in Table 8.5.

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Table 8.5 Summary of parameters obtained by multifractal analysis of species-abundance distributions across different areas in the streams Seebach (SB), Llwch (LL) and Mynach (MY). Dq are Re´nyi’s generalized dimensions given with 1SE; D0 is the capacity dimension, which equals to the slope of the species-area relationship; D1 is the entropy dimension; D2 is the correlation dimension; r2 are the coefficient of variation of the relationship between log partition function and log area for each Dq. Stream

SB LL MY

Species abundance across areas 2

D0

r

D1

r2

D2

r2

0.233  0.025 0.448  0.031 0.200  0.024

0.959 0.973 0.968

0.126  0.001 0.241  0.003 0.109  0.002

0.833 0.901 0.921

0.105  0.013 0.116  0.021 0.080  0.009

0.868 0.894 0.925

between the log-partition function and log area remains roughly fulfilled (Fig. 8.9; r2 > 0.95; P < 0.001). Excluding slight methodological differences, these results resemble those obtained for the species-abundance distribution of a tropical forest in Panama by Borda-de-A´gua et al. (2002), where Dq was not defined for q > 1. This more general class of multifractal distributions, for which not all q-moments exist, also indicates certain scale-related limitations in the application of Re´nyi’s generalized dimension for species-abundance distributions. Nevertheless, if a single fractal dimension does characterize the SAR then values of D0, D1 and D2 would be all equal. This equality would only be attained if the densities are equally represented among species. The capacity dimension, D0, is equivalent to the value for the single fractal dimension and to the exponent z of the SAR, which differs between the three streams (Table 8.5). Comparatively low values of the capacity dimensions indicate that irregularities in the abundance distribution are more concentrated in samples from smaller areas, emphasizing small-scale patchiness in streams. An entropy dimension, D1, with a value close to 1 signifies an evenly spread distribution of irregularities in species-abundance patterns across different scales. However, D1 values varied among the three stream communities, ranging from 0.11 in the MY, 0.13 in the SB, to 0.24 in the LL (Table 8.5). Therefore, higher values of D1 in the LL implied a greater evenness in the species-abundance distribution contrasting with the other stream communities. Similarly, the low values of the correlation dimension (D2) between communities illustrated uncorrelated irregularities of speciesabundance patterns within the same spatial scale range. Following Borda-de-A´gua et al. (2002), results of the generalized dimension strengthen the positive relationship between the density and spatial range of species. Considering the extremes of the distribution (e.g. q ! 10; q ! þ10), that respectively correspond to the rarer but larger and the abundant but

BODY SIZE AND SCALE INVARIANCE

smaller species, the density of the larger species declines faster with area than the abundance of smaller species. The reason for this observation is that rare species have a smaller geographic range than abundant, mostly small-sized, organisms (Schmid et al., 2002). Small aquatic invertebrates such as testate amoebae or benthic rotifers have a much wider geographic distribution than larger species, and free-living microbial eukaryotes are probably sufficiently abundant to have a global distribution (sensu Finlay, 2002; see also Finlay & Esteban, this volume).

Conclusions During the last few decades, evidence for scale invariance has appeared in several fields other than physics, and ecology is no exception. All these rather recent findings on power-law relationships and scaling in ecology, ranging from species-biomass invariance to body-size mediated patterns of community structure, are suggestive of an underlying scale-free pattern of complex systems. Biomass invariance across sites and stream systems may reflect the relative balance between resource supply and use, mediated and maintained through size-dependent resource partitioning processes of communities (Schmid et al., unpublished). The fit of species-abundance patterns to random resourceassembly, but not to neutral models, emphasizes the link between resource dependence, body size and species composition, irrespective of trophic group. This also stresses that differences between species in response to variations in resource supply and environmental heterogeneity question the core assumption of demographically identical species under Hubbell’s (2001) neutral concept. It is also evident that the dispersal probability of individuals plays a limited role in shaping patterns of observed benthic community structure at local scales. Moreover, food in the form of biofilm-enriched particles is not a limiting factor in most temperate stream ecosystems (Schmid et al., 2000), while habitat complexity has a profound influence on species composition and size structure (e.g. Jeffries, 1993; Schmid et al., 2002; Taniguchi & Tokeshi, 2004). In benthic stream systems, resource complexity is the product of physical and biological processes acting on the shape and size distribution of organic particles (Schmid et al., unpublished). The results presented here substantiate the view that the dynamics of the interstitial habitat and the various scaling domains of particles, which serve both as food and habitat, influence the size distribution of invertebrates and therefore, diversity and species composition in stream communities. Fractals are certainly the simplest method we have for quantifying a measure across a range of scales. As such, they provide the best null model against which to judge the real behaviour of natural patterns across different spatial scales, just as stochasticity is the null model against which to test spatial patterns at a single scale. Moreover, measures on aggregates such as (a) species-abundance distributions which influence SARs, (b) population densities underlying BSDs, or (c) particle densities underlying PSDs, give rise to a very different type of scaling

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known as multifractal. Thus, through the examination of multifractal measures, subtle differences in spatial and size structure can be explored. Fine-scale patterns embedded within coarser patterns apparently reflect ecological processes operating across a wide size spectrum and spatial scales, such as the resource utilization among invertebrate species in streams. The fact that multifractals can mirror compound phenomena may prove increasingly useful in the characterization, modelling and understanding of complex phenomena in ecology.

Acknowledgements This work has been supported by grants from NERC (NER/A/S/2001/00566), the Royal Society, and in parts from the Austrian Science Fund FWF: P15597-B03. We thank Dr Luı´s Borda-de-A´gua and an anonymous reviewer for valuable comments and suggestions on an early draft of this chapter.

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CHAPTER NINE

Body size and biogeography B . J . FINLAY Natural Environment Research Council, UK

G . F . ESTEBAN Natural Environment Research Council, UK

Introduction June 9th, having received early in the morning some rain-water in a dish . . . and exposed it to the air about the third story of my house . . . I did not think I should then perceive any living creatures therein; yet viewing it attentively, I did, with admiration, observe a thousand of them in one drop of water, which were the smallest sort that I had seen hitherto. (From a letter written in 1676 by Antonie van Leeuwenhoek, who had a passion for designing and building ‘magnifying glasses’.)

Leeuwenhoek was almost certainly the first person to see protozoa and other microfauna, and the first to record their huge population sizes. He could not explain how the microbes got into the ‘dish of rainwater’, and this rather disappointing level of understanding has not changed much in 300 years. The debate is rather polarized. On one hand are those who draw attention to the possibility that a significant proportion of free-living microbial species may be geographically restricted (examples include Mann & Droop, 1996; Foissner, 1999). On the other hand are those who recognize that this is at odds with the alternative hypothesis that neutral dispersal of small organisms is driven by extraordinarily large numbers of the individuals themselves. Although the probability of an individual microbe being transported over great distance is vanishingly small, a multitude of interacting processes and events, both common and rare (hurricanes, transport in wet fur and feathers, etc.), in combination with huge population sizes, are expected to drive large-scale dispersal across all spatial scales. A fitting analogy is the purchase of lottery tickets – buying many tickets increases the probability of winning. Similarly, if a speciespopulation is big enough, some individuals will, for purely statistical reasons, be transported over great distances. Over time, therefore, the dispersal of microbes may be essentially random, with the rate and scale of dispersal determined mainly by global population size (Finlay, Monaghan & Maberly, 2002). This view is supported by the discovery of ‘signatures’ of randomness (Fig. 9.1) in the spatial distribution of soil protozoan species, and by the observation that local and global abundances of a wide range Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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Figure 9.1 Random distribution of soil protozoa – the spatial distributions of rare and abundant species of testate amoebae in a grassland soil. Each line is the regression through six data points for each species. For clarity only the six most abundant species and the six rarest species are included. The bold line represents the equality of variance and mean. The rare species may simply have been transported randomly to the site but unable to produce a population in this particular soil habitat type. Further details are in Finlay et al. (2001).

Figure 9.2 The local and global abundances of individuals in soil protozoan species are significantly correlated (p < 0.001). This analysis is based on frequency of detection (a surrogate measure of abundance per species) of 95 ciliated protozoan species in 150 soil samples from a onehectare upland grassland in Scotland, and of the same species in 606 soil samples collected worldwide. Adapted from Finlay et al. (2001).

of microbial species are correlated (Fig. 9.2). Unlike most macroscopic organisms, whose dispersal and spatial distribution are determined by historical factors such as continental drift, or physical barriers such as mountain ranges, these probably have little influence on the geographical distribution of microbes. The microbial species that thrive in a particular habitat are probably the result of habitat properties alone and, with their capacity for ubiquitous dispersal, we can assume that they thrive wherever their preferred habitat type is realized on Earth.

BODY SIZE AND BIOGEOGRAPHY

Table 9.1 The two provinces of biodiversity – adapted from Finlay, Esteban and Fenchel (2004).

Absolute abundance Rates of dispersal Rates of allopatric speciation Rates of species extinction Relative number of endemics Global number of morphospecies Proportion of global species pool found locally Cryptic persistence of species Persistence of specific morphotypes over geological time Large-scale distribution determined by historical factors e.g. continental drift

Macro-organisms

Micro-organisms

Low Low High High High High Low Variable Low

High High Low Low Low/None Low High High High

High

Low

One of the more awkward and contentious problems for supporters of the ‘restricted distribution’ of microbial species has been the difficulty in establishing the existence of microbial ‘endemics’. This problem may be insurmountable. We can be confident in the knowledge that a particular large mammal species does not exist outside of its ‘endemic range’, but it is probably impossible to demonstrate that a microbial species does not exist elsewhere in the biosphere. Moreover, if the geographical ranges of microbial ‘endemics’ cannot be established, the term ‘endemic microbial species’ is probably meaningless. The fundamental characteristics of biodiversity at the microbial and macroscopic levels (Table 9.1) are markedly different – indeed they appear to represent two distinctly different ‘provinces’ of biodiversity. That most macroscopic organisms have biogeographies is well established, but the case for ubiquitous neutral dispersal and cosmopolitan distribution driven by population abundance in free-living organisms <1 mm has not yet received unanimous support.

The absolute abundance of microbial species-populations Various independent studies confirm that the abundance of individuals within morphospecies is inversely related to body size, and that microbial species therefore contain extremely large numbers of individuals (see for example Damuth 1981; Schmid, Tokeshi & Schmid-Araya, 2000; Finlay, 2002). This is readily confirmed with empirical evidence from any small ecosystem.

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Figure 9.3 Body size and areal abundance of free-living organisms, adapted from Finlay (2002), where more detailed information is available. In the microbial eukaryotes, each data point represents a species. The ‘mammals’ data are included only to establish the existence of a consistent pattern stretching over 12 orders of magnitude in abundance.

A one-hectare freshwater pond will support something in the region of 1018 bacteria, 1016 protists and 1011 small animals (Finlay & Maberly, 2000). Most of the organisms that Leeuwenhoek observed were protozoa, microalgae, and a diversity of mixotrophic protists that mostly lie in the size range 2–200 mm. Flagellates are very small (mostly 2–5 mm, and almost all <20 mm). Most amoebae are 5–50 mm, and most ciliates are 15–200 mm. Thus the protozoa, together with meiofauna such as rotifers, tardigrades and gastrotrichs (almost all <1 mm), have body sizes roughly 100 times bigger than the bacteria on which many of them feed. Compared with macroscopic animals, protozoa are extremely abundant: one gram of soil typically contains around 15 000 naked amoebae (Finlay et al., 2000), and every millilitre of fresh- or seawater on the planet supports 102 to 106 heterotrophic flagellates (Berninger, Finlay & Kuuppo-Leinikki, 1991). The absolute abundance of organisms in any aquatic habitat is typically astronomical (Finlay, 2002) – indeed the areal abundance of individuals is more than, say, ten orders of magnitude greater than that of average-sized mammal species (Fig. 9.3). At the global scale, the number of individuals of a typical protozoan species is virtually incalculable. One consequence of great abundance is that the probability of dispersal is significantly elevated. An individual protozoon may not survive transport through groundwaters, or attached to a duck’s foot, or carried across the Atlantic in a harmattan dust cloud. However, population sizes with astronomical dimensions must increase the probability that geographical barriers will be crossed in the course of time, leaving few if any absolute barriers to (free-living) microbial dispersal.

BODY SIZE AND BIOGEOGRAPHY

The ubiquitous dispersal of microbes initiates a train of patterns and phenomena, such as low rates of allopatric speciation, species extinction and endemism, as described below.

The cosmopolitan–biogeography transition Over the past 200 years or so, luminaries such as Darwin, Ehrenberg and Beijerinck formed an opinion based largely on anecdotal evidence that small species had cosmopolitan distribution and large species did not. Until quite recently, the body-size range of the transition zone remained unknown, although Lawton (1998) surmised that it might be in the region of 1 mm. The largest (and least abundant) macroscopic organisms may not be cosmopolitan, but the smallest (and most abundant), ranging from bacteria (Glo¨ckner et al., 2000; Hagstro¨m, Pinhassi & Zweifel, 2000; Massana, DeLong & Pedro´s-Alio´, 2000) to protists (Fenchel, Esteban & Finlay, 1997; Finlay & Clarke, 1999a, b; Darling et al., 2000; Lee & Patterson, 2000; Finlay et al., 2001; Fenchel & Finlay, 2004), tardigrades (Morgan & King, 1976), nematodes (Abebe & Coomans, 1995) and rotifers (Shiel & Green, 1996) do in many cases appear to be cosmopolitan. This suggests that the global biota can be divided into two broad groups – small species each consisting of a single, cosmopolitan metapopulation, and larger species composed of one or more regionally restricted metapopulations. There must be a crossover body-size range – a cosmopolitan-biogeography transition – but neither the steepness of this transition zone, nor the organism size range in which it occurs, was known. Finlay and Fenchel (2004) obtained extensive inventories of free-living eukaryote species from two contrasting aquatic habitats – a brackish, two-hectare, estuary-like habitat (Niva8 Bay, north of Copenhagen) that is permanently covered by the waters of the Øresund, and a eutrophic freshwater pond in the English Lake District, Priest Pot (Finlay & Maberly, 2000). The pond consists of one hectare of open water, surrounded by roughly one hectare of floating bog. By restricting taxonomic coverage to aquatic eukaryotes, it was possible to apply a single species concept (the morphospecies) to all biota. Finlay, Fenchel and their collaborators searched all accessible resources for geographic records worldwide of the species recorded in Priest Pot and Niva8 Bay, but the level of undersampling of meiofauna and protists created difficulties. Much published information is available for the northern hemisphere, but some taxonomic groups (e.g. marine ciliates, rotifers and gastrotrichs) have hardly been studied in the southern hemisphere. Almost all geographical records for southern hemisphere chrysomonads, heliozoans and heterotrophic flagellate, for example, can be attributed to the efforts of four or five workers in the last three decades. The authors obtained extensive inventories of naked amoebae in both Priest Pot and Niva8 Bay, but there has been only very limited sampling and species-level identification of naked amoebae outside of the Holarctic.

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Figure 9.4 The proportion of eukaryote species at Priest Pot that are cosmopolitan, arranged in logarithmic size classes. The principal taxa contributing to the upper shoulder of the curve are protozoa, gastrotrichs, rotifers, ostracods, nematodes and cladocerans. The main taxa in the lower part of the curve are triclads, molluscs, aquatic insects and leeches. Adapted from Finlay and Fenchel (2004).

Of the >2000 eukaryote taxa recorded, those identified to species level with sufficient associated geographical information were allocated to size classes, and the percentage of cosmopolitan species calculated for each size class. The curve that emerged for Priest Pot (Fig. 9.4) appeared fairly smooth, apart from the low value datapoint marking the smallest size class (arrow), which was almost certainly a consequence of undersampling worldwide. Most species in that size class were chrysomonads, and species-level identification requires electron microscopy and other specialized techniques. Nevertheless, 43 of the 50 species of the flagellated chrysomonad Paraphysomonas known worldwide were recorded from Priest Pot.

Testing the theory of cosmopolitan distribution Cryptic protist diversity exceeds the diversity of ‘active’ species, and the habitat selects Ubiquitous dispersal of free-living microbial eukaryotes implies that a large species richness will exist wherever life is possible. This will rarely be obvious, however, because most microbial species are usually encysted or in some other cryptic, inactive state, waiting for the arrival of conditions that support population growth. However, with patience and experimental manipulation (e.g. Finlay, Esteban & Fenchel, 1996a; Fenchel et al., 1997) it is usually possible to coax these cryptic species to excyst and grow so that they become detectable. The limited information available indicates that the ‘seedbank’ of cryptic species richness can be very diverse. In order to investigate this, we examined

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Figure 9.5 The ubiquitous ‘seedbank’. A small sample of sediment from a freshwater lake was ‘manipulated’ (see text and Finlay et al., 1996a; Fenchel et al., 1997) to produce a wide variety of niches for ciliate species – e.g. a range of microbial food sources, redox gradients, changes in light and temperature. About 20 ‘trophic’ species were identified at the beginning of the experiment, and this number increased to more than 130 species over a period of three months.

approximately one gram of superficial lake sediment, and recorded 20 active ciliate species at the time of sampling. In response to experimental treatments (e.g. addition of a variety of microbial food sources, establishment of redox gradients, and changes in light and temperature regimes) over a period of three months, the species total rose to 137, at which time it was still increasing (Fig. 9.5). More specific evidence that the ‘habitat selects’ is provided by the discovery of typical marine ciliate morphospecies living in inland evaporation salt pans in Central Spain at 300 km from the nearest coastal marine environment (Esteban & Finlay, 2004). These salt pans are fed from saline underground water originating in Triassic marine sediments. Water flows to the surface and into permanent evaporation pools, where the salt concentration varies from brackish to characteristic seawater, and up to hypersaline. Conversely, when samples from a hypersaline coastal lagoon in Southern Spain were progressively diluted with freshwater, a large number of typically freshwater protozoan species appeared (Esteban & Finlay, 2003). It is surprising that simple

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experiments such as these are not carried out more frequently, especially when the rewards (for example, discovering the true dimensions of microbial eukaryote diversity in a very small sample) are so easily gained. Dispersal of free-living protists is essentially random Any contender for a randomly distributed free-living species will have small body size, high absolute abundance, be easily dispersed and have minimal or nonexistent social or parasitic behaviour. Probably all soil protozoa fit the bill. They are adapted for life in soil, they form protective cysts (Finlay & Fenchel, 2001), there is evidence they spend much of their time as cysts, and the cysts remain viable for long periods of time (e.g. 49 years, Goodey, 1915). Thus, encysted soil protozoa could fit the criteria for random distribution. To test this hypothesis, we examined the possibility that the rarer testate amoebae species in a one-hectare grassland site in the southern uplands of Scotland could be randomly distributed (for a review see Esteban et al., 2006). We compared the spatial distributions of six rare species and six abundant species, obtaining a mean and variance for each species across the 25 plots in which the grassland site was divided, and repeating this on six sampling occasions (Finlay et al., 2001). We found that the rare and abundant species did appear to have different spatial distributions. Like most animal species the abundant testate species had aggregated distributions (Fig. 9.1), whereas the distributions of rare species were close to random (logvariance was closely proportional to the log-mean, the intercept was small, and we concluded that the distributions of these species were effectively random). Unlike the abundant species, with sustained population growth at this site, the rare species were probably transported randomly to the site but unable to initiate population growth in this particular habitat type. Cosmopolitan distribution implies the existence of similar species inventories in similar habitats irrespective of geographical distance This could be tested by investigating the ciliated protozoa living in a habitat that is separated from Northern Europe by geographical barriers and great distance – the sediment of a Holocene volcanic crater-lake in Australia (Finlay et al., 1999; Esteban et al., 2000). Of the 85 ciliate species recorded, all were already known from northern Europe by the year 1935 except one that was described in 1985. As the crater is only 2 km from the Southern Ocean, seaspray renders the water brackish (2–5%), and eight of the species recorded were typical of brackish waters. One of them (Tracheloraphis caudata) was a typical marine interstitial ciliate. This species is fragile and it does not form protective cysts – so, it was unclear how it may have reached the crater-lake sediment. The same can also be said for the anaerobic ciliate Plagiopyla frontata, a marine ciliate that contains unmistakable endosymbiotic methanogenic bacteria in both Northern Europe and Australia.

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Endemic species Endemic protist species – if they exist – would seriously challenge the theory of ubiquitous dispersal. Until recently, the large and distinctive ciliate Loxodes rex had been found only in freshwater in tropical Africa (Dragesco, 1970), where it was considered to be an example of an endemic ciliate. However, 30 years later, it was discovered thriving in a pond in Thailand (Esteban et al., 2001), where it joined an expanding collection of large ciliate species previously believed to be endemics – a status they all subsequently lost with additional sampling effort. Neobursaridium gigas was originally recorded from Argentina (Balech, 1941), and subsequently in Uganda (Nilsson, 1962). The very large (2–3 mm) Avelia martinicensis from the West Indies (Nouzare`de, 1975) was found in Brazil and, later, in Saudi Arabia. Condylostoma reichi from Israel (Wilbert & Kahan, 1981), was found in tropical Africa (Dragesco & Dragesco-Kerne´is, 1986). These few examples show that it is difficult to find protist species whose status as ‘endemics’ stands the test of time. Disproof of ubiquitous dispersal might have been provided by the protist community described by Gajewskaja (1933) from Lake Baikal – the world’s oldest and deepest lake. But the dozen or so new ‘forms’ and new species have all been found in other parts of the world. Loxodes rex would, because of its very large size (2 mm long), fragility, and lack of cyst formation, have been a prime candidate for an endemic ciliate, but it is not and it seems to thrive in tropical freshwater habitats on different continents (Esteban et al., 2001). In contrast, the unusual desmids of Tasmania (Tyler, 1996) indeed appear to be endemic. A possible explanation, however, is that unusual habitats (supporting unusual, even endemic, semi-aquatic plants) provide local microhabitats for particular, globally rare, micro-organisms. Thus, the unusual desmids may still disperse over a large area, but remain rare or undiscovered outside their place of discovery. It is generally agreed that the composition of diatom communities is dominated by cosmopolitan species with high dispersal ability (e.g. Soinen, Paavola & Muotka, 2004), but the relative importance of (a) physical barriers that may limit species dispersal, and (b) the extent to which diatoms have limited access to suitable habitat, was unknown. Recent analyses (Potapova & Charles, 2002) suggest that the availability of suitable habitat is the principal determinant of diatom community structure in rivers. Further, if the presence of a diatom in a habitat is limited primarily by the quality of the local environment rather than by physical barriers to dispersal, the diatom can potentially be found wherever the same habitat type occurs. In a quantitative approach using canonical correspondence analysis, Potapova and Charles (2002) showed that habitat factors consistently explained more variation than physical barriers. At the national (USA) scale, more than two-thirds of explicable variation in diatom species composition could be attributed to habitat factors, with less than one-third attributable to the role of physical barriers and other spatial factors.

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The list of the most frequently occurring diatom species consists solely of taxa with cosmopolitan distribution. This is presumably because common species are adapted to the most common habitat, which in the case of the United States and Europe is a nutrient-enriched, moderately alkaline river of the temperate climatic zone. Abundance of this habitat type in one continent increases the probability of dispersal to other parts of the world – with (a) the consequence that locally abundant diatom species tend to be globally abundant (Finlay et al., 2002), and (b), the corollary, that rare habitats such as oligotrophic waters, support much lower dispersal. The thesis that locally abundant or rare species tend to be globally abundant or rare is a recurring theme within this chapter and in macroecology more generally (Bell, 2001). See, for example, exactly the same phenomenon revealed within the soil protozoa (Fig. 9.2). Local:global species ratios Within any taxonomic group of small organisms, a large proportion of the global species richness is found in a local area, and the local:global species ratio for that group tends to be very high (Finlay & Clarke, 1999a, b; Hillebrand & Azovsky, 2001). For example, the percentage of the global species pool recorded from Priest Pot is >15% for ciliates, >50% for heliozoa and >80% for chrysomonads (all recorded species were actually recorded from roughly one tenth of a cubic centimetre of sediment). It follows that, if cosmopolitan distribution is the product of high absolute abundance, populations of the larger, non-cosmopolitan organisms will have low local:global ratios. This appears to be the case – the percentage of the global species pool of aquatic insects recorded in Priest Pot is <0.001, but with decreasing mean body size, local species richness represents an increasing fraction of global species richness, and it approaches 100% in the case of protozoan species with body sizes 0.004 mm. Finlay and Fenchel (2004) found that a systematic relationship does exist. Even in the case of two small aquatic ecosystems – one freshwater, the other marine – the local:global species ratio increases with decreasing organism size, incorporating the combined freshwater and marine species in a single relationship (Fig. 9.6). Undersampling The problem of undersampling persists because sampling regimes are often inadequate for detecting protists and other microfauna. This is especially so for the rarer species. The frequently cited argument of undersampling – ‘this species must be an endemic because it is morphologically so distinctive that if it existed elsewhere, it would have been recorded by now’ – might be convincing for large mammal species but, with respect to the protists, it evades the crucial question. It can confidently be demonstrated that a large mammal species does not exist outside of its endemic range, but how are we to demonstrate that a particular protist species does not exist elsewhere on the planet?

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Figure 9.6 Local species richness calculated as a ratio of the known or ‘best estimate’ global species richness for the same taxonomic group (adapted from Finlay & Fenchel, 2004). Moving from taxa with the largest to the smallest mean size, the symbols represent, (a) Priest Pot (filled symbols) – name of taxon followed in parenthesis by organism size (mm), and number of species in taxonomic group: fish (220, 5); Odonata (43, 15); leeches (20, 10); Chironomidae (14, 12); Mollusca (9.8, 71); Tricladida (6, 3); Ostracoda (0.804, 9); Nematoda (0.8, 71); Cladocera (0.73, 31); Rotifera (0.236, 22); gastrotrichs (0.164, 6); testate amoebae (0.097, 39); ciliates (0.076, 274); euglenids (0.048, 21); Synura (0.047, 6); Korotnevella (0.045, 6); naked amoebae (0.037, 64), Cochliopodium (0.03, 13); heliozoans (scale-bearing; 0.0271, 57); diatoms (0.0234, 93); Mallomonas (0.016, 24); heterotrophic flagellates (0.0158, 86), Spiniferomonas (0.006, 8); Paraphysomonas (0.005, 40); Cyathobodo (0.005, 7); Luffisphaera (0.004, 15). (b) Niva8 Bay (open symbols) – fish (165, 9); polychaetes (45, 9); Mollusca (30, 11); Crustacea (13, 44); Nematoda (1.3, 55); Turbellaria (1.2, 34); Ostracoda (0.557, 15); gastrotrichs (0.29, 4); ciliates (0.11, 201); dinoflagellates (0.0446, 103); Prasinophyta (0.0337, 25); naked amoebae (0.0242, 42); flagellates (0.0077, 75). The least squares regression through the combined data set is highly significant (p < 0.001).

The ‘problem’ is readily illustrated with the following simple example (Finlay & Fenchel, 2004). Consider the aforementioned proposition ‘if it did exist elsewhere, it would have been found already’. On the basis of results from previous sampling campaigns, we might predict that a certain ‘rare’ protist species lives in the oxygen-depleted hypolimnion of a productive freshwater pond. Priest Pot, in the UK, is such a pond. It has an area of one hectare, and a 1.75 m-deep hypolimnion holding roughly 6300 tonnes of water. Assume that the protist species we are looking for exists in the pond as a population of one million individuals. This figure may appear to have little to do with the idea of rarity, but each individual would, on average, be surrounded by 6.3 litres of water, giving it a volume

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fraction in the region 10 11 –10 13 if we consider, for example, the size range that includes most ciliate species. But ‘rarity’ is a relative term that is strongly influenced by organism size. A million perch in the same pond would never be considered ‘rare’, but a protist population of a million individuals would probably never be detected – even after years of sampling. For most of the relatively rare protist species (those that are orders of magnitude scarcer than the abundant species; Finlay, Esteban & Fenchel, 1998), undersampling is inevitable using typical sampling procedures. For that reason alone, ‘endemic’ species are not found elsewhere (see also Fenchel & Finlay, 2003). However (see above), a growing body of evidence indicates that selective-enrichment culture techniques can reveal the rare or cryptic diversity of protists (Fenchel et al., 1997), such as freshwater ciliates in hypersaline ponds (Esteban & Finlay, 2003), but the use of such methods is not common practice in the search for species that may have escaped from their ‘endemic’ ranges. Figure 9.7 illustrates this point. Species concepts Is the resolution of morphospecies poorer for smaller than for larger organisms? For protists with complex and varied morphologies, such as the ciliated protozoa, this is probably not the case. However, the species taxonomy of the smaller organisms depends on a proportionately higher optical resolution. The species systematics of chrysomonad flagellates, for example, is necessarily based on electron microscopy. If protists in general demonstrated the degree of morphological richness normally perceived in the naked amoebae, we would have a major problem with the morphospecies concept. But naked amoebae were not included in our analysis for the detection of the cosmopolitan-biogeography transition (see above), and the morphological richness that can be perceived in the protists we did use – including the ciliates, diatoms, foraminifera, chrysomonads, desmids, heliozoans, choanoflagellates and testate amoebae, as well as microbial metazoans such as the rotifers, gastrotrichs and microcrustaceans – indicates that microfauna, meiofauna and macrofauna may share a similar degree of morphological richness. Do ‘cryptic species’ or ‘sibling species’ (i.e. species that are morphologically similar but reproductively isolated) show any large-scale geographical patterns in their distribution. This has been investigated in some protists, especially the ciliates, and the evidence indicates that members of sibling species complexes have worldwide distribution. Mating experiments with isolates of nominal species from different continents have also shown that the isolates are interfertile (for discussion and references, see Finlay, 2002; Finlay et al., 1996b). Cosmopolitan genotypes Recent molecular studies of isolates of the small ciliate morphospecies Cyclidium glaucoma from across the world have disclosed multiple, distinct (rDNA)

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Figure 9.7 Intensive examination of grassland soils in Scotland (Finlay et al., 2000) revealed many rare species of ciliated protozoa. Amongst them was the ciliate shown here – Notohymena antarctica – which we found in re-wetted soil. This isolate from Scotland represents the first record of the species outside of the Antarctic continent, and in the northern hemisphere (Esteban et al., 2006). Protargol silver-impregnated specimen. Scale bar 20 mm.

genotypes, but there appears to be no evidence for any geographical pattern in their distribution (Finlay et al., unpublished), although particular genotypes do seem to be correlated with particular habitat types. Identical genotypes have been recovered from Great Salt Lake, and from hypersaline ponds in Spain. A single genotype has been isolated from brackish waters in Argentina, Japan, Morocco and Ukraine. A further single genotype was recorded from freshwater habitats in Guatemala and Ukraine, and another from France and Mongolia. These data are still being gathered, but they do suggest that protist genotypes can have cosmopolitan distribution, with no apparent biogeography. For asexual organisms with clonal evolution there is no theory-based species concept analogous to the biological species concept, so that in bacteria and the asexual microbial eukaryotes, a large degree of genotypic variation is expected

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within nominal species. We do not believe there is yet any convincing evidence for a biogeography of such variation in asexual protists. In the case of bacteria too, similar or identical genotypes occur worldwide (Glo¨ckner et al., 2000; Hagstro¨m et al., 2000, Massana et al., 2000). At the present time, the findings of identical rDNA genotypes in specific (and similar) habitat types worldwide is strong evidence supporting cosmopolitan distribution of microbial eukaryotes. ‘Biogeography’ of microbes? Some recent studies indicate that unicellular organisms may demonstrate ‘biogeography’. We do not subscribe to the view that microbial eukaryotes have ‘biogeography’ in the classical sense of, for example, geographically restricted tropical birds and mammals. It is unquestionably true that the distributions of microbes may show some structure and patterns (Green et al., 2004; HornerDevine et al., 2004; Noguez et al., 2005) that vary over time, and may demonstrate ‘at least some geographical differentiation’ (Green et al., 2004), but this is rather weak evidence for biogeography when compared with the stunning geographical patterns demonstrated by macroscopic organisms with real biogeography in established biogeographic regions. We resort to the key characteristic that free-living microbes thrive wherever their preferred habitat requirements are realized. Interestingly, Horner-Devine et al. (2004) provide evidence that this is so, using their example of bacteria. They discovered that habitats that are similar in environmental characteristics, are also similar in bacterial composition (i.e. even specific bacteria thrive wherever their habitat requirements are realized). On the other hand, if a microbial habitat becomes so degraded that it can no longer sustain a particular microbial community, the pattern of ‘biogeography’ may simply be ephemeral.

General validity Finlay and Fenchel (2004) revealed a cosmopolitan-biogeography transition in the region 1–10 mm for aquatic microbial eukaryotes, but is it in the right place? The data set used was the biggest available, but additional data, particularly for the 1–10 mm size range, would be especially useful. Unfortunately, the absence of any centralized, accessible source of data makes it extremely laborious to collect the information that would indicate the extent of geographical distribution of individual taxa. The two study sites used in the investigations by Finlay and Fenchel (2004) – Niva8 in Denmark and Priest Pot in the UK – are situated at roughly the same latitude in the northern hemisphere, and it is possible that the macrofauna would present a different picture if the field sites had been placed elsewhere, such as an area with a large number of endemic species. The existence of a large pool of undiscovered small tropical organisms cannot be ruled out, but the fact that Finlay and Fenchel (2004) found a substantial fraction of the global

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inventory of <1 mm species in two small water bodies, suggests that a similar picture would have emerged irrespective of where the investigation had been carried out. This interpretation is supported by the finding that protist species richness is generally the same at all latitudes (Hillebrand & Azovsky, 2001). This is not to say that all protist species thrive at all latitudes. The conspicuous pantropical ciliate Neobursaridium gigas grows only within a narrow temperature range of a few degrees on either side of 25 8C (Dragesco, 1968) but it does so in more that one geographical region (i.e. Africa and South-East Asia). The coldwater planktonic foraminiferan species (Darling et al., 2000), and the dinoflagellate Polarella glacialis (Montresor et al., 2003) have bi-polar distributions. The vast majority of free-living protists probably tolerate fairly broad ranges of environmental factors (e.g. salinity, temperature) and the few taxa that have been investigated experimentally (e.g. Paraphysomonas, Cyclidium) indicate that they also have great capacity for physiological adaptation within genetically determined limits that are much broader than those of macrofauna. It is perhaps not surprising then, that an intensive study of ciliate morphospecies in an Australian crater-lake (Esteban et al., 2000) should reveal a species list consisting entirely of species already known from northern Europe.

Neutral theory – local:global species ratios Finlay and Fenchel (2004) showed that the size dependence of local:global species ratios in small aquatic organisms appears to exist independently of the taxonomic identity of the organisms concerned. The common factor underlying these patterns is organism size, because size is inversely correlated with population size, which largely determines the probability of dispersal (Finlay, 2002). To some extent, a neutral model of community structure (Bell, 2001; Hubbell, 2001) is supported. While we do not necessarily endorse all of the assumptions in current neutral community theories (e.g. that the aquatic species we have catalogued are ecologically identical), our results support some of the predictions of neutral theory – in particular that high absolute abundance of microbes drives their large-scale random dispersal, resulting in high local species richness, correlated local and global abundances of individuals within species, and the creation of metapopulations with global-scale distribution (Fenchel, 1993; Finlay et al., 2001). Cosmopolitan distribution means that the global species richness of freeliving micro-organisms will be relatively small because a microbial species carries out the same function in places that are geographically distant from each other, which explains why there are apparently relatively few small species, as originally highlighted by May (1988). These patterns support the dominating role of dispersal and local extinction in moulding the composition of biotic communities. We also note that in contrast to results obtained from higher plant communities (Condit et al., 2002), the application of neutral models

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to organisms with microbial dimensions will probably not break down at the global scale (Finlay et al., 2001).

Concluding remarks It may be easier to detect the footprints of cosmopolitan distribution (e.g. identical genotypes across the global scale) than to establish the cause of an apparent biogeographic pattern. Take for example the relationship between species richness and latitude. Most latitudinal gradients have been described for macrofauna and plants, and species richness tends to be significantly higher at low latitudes. In the case of (cosmopolitan) microbial eukaryotes, however, we do not expect any discernible latitudinal gradient in species richness. Hillebrand and Azovsky (2001) pursued an approach that nearly succeeded. Following expectations, no correlation was found between latitude and species richness; but in the southern hemisphere, there was a significant negative correlation – probably an artefact based on some very low richness values from the Antarctic. This whole area of science seems to have acquired the status of a ‘hot topic’, and we can expect to see previously unforeseen developments in the near future. We close here with three points: (1)

(2)

(3)

Protists thrive wherever their preferred habitat requirements are met and there are no barriers to dispersal. This is a key point. It is usually relatively straightforward to observe microfaunal species thriving in their preferred habitat type, but with few exceptions, this is not so straightforward with bacteria. Nevertheless, Horner-Devine et al. (2004) discovered that sites sharing similar environmental characteristics were also similar in bacterial taxonomic composition – i.e. bacteria, like protists, thrive wherever their preferred habitat is realized. With decreasing mean body size, local species richness becomes an increasing fraction of global species richness. This helps to explain the relatively flat taxon richness-area relationships in microbial eukaryotes (e.g. Green et al., 2004), and the observation that local species richness (body sizes 0.004 mm) can be almost as great as global species richness. The undersampling problem. Historically, undersampling has been a major problem, and in the ‘molecular age’ the almost infinitely variable ribosomal DNA sequences contribute little if anything to ease the problem. Now that species-specific primers can be developed routinely, our experience is that the scale of sampling protists and microfauna could potentially increase dramatically.

Acknowledgements This work was carried out with financial assistance from the Natural Environment Research Council (Marine and Freshwater Microbial Biodiversity

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Thematic Programme). We are grateful to Professor Tom Fenchel (Copenhagen) for sharing ideas and contributing very useful suggestions.

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and Environmental Microbiology, 66, 5053–5065. Goodey, T. (1915). Notes on the remarkable retention of vitality by Protozoa from old stored soils. Annals of Applied Biology, 1, 395–399. Green, J. L., Holmes, A. J., Westoby, M. et al. (2004). Spatial scaling of microbial eukaryote diversity. Nature, 432, 747–750. Hagstro¨m, A8 ., Pinhassi, J. & Zweifel, U. L. (2000). Biogeographical diversity among marine bacterioplankton. Aquatic Microbial Ecology, 21, 231–244. Hillebrand, H. & Azovsky, A. I. (2001). Body size determines the strength of the latitudinal diversity gradient. Ecography, 24, 251–256. Horner-Devine M. C., Lage, M., Hughes, J. B. & Bohannan, J. M. (2004). A taxa-area relationship for bacteria. Nature, 432, 750–753. Hubbell, S. P. (2001). The unified neutral theory of biodiversity and biogeography. Monographs in Population Ecology, 32, Princeton, NJ: Princeton University Press. Lawton, J. H. (1998). Small is beautiful, and very strange. Oikos, 81, 3–5. Lee, W. J. & Patterson, D. J. (2000). Heterotrophic flagellates (Protista) from marine sediments of Botany Bay, Australia. Journal of Natural History, 34, 483–562. Mann, D. G. & Droop, S. J. M. (1996). Biodiversity, biogeography and conservation of diatoms. Hydrobiologia, 336, 19–32. Massana, R., DeLong, E. F. & Pedro´s-Alio´, C. (2000). A few cosmopolitan phylotypes dominate planktonic archaeal assemblages in widely different oceanic provinces. Applied and Environmental Microbiology, 66, 1777–1787. May, R. M. (1988). How many species are there on Earth? Science, 241, 1441–1449. Montresor, M., Lovejoy, C., Orsini, L., Procaccini, G. & Roy, S. (2003). Bipolar distribution of the cyst-forming dinoflagellate Polarella glacialis. Polar Biology, 26, 186–194.

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Morgan, C. I. & King, P. E. (1976). British Tardigrades Synopses of the British Fauna No. 9. London: Linnean Society of London; and Academic Press. Nilsson, J. R. (1962). Observations on Neobursaridium gigas Balech, 1941 (Ciliata, Heterotrichida). Journal of Protozoology, 9, 273–276. Noguez, A. M., Arita, H. Y., Escalante A. E. et al. (2005). Microbial macroecology: highly structured prokaryotic soil assemblages in a tropical deciduous forest. Global Ecology and Biogeography, 14, 241–248. Nouzare`de, M. (1975). Sur un nouveau genre de protozoaires cilie´s ge´ants me´sopsammiques appartenant a` la famille des Geleidae, Kahl. Comptes Rendus de l’Acade´mie des Sciences, Se´rie D., Paris, 280, 625–628. Potapova, M. G. & Charles, D. F. (2002). Benthic diatoms in USA rivers: distributions along

spatial and environmental gradients. Journal of Biogeography, 29, 167–187. Schmid, P. E., Tokeshi, M. and Schmid-Araya, J. M. (2000). Relation between population density and body size in stream communities. Science, 289, 1557–1560. Shiel, R. J. & Green, J. D. (1996). Rotifera recorded from New Zealand, 1859–1995, with comments on zoogeography. New Zealand Journal of Zoology, 23, 193–209. Soinen, J., Paavola, R. & Muotka, T. (2004). Benthic diatom communities in boreal sreams: community structure in relation to environmental and spatial gradients. Ecography, 27, 330–342. Tyler, P. A. (1996). Endemism in freshwater algae. Hydrobiologia, 336, 127–135. Wilbert, N. & Kahan, D. (1981). Ciliates of Solar Lake on the Red Sea shore. Archiv fu¨r Protistenkunde, 124, 70–95.

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By wind, wings or water: body size, dispersal and range size in aquatic invertebrates SIMON D . RUNDLE University of Plymouth

DAVID T . BILTON University of Plymouth

ANDREW FOGGO University of Plymouth

Introduction The past 15 years have seen a dramatic increase in the study of large-scale patterns and processes in ecology under the banner of macroecology (Brown & Maurer, 1989). Organismal body size is one of the key components of many of these studies, and the distribution of body size and its relationship with range size and abundance figure extensively in the macroecological literature (Gaston & Blackburn, 2000; Blackburn & Gaston, 2003; Gaston, 2003). Body size is also the central component of the ‘three-quarters scaling law’, which predicts that metabolism scales to body mass0.75 (e.g. Gillooly et al., 2001) and is seeing increasing use in ecological predictions, including those concerning trophic interactions (Woodward et al., 2005), population dynamics (Marquet et al., 2005), species diversity (Allen, Brown & Gillooly, 2002) and energy flow (Enquist et al., 2003); indeed, the scaling of metabolism with body mass has also recently been used in attempts to make macroecological predictions (e.g. Jetz et al., 2004). Despite the recent surge of interest in large-scale ecological patterns, aquatic ecologists have been slow to take up the concept of macroecology. It could perhaps be argued that much of the aquatic ‘community ecology’ over the past couple of decades, relating assemblage composition in aquatic systems to environmental variables, was macroecology of sorts. However, this research has rarely progressed to examine over-arching patterns and their potential underlying mechanisms, and is therefore somewhat limited in how it can inform general ecological theory. Hence, with the exception of some work on fishes (Taylor & Gotelli, 1994; Pyron, 1999; Rosenfield, 2002; Goodwin, Dulvy & Reynolds, 2005) and on eukaryotic microbes (see Finlay, 2002 and Finlay & Esteban, this volume), there is a dearth of research on the macroecological Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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importance of body size in the aquatic compared with the terrestrial realm, and little has been published explicity on the macroecology of aquatic invertebrates a deficit that this symposium was designed to rectify. A species’ dispersal ability has fundamental and far-reaching consequences for its biogeography, evolutionary persistence and, therefore, its macroecology. Yet dispersal has not figured heavily in macroecological investigations (Gaston, 2003), which almost certainly stems from the lack of good data on actual dispersal propensity for groups other than vertebrates (e.g. Paradis et al., 1998). At the same time, dispersal is an emergent property that is likely to be influenced by a combination of traits, which complicates investigations of its role in ecological terms (Table 10.1). It is likely, however, that some of the traits that influence the dispersal abilities of taxa are likely to be linked to body size and, hence, that dispersal is a key, emergent trait that may provide a link between organismal size and distribution (Table 10.1). Dispersal presents a variety of challenges for aquatic organisms, from freshwater taxa occupying discrete water bodies surrounded by an inhospitable terrestrial landscape mosaic to microscopic passive dispersers at the mercy of large-scale oceanic currents (Finlay & Esteban, this volume). Our aims in this chapter are, first, to review what is known about how invertebrates disperse in aquatic habitats, including the ways in which body size and dispersal may interact and, second, to explore whether there are potential links between body size, dispersal ability and macroecological patterns (i.e. range size). The difficulty of obtaining empirical data on the actual dispersal abilities of individual aquatic taxa makes investigation of the relationships between body size and dispersal per se intractable at present. Instead, we concentrate on the relationship between surrogate measures of dispersal that potentially relate to body size and range size.

Table 10.1 Traits potentially influencing dispersal in aquatic invertebrates: * indicates those traits most likely to be linked to body size. Life history Production of dispersive stages (e.g. resting eggs, cysts) Timing of reproduction Reproductive output* Ecological Habitat requirements (i.e. specialists vs. generalists) Metabolic/mechanical Flight efficiency*

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Dispersal and body size in aquatic invertebrates Active dispersers in freshwaters Freshwater habitats are typically isolated, and relatively short-lived on geological timescales (Moss, 1998; Ribera, Foster & Vogler, 2003), and so freshwater organisms need to retain the ability to disperse, at least occasionally, if they are to persist. As noted by Darwin (1859), many freshwater taxa have relatively wide ranges, suggesting that they are capable of moving long distances. Movement between sites is achieved by active or passive means (Fig. 10.1; Bilton, Freeland & Okamura, 2001), although the dichotomy between these is not clear cut (see below). Active dispersal in freshwaters is achieved by self-generated movement of individuals, which may use sensory cues to seek out new areas of habitat or patches occupied by conspecifics. Insects constitute the overwhelming majority of actively dispersing freshwater organisms, and here movement between sites occurs during the adult stage. One obvious factor that could influence the dispersal ability of such flying taxa is their ability to travel large distances.

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Figure 10.1 Approximate size ranges of adults in selected groups of freshwater invertebrates, divided into active and passive dispersers. Passive dispersers (open bars) generally have smaller modal body sizes than active dispersers (shaded bars). The shaded area indicates the size range in which the transition to cosmopolitanism has been predicted to occur (Finlay, 2002), whilst the dotted line indicates the size below which flying insects are frequent members of the aerial plankton (see text).

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Small, flying insects, particularly those <4 mm in length (Fig. 10.1) such as many Diptera and Coleoptera, ‘sail with the wind’ as aerial plankton during long-distance movements and control their direction largely during takeoff and landing (Johnson, 1969; Compton, 2002). Movement in such species clearly combines aspects of both active and passive dispersal, and the factors influencing long-range movement may have more in common with passively-dispersing non-insects (see below) than with larger flying animals. Larger insects associated with freshwaters have more control over their flight direction and speed, and achieve long-distance dispersal largely through active means (Fig. 10.1). Although active dispersal could be considered comparatively low risk, in that the dispersers have the ability to seek out appropriate habitats, there are other costs associated with active dispersal, including trade-offs with reproduction (Tanaka & Suzuki, 1998; Zera & Brink, 2000). Hence, flight efficiency may play an important role in dispersal ecology. The subject of how flight efficiency scales with body size and related morphological parameters has received considerable attention in the literature. In general terms, the muscles of larger animals perform the same mass-specific work for a lower metabolic cost and are thus more efficient than those of small animals (Ellington, 1991; Harrison & Roberts, 2000; Wakeling & Ellington, 1997). Aquatic insects broadly fit this model, although there are some subtleties that may determine the differences in dispersal potential among groups. Ellington (1991) suggested that flight performance in the closely related dragonflies and damselflies scaled positively with massþ 0.27 and negatively with mass 0.23, respectively, and Marden (1994) also suggested a negative scaling of body mass and maximum sustainable flight performance in damselflies. It seems that damselflies may be less efficient fliers than dragonflies. Based on estimates of lift and power from wings, Wakeling and Ellington (1997) also suggested that dragonflies and damselflies were adapted to different styles of flight, dragonflies being better adapted to fly rapidly in large spaces and damselflies for manoeuvring in small spaces. Based on these data it might be predicted that dispersal ability should be positively and negatively correlated with body size in dragonflies and damselflies, respectively, and that larger-bodied insects would generally have a greater dispersal potential than small. It is also clear, however, that other morphological characters, such as wing size (Guitie´rrez & Mene´ndez, 1997; McLachlan, 1985) and wing muscle mass and lever length scaling (e.g. Schilder & Marden, 2004), may also play a major role in dispersal dynamics of dragonflies and damselflies, and indeed other insects. At the same time, it is highly unlikely that flight efficiency alone explains dispersal ability in freshwater insects; other factors including levels of interspecific competition, habitat quality and persistence will also have an influence on successful dispersal (Travis & Dytham, 1999; Ferriere et al., 2000; Clobert et al., 2001; Ribera et al., 2003; Vogler & Ribera, 2003).

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Passive dispersers in freshwaters In terms of overland, inter-site dispersal, both wind and animal vectors have been implicated in the passive transport of freshwater invertebrates (Dumont, 1994; Dahms, 1995; Korovchinsky & Boikova, 1996; Maguire, 1963). Anostracan eggs may be dispersed by the wind (Riddoch, Mpoloka & Cantrell, 1994; Brendonck & Riddoch, 1999), and such movement is likely to occur in other taxa with small, desiccation-resistant stages. Transport by mobile animal vectors has also been noted in a number of freshwater invertebrates (Bohonak, 1999; Bohonak, Smith & Thornton, 2004) including the movement of resting stages or individuals on and in waterfowl and other aquatic vertebrates (Proctor & Malone, 1965; Bilton et al., 2001; Green & Figuerola, 2005). Whilst being classed as passive, from the point of view of the dispersed organism, such movement differs fundamentally from wind-mediated transport in that the vector itself is dispersing actively, which may have important consequences for population structure and dynamics (Bohonak et al., 2004; Figuerola, Green & Michot, 2005). The majority of such passive dispersal in freshwater metazoans occurs during early life-history stages, and often involves resting eggs or cysts, which are resistant to desiccation and other adverse environmental conditions (Bilton et al., 2001). In many respects dispersal in such animals resembles dispersal in higher plants via seeds (De Stasio, 1989; Levin et al., 2003). Given the constraints of dispersal of propagules via wind, rain or animal vectors, these taxa would be expected to be relatively small. On the basis of the apparent ubiquity of many microbial eukaryotes Finlay (2002) and Finlay and Esteban (this volume) propose a transition between species with a biogeography and those which are ubiquitous at between 1 and 10 mm in length (see Fig. 10.1). In the case of testate amoebae, Wilkinson (2001) shows that this transition apparently occurs at around 100 mm, and indeed most of the organisms within the shaded area of Fig. 10.1 do have biogeographies, i.e. they are not cosmopolitan. As in the case of marine larval dispersers (see below), however, it is difficult here to identify the life-history stage where body size may be most relevant in shaping the evolution of dispersal. As with many wind-dispersed plant taxa (Fenner & Thompson, 2005), passive dispersers may be under selection for small propagule size, since these may be better dispersed. Unfortunately, data on propagule size in passively-dispersing freshwater metazoans are lacking or disparate (but see Poulin, 1995), making explicit tests of the relationship between propagule size and dispersal ability impossible at present. However, passive dispersal may also be related to the number of propagules produced, with fecundity related positively to dispersal potential. At the same time, if fecundity scales positively with body size in these passively dispersing freshwater taxa, we would predict a positive relationship between adult body size and dispersal ability, with larger-bodied taxa producing more propagules and being more widespread

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than small taxa, paralleling the scenario in marine environments but contrasting with Finlay (2002) and Finlay and Esteban’s (this volume) proposed model. Dispersal in marine systems In contrast to many of their freshwater counterparts, marine invertebrates are often benthic as adults and disperse as planktonic larvae. Three main types of developmental strategy have been described in marine taxa: (i) non-planktonic development, in which species are either viviparous, eggs and young develop demersally, or eggs are maternally brooded; (ii) lecithotrophy, in which a relatively large egg is produced and the yolk provisions the developing larva for at least part of its planktonic existence; and (iii) planktotrophy, in which the larvae derive their sustenance from exogenous sources, usually by predating other plankton. The division of development along such simple grounds, however, represents a considerable over-generalization (see Poulin, von Boletsky & Feral, 2001). For example, most planktotrophs develop feeding structures during their planktonic phase and therefore commence their development with maternal provisioning (Miner, McEdward & McEdward, 2005) whilst others which are primarily lecithotrophic may become facultatively planktotrophic (Emlet, McEdward & Strathmann, 1987). The relative frequency of different developmental modes differs both across clades of marine organisms, and across biogeographic regions within clades. Opisthobranch molluscs from the northeast Pacific are primarily planktotrophic (Goddard, 2004), whilst the relative proportions of lecithotrophs and brooders are higher in other groups such as echinoderms and prosobranchs in the same region. Groups such as peracarid crustaceans, meanwhile, are almost exclusively brooded, whilst most decapods have planktonic phases. The most profound patterns affecting dispersal mode are biogeographic trends in developmental pattern. Thorson’s rule (Mileikovsky, 1971) describes a trend towards decreased incidence of pelagic and planktotrophic development (towards direct demersal development) with increasing latitude (Collin, 2003). These trends mean that dominant modes and extents of dispersal may vary significantly with latitude. Most marine phyla exhibit a spectrum of modes of development, indicating that evolution of traits such as lecithotrophy and direct development have occurred separately in most of these groups (e.g. Jeffery & Emlet, 2003). It is difficult to justify the dichotomy of dispersal into active and passive modes in the marine environment. Whilst there are active components to planktonic existence, for example migrations within the water column, and small-scale dispersal by viviparous or brooding species can be highly effective (Kelaher, 2005), the majority of large-scale dispersal by both planktonic (both lecithotrophic and planktotrophic) and non-planktonic organisms is primarily passive. The duration (and therefore, potentially, scale) of pelagic transport may be influenced by a variety of both passive and active factors ranging from

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current movements (Largier, 2003; Shanks, Largier & Brink, 2000; Siegel et al., 2003) to larval responses to their own energetic status or settlement cues (e.g. Marshall & Keough, 2003a). Non-planktonic species, meanwhile, may display both active dispersal by swimming or crawling, and passive dispersal, the latter being by means of rafting on floating objects (see Grantham, Eckert & Shanks, 2003). Given these considerations, it is possible to make some generalizations as to how body size could relate to dispersal ability in marine invertebrates. Some life-history models predict a dichotomy of egg sizes in planktonic marine invertebrates, with eggs giving rise to planktotrophic larvae having small optimal size and those giving rise to lecithotrophic larvae being optimally large (Vance, 1973, reviewed in Roff, 1992). However, empirical data do not support such a bimodal distribution of egg sizes, and instead often demonstrate a right-skewed or intermediate size distribution, even within wholly planktotrophic groups (Levitan, 2000). It remains possible, however, to make the generalization that, compared with lecithotrophic propagules (eggs and larvae), those of planktotrophic taxa tend to be smaller, spend longer suspended in the water column, and disperse further, especially in the case of specialized long-lived ‘teleplanic’ forms (Eckert, 1999; Largier, 2003; Shanks et al., 2000). Amongst planktotrophic dispersers, there is evidence for a positive correlation between adult body size and egg size within species (e.g. Marshall & Keough, 2003b; Miner et al., 2005), but little evidence for patterns between species, although a trade-off between size and number of eggs as a result of energetic and physical constraints might be expected. Second, there is a tendency within clades for small body size to be correlated with either brooding or lecithotrophy, especially amongst co-occurring species (Strathmann & Strathmann, 1982). A variety of hypothesized mechanisms exist to explain these relationships between life-history traits and dispersal patterns (Sewell, 1994). Chia (1974) hypothesized that limitations upon energetic reserves for reproduction in small-bodied taxa limit gamete production and hence favour viviparity, brooding or lecithotrophy. Strathmann and Strathmann (1982) cite three hypotheses to explain this trend: dispersal limitation, adult longevity and recruitment, and allometries in scaling of fecundity and space available for brooding. It is also possible that smaller, more specialized species may experience increased selection for retention of juveniles if their habitats are widely dispersed and the probability of successful dispersal to new habitats is low. Such a case has certainly been made for organisms inhabiting estuaries (Bilton, Paula & Bishop, 2002; Foggo, Frost & Attrill, 2003). Finally, it is probable that smallbodied organisms face a double jeopardy in employing broadcast spawning: quantities of sperm and eggs produced by small organisms may be inadequate to ensure fertilization (especially in denser waters at higher latitudes) (Yund, 2000). Also, the probability of successful development of relatively few

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planktotrophic propagules would be low given the attrition rates normally encountered in the plankton. Lecithotrophs and brooders might also be expected to face a higher extinction risk depending upon the availability of their habitats, and might be less likely to form widespread ‘open’ populations (Berryman, 2002; Camus & Lima, 2002; Grimm, Reise & Strasser, 2003). In general then, the trend is for increasing degrees of lecithotrophy, brooding and viviparity as organisms get smaller, with larger organisms in general tending towards planktotrophic development and broadcast spawning. We, therefore, would expect planktotrophic organisms to be the most widely dispersed marine forms with the greatest range sizes; this is supported for several published studies of both living (Scheltema, 1989; Kohn & Perron, 1994; Emlet, 1995) and fossil (Hansen, 1978; Jablonski, 1986) marine invertebrates. Lecithotrophic and brooding species should be less widely distributed, which is supported by the analyses presented by Emlet (1995). The picture is confused somewhat by the increased probability of passive transport in smaller lecithotrophic propagules and smaller brooding or direct-developing individuals, such that the overall particle size-range size distribution might be expected to be ‘U’- or ‘J’-shaped. However, if selection for intermediate egg size in planktotrophic species is indeed strong (sensu Levitan, 2000), then it is likely that the number, and planktonic duration, of dispersing propagules is the primary constraint upon dispersal in planktotrophic forms. Many taxa demonstrate trade-offs between egg number and size (see Llodra, 2002 for review), and significant relationships between adult female size and fecundity. Thus, larger individuals will tend to produce more eggs, and ultimately become more successful at dispersal through weight of numbers of dispersing propagules in a fashion similar to that proposed for passively-dispersing freshwater taxa.

Dispersal, macroecology and body size: case studies Active dispersers in freshwaters . . . several species of Sympetrum and Aeshna have most often been seen engaging in mass flights, sometimes settling in large numbers on ships at sea or flying in swarms, together with other migrating insects, through high mountain passes. (Askew, 1988.)

As the above quote suggests, the exemplary active dispersers in freshwater insects are the dragonflies and damselflies (Fig. 10.1), the adults of many species being known to disperse long distances. This ability to disperse is due to their highly aerodynamic wings, efficient flight muscles and very high flight muscle to body mass ratios (up to c. 60%; Marden, 1987). Despite the general efficiency of odonate flight, however, there are substantial differences between species in traits related to power production and efficiency that may have implications in terms of dispersal potential and could relate to body size or other morphological characteristics related to size (see above).

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The odonates are ideally suited for investigating macroecological patterns and the potential role of body size and dispersal in influencing these patterns. First, they are used as models for exploring the biomechanics of flight (see above) and, hence, there is the potential for future studies to make robust macroecological predictions based on scaling relationships between body size and key traits related to dispersal ability (e.g. wing size and shape, mass of thoracic muscles, and ratios within muscle-lever systems). Second, the vivid markings and relatively large size of dragonflies and damselflies means that they are one of the groups of invertebrates that attract the most attention. Hence, they are well-known taxonomically and ecologically, and extensive distributional data exist for dragonflies and damselflies in many areas of the world, particularly the Holarctic. Data for North American damselflies and dragonflies have recently been made available electronically on the OdontataCentral database (Abbott, 2005) and these data were used to explore how range size related to patterns in relation to body size and wing size (see Fig. 10.2 for details). Based on some of the evidence presented above, significant positive relationships between size measures and distribution extent might have been expected. Although dragonflies were, on average, significantly larger than damselflies, they did not have significantly larger ranges (Fig. 10.2). However, within the dragonflies, there was some evidence for positive relationships between wing size and both range size and occupancy (Figs. 10.2c & d), no such relationships being evident for damselflies. Although these findings should be viewed with some caution, given the very high scatter around the derived regressions, they do suggest that the further exploration of such macroecological patterns, perhaps using more sophisticated regression techniques (e.g. McClain & Rex, 2001) may be instructive in revealing the potential role for traits linked to dispersal in macroecology. There have been a few previous attempts to relate dispersal potential to range size in freshwater invertebrates, with mixed findings. Ribera and Vogler (2000) consistently found that range size was significantly smaller in lotic versus lentic taxa in a comparison of clades of aquatic beetle differing in habitat preference. It was suggested that this macroecological pattern resulted from differing dispersal abilities in lentic versus lotic taxa, these differences being driven by differences in the duration of running (relatively long persistence) and standing waters (short persistence) over evolutionary timescales. Malmqvist (2000) examined the relationship of wing and body size with range size measures in mayflies and stoneflies in Sweden. He showed that there was no relationship between body size and range size, but that the ratio of wing length to body length was positively related to range extents in both groups. Hence, for at least two groups of freshwater taxa, there was evidence that a size-related trait might be related to distribution patterns. These results should be viewed with some caution, however, as the analysis was only partial (for most taxa studied, Sweden

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represents only a small part of their range). In a recent analysis on a subset of the data collated from the OdonataCentral database Rundle et al. (2007) were able to demonstrate, for a much fuller analysis, a significant positive relationship between wing size and range size in North American species of the damselfly genus Enallagma (Fig. 10.3). The recent publication of a phylogeny for these damselflies (Turgeon et al., 2005) also facilitated an analysis that controlled for phylogenetic relatedness (Harvey & Pagel, 1991). This comparative analysis confirmed that evolutionary changes in wing size were correlated with those in range size (Fig. 10.3). As in Malmqvist’s (2000) study, and the analysis for North American dragonflies as a whole, there were no significant relationships

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Figure 10.3 The relationship between: (a) wing length (mm) and range size (km2); and (b) wing length contrasts and range size contrasts from comparative analyses for Enallagma damselflies in North America. Analysis includes only species in the USA and Canada and range size data were collected as for Fig. 10.2. Contrast scores, representing independent, ancestral trait values were derived using Comparative Analysis by Independent Contrasts. Stepwise regressions (using body length and wing length and contrast scores for both as predictors) demonstrated significant relationships in both instances. The best model for the species comparison included both wing length and body length: R2 ¼ 0.57; y ¼ 16.1x  10.2x þ 0.71; F2,24 ¼ 16.9; p < 0.001, but the plot shown is for wing length only (a) y ¼ 7.84x  4.13, F1,24 ¼ 17.7, p < 0.001. For contrast scores only wing length was included in the model: (b) y ¼ 24.15x, F1,20 ¼ 60.1, p < 0.0001; here regression for contrast scores was forced through the origin (hence, there is no constant in the equation) and the ordinate axis was scaled to be positive.

with body length for either species comparisons or using contrast scores generated by independent contrasts analysis, which suggests that it is an increase in wing size rather than size per se that is correlated with increased range size in these freshwater invertebrates. Passive dispersers in freshwaters Empirical estimates of dispersal are either direct, involving mark-release-recapture, originally developed for population size estimation (Angelibert & Giani, 2003; Southwood & Henderson, 2000), or indirect, typically employing genetic analyses (see Bilton et al., 2001; Bullock, Kenward & Hails, 2002; Nathan et al., 2003 for reviews). Given the difficulty of obtaining direct estimates, many of the data on dispersal of aquatic invertebrates relate to the feasibility of dispersal rather than the frequency of successful dispersal events (Bilton et al., 2001). This is particularly true of passive freshwater dispersers, whose small, cryptic propagules do not lend themselves to direct study. In recent years, a combination of observational data and population genetic analysis have greatly expanded our understanding of dispersal in organisms such as bryozoans and zooplankton (see De Meester et al., 2002; Okamura & Freeland, 2002; Green & Figuerola, 2005; Figuerola et al., 2005), and several experimental studies have examined the relative ability of

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zooplankton species to disperse rapidly over local scales (Ca´ceres & Soluk, 2002; Cohen & Shurin, 2003; Largier, 2003; Louette & De Meester, 2005). Since the nineteenth century, many authors have considered the biogeography of selected passively-dispersing freshwater taxa – see for example accounts in Rundle, Robertson and Schmid-Araya, (2002a) for various meiofauna. Some of these studies have attempted to search for general macroecological patterns. Gillooly and Dodson (2000), for example, demonstrated that, for New World Cladocera, there was a peak in body size at around 60 degrees latitude in both the Northern and Southern Hemispheres and suggested that within these temperate regions body size was also maximal at intermediate temperatures during the year. However, there have been relatively few studies that attempt to assess macroecological patterns across taxa. Rundle, Bilton and Shiozawa (2000) and Rundle et al. (2002b) presented an analysis of distribution patterns at a variety of spatial scales (local-regional) employing parsimony analysis of endemicity to assess whether there were species assemblages characteristic of different areas of the globe. Analysis of the copepod family Canthocamptidae demonstrated that only 4% of described species were widespread (i.e. occurred in more than one biogeographical region – sensu Wallace, 1876). Galassi et al. (2002) suggest that even this may be an over-estimate, since recent taxonomic studies of microcrustacea (e.g. Galassi, Dole-Olivier & De Laurentiis, 1999; Stoch, 2001) tend to favour the splitting of species considered to be cosmopolitan on the basis of morphology alone, with genetic studies (e.g. Hebert & Finston, 1996) typically revealing additional phenotypically cryptic taxa. Despite the low number of widespread species, relationships between regions revealed from these analyses made biogeographic sense. At a global scale there was evidence of vicariant links, such as that between western Palaearctic and eastern Nearctic faunas, whereas within western Europe, there was a suggested role for post-glacial dispersal in shaping northern faunas. In relation to body size, it is worth noting that all species of Canthocamptidae are relatively small (lengths < 1000 mm), and that freshwater copepods are believed to disperse between water bodies largely via eggs, which are typically <50 mm in length. Such a size range is well below the transition to cosmopolitanism proposed by Finlay (2002) and Wilkinson (2001) (Fig. 10.1). Despite this, however, the vast majority of canthocamptids do indeed have a biogeography, and such a statement is true of most other meiofauna (Rundle et al., 2002a). Obviously, small dispersing propagules alone do not result in cosmopolitan distributions in freshwater taxa, and other factors such as population size, dispersal vector and the resistance of propagules must play an important role, as will the distribution of resulting dispersal distances themselves (Levin et al., 2003). Unfortunately, comparative data on such traits are lacking for freshwater copepods and, indeed, it is unclear how life-history features such as resting egg duration influence dispersal and range size. Many species of zooplankton

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produce long-lived diapausing egg banks (De Stasio, 1989; Hairston et al., 1995; Ca´ceres, 1998; Brendonck & De Meester, 2003; Vandekerkhove et al., 2005), which lower local extinction risk. Such dormancy can be seen to represent dispersal in time, and theoretical and empirical data predict trade-offs between spatial and temporal dispersal (Venable & Lawlor, 1980; Levin, Cohen & Hastings, 1984; Hairston & Ca´ceres, 1996), suggesting that dispersal rate may actually be lower in taxa whose eggs can remain dormant for long periods. This may impact on the timing of local colonization events (Ca´ceres & Soluk, 2002), but over larger spatial and temporal scales the production of resting propagules is likely to lead to larger ranges due to increased propensity for long-distance dispersal. Adult body size is well documented for the canthocamptid species considered by Rundle et al. (2000; 2002b), and reanalysis of these data reveal a consistent tendency for widespread taxa to be larger than their restricted relatives, at both a global and European scale (Fig. 10.4). Mechanisms that may underlie this apparent trend are unclear, but may relate to relative reproductive output: if larger-bodied taxa have higher fecundity this may increase the likelihood of long-range dispersal. Studies of other groups such as Cladocera would be useful here, as would comparative data on egg size, survivorship and estimates of effective dispersal distances. As discussed above, the dispersal biology of many passively-dispersing freshwater taxa has similarities with that in seed plants. Levin et al. (2003) note that modelling studies of seed dispersal demonstrate that both mean dispersal distance and the overall distribution of dispersal distance are critical in

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Figure 10.4 Mean body size (SE) of freshwater canthocamptid copepods, which can be considered as geographically restricted, i.e. found in one area of endemicity (white bars), or widespread, i.e. found in >1 area of endemicity (grey bars), at global and Western European scales. Widespread species were significantly larger for both global (T40 ¼ 2.02, p ¼ 0.015) and European (T81 ¼ 1.99, p < 0.050) data.

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determining rates of spread. No attempt has been made explicitly to model spread in passively dispersing freshwater taxa, but future studies should focus on this, and on including the influence of dispersal vectors (cf. animal dispersal of seeds), fecundity and propagule resistance into rates of spread. Hard data on these parameters are lacking in freshwater taxa, and at present our empirical understanding of the comparative dispersal biology of passive dispersers in freshwaters is cursory, limiting our ability to explore the possible influence of body size. Dispersal in marine systems There have been few studies of body size and range size in marine systems (Gaston, 2003) and fewer still that consider invertebrates and their modes of development and dispersal. For marine invertebrates, passive dispersal via planktotrophic larvae represents the most effective means of achieving long-distance transport. However, the probability of successful recruitment to adulthood from such meroplanktonic or teleplanic lifestages is low, and broadcast spawners adopting such a strategy must compensate by producing larger numbers of dispersing propagules. For brooding and viviparous species such as Amphipoda, active movement, whilst effective at small spatial scales, is likely to contribute little to their large-scale dispersal (Costa et al., 2004; Kelaher, 2005), with rafting and other passive means of dispersal dominating (Thiel & Gutow, 2005). We might draw comparisons, therefore, between all marine invertebrates (given that passive dispersal dominates in this realm) and passively dispersing freshwater taxa, with the caveat that size spectra in these two groups overlap little, if at all, with the marine organisms representing orders of magnitude greater adult body sizes than their freshwater counterparts. Given that selection for egg sizes in planktotrophic taxa tends to produce intermediate sizes of egg across species (Levitan, 2000), and that there is no overall observed relationship between egg size and adult body size (Eckert, 1999), we might expect no relationship to result between range size and body size in passively dispersing marine taxa. Larger propagules should develop faster and have a shorter pelagic larval duration and, thus, we might expect an egg size-range size relationship to exist amongst planktotrophic taxa. However, larger species are generally longer lived and more fecund (Llodra, 2002), and therefore generate more dispersing individuals. Goodwin et al. (2005) demonstrate that in the case of marine egg-laying teleosts, geographic range indeed scales positively with body size, and Reaka (1980) reported a similar relationship for Stomatopods (most species initially brood their eggs, which then hatch and the larvae disperse planktonically). These trends are probably related to adult fecundity rather than to the size of the dispersing particle.

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600 500 Egg/larval size (µm)

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400 300 200 100 0 0

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40 Adult shell length (mm)

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Figure 10.5 Relationships between adult shell length and egg size (open circles, dashed line) and hatching larvae (closed circles, solid line) for a set of planktotrophically dispersing calyptraeid gastropods: eggs R2 ¼ 0.342, F1,28 ¼ 14.58, P ¼ 0.001; larvae R2 ¼ 0.328, F1,19 ¼ 9.28, P ¼ 0.007. Data from Collin (2003).

Re-analysis of data from Collin (2003) describing sizes and distributions of planktotrophically dispersing calyptraeid gastropods, shows a weak relationship between adult body size and both eggs and hatching larvae (Fig. 10.5), although there is no evidence for an effect of adult size upon range. A similar pattern linking egg size to adult (i.e. test) size is evident in re-analysis of data describing regular echinoids (composite data from Emlet, 1995; Levitan, 2000; Moyse & Tyler, 1990; Meinkoth, 1981) (Fig. 10.6a). However, there is again no apparent trend in either of these cases for an effect of egg or adult size upon overall geographic range (Figs. 10.6b & c), although Emlet (1995) does demonstrate a clear effect of reproductive/dispersive strategy upon range size, with planktotrophs having significantly greater geographic ranges than non-feeding planktonic dispersers. Foggo et al. (unpublished) summarize trends in abundance, distribution and body size for British marine macroinvertebrates (see Foggo et al., 2003 for methods and data sources). These data were examined for evidence of patterns linking adult body size to a measure of range (proportion of sampled sites occupied). Polychaetes represent a group with a range of reproductive/dispersive strategies and, although there was no evidence of linear trends in range size with increasing body size, there were clear differences between non-planktonic, lecithotrophic and planktotrophic developers in terms of both the mean proportion of sites they occupied (Fig. 10.7a) or their mean body lengths (Fig. 10.7b). Thus, there appears to be a general trend for smaller passively dispersed marine invertebrates to be less widespread, echoing the trends encountered in some freshwater passive dispersers (see above). The comparison between passive dispersal in marine and freshwater systems seems at the outset to be somewhat contrived. Freshwaters are highly disjunct

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(a)

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Figure 10.6 Relationships between: (a) adult test diameter and egg size (R2 ¼ 0.322, F1,18 ¼ 8.56, P ¼ 0.009), (b) egg diameter and adult range size, and (c) adult test diameter and range size in regular echnoids. Data from various sources (see text).

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(a)

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0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Planktotrophs

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Figure 10.7 Mean (SE) proportional site occupancy (F2,125 ¼ 1.66, ns) (a) and body length (F2,125 ¼ 0.69, ns) (b) of planktotrophic (n ¼ 66), lecithotrophic (n ¼ 34) and non-planktonic (n ¼ 26) polychaetes. Planktotrophic taxa are more widespread (ANOVA p < 0.05, data subjected to p Asin (x) transformation to normalize variances) than non-planktonic dispersers, and tend to be larger. Data from Foggo et al. (unpublished).

systems, discrete and surrounded by inimical habitat. They have relatively low persistence on both ecological and geological timescales compared with marine systems, which are also highly connected (Moss, 1998). In addition, marine populations might be viewed as effectively open systems, with lower probabilities of local extinctions occurring, especially in species dispersing planktonically (Eckert, 2003). Marine habitats have historically been more stable and less disturbed than terrestrial or freshwater systems (Moss, 1998), and may therefore be less shaped overall by dispersal patterns modes and hence by body sizes. However, the parallel between the two systems may be most valid at the level of dispersal viewed as a lottery with a high risk associated. The greater the number of tickets a species buys, the greater the probability of success, thus

BODY SIZE, DISPERSAL AND RANGE SIZE IN AQUATIC INVERTEBRATES

the key effect of body size in these passive dispersing species is upon fecundity. In marine systems it is also possible that the main consequences of body size for dispersal act through dictating reproductive-dispersive strategies.

Conclusions In the case of freshwater environments the data we present suggest that there may be some positive relationships between range size and body size or traits that may be linked to dispersal. For passive dispersers, rather than metabolic costs associated directly with dispersal there may be a link between propagule output and body size – a possibility worth further investigation. For at least some active dispersers, there is evidence that wing size rather than body size per se is of particular importance. We would suggest that aquatic insects could provide a valuable model system in which scaling laws for flight (e.g. Schilder & Marden, 2004) could be used alongside those for metabolism for making robust macroecological predictions. In the marine environment links between dispersal, range and body size are most likely to be moderated by developmental mode and lifetime reproductive output. Smaller organisms, tending towards viviparity or brooding, invest more in each individual offspring and have more rapid generation times. Such a strategy is likely to be less successful for dispersing over long distances than the possession of a planktonic stage. Body size is likely to manifest itself more through relationships with fecundity, as larger organisms will be able to produce greater numbers of eggs. This is, however, less likely to result in strong range size–body size correlations due to the kind of allometries in fecundity and size of area for brooding described by Strathmann and Strathmann (1982). In intermediate size organisms that produce lecithotrophic larvae the size and number of dispersing particles will dictate range, with the trade-off between maternal investment (size, and hence developmental time spent in the plankton; Levitan, 2000) and fecundity being key. Larger organisms will be able to generate larger numbers of eggs irrespective of egg size, and this effect of fecundity is likely to result in any observed trends between body size and range. In marine planktotrophs there is both theoretical (Levitan, 2000) and empirical (Eckert, 1999) evidence that no general body size–egg/larval size relationship exists, although some taxa do seem to indicate such a trend (see Figs. 10.5 & 10.6). No inherent ‘dispersability–body size’ relationship can be predicted for individual species groups, as is the case of freshwater dispersers. Body size–range size relationships in these taxa may instead be determined by fecundity, which in turn is likely to scale directly with body size, invoking the same basis in metabolic rules as proposed for other macroecological patterns (Gillooly, et al., 2001; Marquet et al., 2005). In summary, we hope that we have demonstrated that the exploration of macroecological patterns in aquatic invertebrates can be profitable and that it

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may be possible to use dispersal as an organismal property that links body size and distribution patterns. Certainly, the production of databases such as OdonataCentral for other groups of aquatic invertebrates and for other regions will allow the continued search for links between dispersal propensity, body size and range size. It is key, however, that the exploration of these patterns is driven by robust predictions based on traits that are likely to influence dispersal ability and that some attempts are made to gather empirical data on dispersal.

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McClain, C. R. & Rex, M. A. (2001). The relationship between dissolved oxygen concentration and maximum size in deep-sea turrid gastropods: an application of quantile regression. Marine Biology, 139, 681–685. McLachlan, A. (1985). The relationship between habitat predictability and wing length in midges. Oikos, 44, 391–397. Meinkoth, N. A. (1981). National Audubon Society Field Guide to North American Seashore Creatures. New York: A. A. Knopf. Mileikovsky, S. A. (1971). Types of larval development in marine bottom invertebrates, their distribution and ecology significance: a re-evaluation. Marine Biology, 10, 193–213. Miner, B. G., McEdward, L. A. & McEdward, L. R. (2005). The relationship between egg size and the duration of the facultative feeding period in marine invertebrate larvae. Journal of Experimental Marine Biology and Ecology, 321, 135–144. Moss, B. (1998). Ecology of Fresh Waters, Man and Medium, Past to Future. Oxford: Blackwell. Moyse, J. & Tyler, P. A. (1990). Echinodermata. In The Marine Fauna of the British Isles and NorthWest Europe, Vol. 2., ed. P. J. Hayward and J. S. Ryland. Oxford: Clarendon Press. Nathan, R., Perry, G., Cronin, J. T., Strand, A. E. & Cain, M. L. (2003). Methods for estimating long-distance dispersal. Oikos, 103, 261–273. Okamura, B. & Freeland, J. R. (2002). Gene flow and the evolutionary ecology of passively dispersing aquatic invertebrates. In Dispersal Ecology, ed. J. M. Bullock, R. E. Kenward and R. S. Hails. Oxford: Blackwell Science, pp. 194–216. Paradis, E., Baillie, S. R., Sutherland, W. J. & Gregory, R. D. (1998). Patterns of natal dispersal in birds. Journal of Animal Ecology, 67, 518–536. Poulin, R. (1995). Clutch size and egg size in free-living and parasitic copepods: a comparative analysis. Evolution, 49, 325–336. Poulin, E., von Boletzky, S. & Feral, J. P. (2001). Combined ecological factors permit

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classification of developmental patterns in benthic marine invertebrates: a discussion note. Journal of Experimental Marine Biology and Ecology, 257, 109–115. Proctor, V. W. & Malone, C. (1965). Further evidence of the passive dispersal of small aquatic organisms via the intestinal tract of birds. Ecology, 46, 728–729. Pyron, M. (1999). Relationships between geographical range size, body size, local abundance, and habitat breadth in North American suckers and sunfishes. Journal of Biogeography, 26, 549–558. Reaka, M. L. (1980). Geographic range, life history patterns, and body size in a guild of coral-dwelling mantis-shrimps. Evolution, 34, 1019–1030. Ribera, I. & Vogler, A. P. (2000). Habitat type as a determinant of species range sizes: the example of lotic-lentic differences in aquatic Coleoptera. Biological Journal of the Linnean Society, 71, 33–52. Ribera, I., Foster, G. N. & Vogler, A. P. (2003). Does habitat use explain large scale species richness patterns of aquatic beetles in Europe? Ecography, 26, 145–152. Riddoch, B. J., Mpoloka, S. W. & Cantrell, M. (1994). Genetic variation and localized gene flow in the fairy shrimp, Branchipodopsis wolfi, in temporary rainwater pools in southern Botswana. In Genetics and Evolution of Aquatic Organisms, ed. A. R. Beaumant. London: Chapman and Hall, pp. 96–102. Roff, D. A. (1992). The Evolution of Life Histories: Theory and Analysis. London: Chapman and Hall. Rosenfield, J. A. (2002). Pattern and process in the geographical ranges of freshwater fishes. Global Ecology and Biogeography, 11, 323–332. Rundle, S. D., Bilton, D. T. & Shiozawa, D. K. (2000). Global and regional patterns in lotic meiofauna. Freshwater Biology, 44, 123–134. Rundle, S. D., Robertson, A. L. & Schmid-Araya, J. M. (eds.) (2002a). Freshwater Meiofauna

Biology and Ecology. Leiden: Backhuys Publishers. Rundle, S. D., Bilton, D. T., Galassi, D. & Shiozawa, D. K. (2002b). The geographical ecology of freshwater meiofauna. In Freshwater Meiofauna Biology and Ecology, ed. S. D. Rundle, A. L. Robertson and J. M. Schmid-Araya. Leiden: Backhuys Publishers, pp. 279–293. Rundle, S. D., Bilton, D. T., Abbott, J. C. & Foggo, A. (2007). Range size in North American Enallagma damselflies correlates with wing size. Freshwater Biology, 52, 471–477. Scheltema, R. S. (1989). Planktonic and non-planktonic development among prosobranch gastropods and its relationship to the geographic range of species. In Reproduction, Genetics and Distributions of Marine Organisms, ed. J. S. Ryland and P. A. Tyler. Fredensborg: Olsen and Olsen, pp. 183–188. Schilder, R. J. & Marden, J. H. (2004). A hierarchical analysis of the scaling of force and power production by dragonfly flight motors. Journal of Experimental Biology, 207, 767–776. Sewell, M. A. (1994). Small-size, brooding, and protandry in the apodid sea-cucumber Leptosynapta clarki. Biological Bulletin, 187, 112–123. Shanks, A., Largier, J. & Brink, L. (2000). Demonstration of the onshore transport of larval invertebrates by the shoreward movement of an upwelling front. Limnology and Oceanography, 45, 230–236. Siegel, D. A., Kinlan, B. P., Gaylord, B. & Gaines, S. D. (2003). Lagrangian descriptions of marine larval dispersion. Marine Ecology Progress Series, 260, 83–96. Southwood, T. R. E. & Henderson, P. A. (2000). Ecological Methods, 3rd edn. Oxford: Blackwell Science. Stoch, F. (2001). How many species of Diacyclops? New taxonomic characters and species richness in a freshwater cyclopid genus

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(Copepoda, Cyclopoida). Hydrobiologia, 453, 525–531. Strathmann, R. R. & Strathmann, M. F. (1982). The relationship between adult size and brooding in marine invertebrates. American Naturalist, 119, 91–101. Tanaka, S. & Suzuki, Y. (1998). Physiological trade-offs between reproduction, flight capability and longevity in a wing-dimorphic cricket, Modicogryllus confirmatus. Journal of Insect Physiology, 44, 121–129. Taylor, C. M. & Gotelli, N. J. (1994). The macroecology of Cyprinella: correlates of phylogeny, body size, and geographical range. American Naturalist, 144, 549–569. Thiel, M. & Gutow, L. (2005). The ecology of rafting in the marine environment-I – The floating substrata. Oceanography and Marine Biology: An Annual Review, 42, 181–263. Travis, J. M. J. & Dytham, C. (1999). Habitat persistence, habitat availability and the evolution of dispersal. Proceedings of the Royal Society of London B, 266, 723–728. Turgeon, J., Stoks, R., Thum, R. A., Brown, J. M. & McPeek, M. A. (2005). Simultaneous quaternary radiations of three damselfly clades across the Holarctic. American Naturalist, 165, E78–E107. Vance, R. R. (1973). On reproduction strategies in marine benthic invertebrates. American Naturalist, 107, 339–352. Vandekerkhove, J., Declerck, S., Bendonck, L., et al. (2005). Hatching of cladoceran resting eggs: temperature and photoperiod. Freshwater Biology, 50, 96–104.

Venable, D. L. & Lawlor, L. (1980). Delayed germination and dispersal in desert annuals: escape in space and time. Oecologia, 46, 272–282. Vogler, A. P. & Ribera, I. (2003). Evolutionary analysis of species richness patterns in aquatic beetles: why macroecology needs a historical perspective. In Macroecology Causes and Consequences, ed. T. M. Blackburn and K. J. Gaston. Oxford: Blackwell Science, pp. 17–30. Wakeling, J. M. & Ellington, C. P. (1997). Dragonfly flight III. Lift and power requirements. Journal of Experimental Biology, 200, 583–600. Wallace, A. R. (1876). The Geographical Distribution of Animals. London: MacMillan. Wilkinson, D. M. (2001). What is the upper size limit for cosmopolitan distribution in free-living microorganisms? Journal of Biogeography, 28, 285–291. Woodward, G., Ebenman, B., Emmerson, M., et al. (2005). Body size in ecological networks. Trends in Ecology and Evolution, 20, 402–409. Yund, P. O. (2000). How severe is sperm limitation in natural populations of marine free-spawners? Trends in Ecology and Evolution, 15, 10–13. Zera, A. J. & Brink, T. (2000). Nutrient absorbtion and utilization by wing and flight muscle morphs of the cricket Gryllus firmu: implications for the trade-off between flight capability and early reproduction. Journal of Insect Physiology, 46, 1207–1218.

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Body size and diversity in marine systems RICHARD M . WARWICK Plymouth Marine Laboratory

Introduction Much has been written concerning the relationship between body size and biological traits, mostly concerning the terrestrial situation. There is no reason to suppose that many of these relationships will be different in the sea; for example quarter-power scaling with body mass applies to virtually all organisms (West, Brown & Enquist, 1999). For marine animals, metabolic rate and production scales at three-quarters power (e.g. Brey, 1990; Warwick & Price, 1979), while it is likely that life span increases in proportion to body mass raised to the power of one quarter, although so little is known about the natural history of marine animals that this latter relationship cannot yet be established. On the other hand, the very different phyletic composition of terrestrial and marine faunas, and the big differences in life-history characteristics, suggest that relationships between body size and diversity will differ between these two realms. The relationship between body size and diversity is fraught with uncertainties and inconsistencies. Hutchinson (1959) suggested that ‘. . . small size, by permitting animals to become specialised to the conditions offered by small diversified elements of the environmental mosaic, clearly makes possible a degree of diversity quite unknown among groups of larger organisms’. However, it is now suggested that the spatial and temporal structure of the physical environment is fractal (Bell et al., 1993 and references therein; see Schmid & Schmid-Araya, this volume), and if habitat complexity largely determines species diversity this leads to the prediction (for a single perfect fractal) that all organisms, regardless of size, will perceive the environment as equally complex and should have equivalent diversity. A comprehensive study by Orme et al. (2002) did not support any correlation between the median body size of a phylum and the number of species in that phylum, contrary to the Hutchinsonian view that the smallest bodied taxa are the most diverse (Van Valen, 1973; May, 1986; Kochmer & Wagner, 1988) or more recent suggestions that diversity is highest in taxa of intermediate size (Dial & Marzluff, 1988; Fenchel, 1993; Siemann, Tilman & Harrstad, 1996; Etienne & Olff, 2004). Uncertainty also exists as to whether local diversity is controlled by regional processes, involving biogeographic and evolutionary mechanisms, or Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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whether intrinsic local processes involving ecological mechanisms are more important (Cornell & Lawton, 1992; Witman, Etter & Smith, 2004). Translated to the body size/diversity problem, the question arises as to whether the local numbers of species of different sizes, in taxonomic/functional guilds or integral assemblages, are simply a more or less random selection from the regional species pool, or whether local environmental constraints and species interactions are more important in determining this pattern. Problems of definition then arise: what is a ‘guild’ (Adams & Shorrocks, 1985) and how is the ‘regional species pool’ defined (Dupre, 2000)? This chapter attempts to resolve some of the above uncertainties with respect to marine faunas, with particular emphasis on the benthos, which has a much higher diversity than the plankton, and a higher phyletic diversity than any other realm on Earth (Warwick, 1996).

Species guilds Two generalized concepts with respect to species guilds are relevant here. First, the controversial concept that there is a minimum size difference between competing species that will permit their coexistence (Huxley, 1942), that ratio being shown empirically to be 1:28 (Hutchinson, 1959). It has been argued that this ‘Hutchinsonian ratio’ may be more to do with the generalities of assembling sets of tools than with anything directly biological (Horn & May, 1977), or indeed may be an artefact (Eadie, Broekhoven & Colgan, 1987; Greene, 1987). Also, tools or musical instruments with which analogies have been drawn (Horn & May, 1977) are fixed in size, whereas animals increase in size during development and are potentially in competition for resources with their congeners of different sizes and also with other species in the guild (Woodward & Warren, this volume). For taxa with distinct developmental stages (instars) the increase in size between each moult (Dyar’s Constant) is the same as the Hutchinsonian ratio of 1:3 (Dyar, 1890), and this also applies to many marine taxa (see for example Table 11.1). Dyar’s Constant is much better substantiated than the Hutchinsonian ratio, but Lawton and Strong (1981) argue that it is ‘nothing to do with competition or partitioning of food resources’. The second concept relates to the number of species in a guild that are typically found to co-occur, usually seven to eight and never more than ten (Adams & Shorrocks, 1985). Again, the explanation for this also involves competition for resources: more species would intensify competition for resources beyond the limits of the number of species that could coexist. Reverting to the analogy of inanimate objects there are instances where both these ‘rules’ may apply. A new violin family introduced at a conference on musical acoustics in Cambridge in 1997 had a ‘rich, even tone quality; particularly shines in contrapuntal writing’ (Darius, 1977). There were eight viols in the consort, with size ratios of 1:2, 1:2, 1:3, 1:3, 1:3, 1:3, 1:3 (Horne & May, 1977).

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Table 11.1 Dyar’s Constants (increase in length between successive moults) for seven species of free-living marine nematodes. Species

Constant

Calculated from

Monhystera denticulata Chromadora macrolaimoides Steineria ericia Steineria pilosa Subsphaerolaimus litoralis Sphaerolaimus gracilis Parasphaerolaimus paradoxus Mean

1.28 1.41 1.37 1.34 1.32 1.22 1.31 1.32

Tietjen & Lee (1972) Tietjen & Lee (1973) Lorenzen (1978) Lorenzen (1978) Lorenzen (1978) Lorenzen (1978) Lorenzen (1978)

For marine animals very little is known about the species numbers and bodysize distributions of guilds of species that co-occur in specific locations or habitats. A much simpler exercise is to analyze these patterns in regional species pools because comprehensive regional inventories are available for many taxa. In Fig. 11.1 the numbers of species of different sizes in various taxa that might reasonably be defined as guilds, in what might reasonably be defined as regional species pools, are plotted. The term ‘guild’ here is taken to mean a taxonomically coherent group of animals with similar trophic roles. The taxa have been chosen to cover the whole spectrum of marine metazoan body sizes from tardigrades to toothed whales, and the body-length axis is divided into 1.28 geometric size classes. A remarkable feature of these plots is that each guild spans almost the same range of sizes, from nine size classes (tardigrades, shrimps and prawns, regular echinoids) to 14 (mysids), with a mean of 10.6. Thus, there seems to be a rather fixed range of body sizes that a given body plan will allow, irrespective of the nature of that body plan. If local assemblages were a random selection of species from the regional pool, the resulting guilds would not be inconsistent with the size ratio and guild size ‘rules’ noted above, and local competition or partitioning of food resources need not be invoked to explain them.

Adult-body size distributions in integral benthic assemblages The species numbers/adult body size relationship for marine benthic metazoan assemblages is quite unlike that described for any terrestrial or freshwater situation. Warwick (1984) found a highly conservative pattern for temperate soft-bottom benthic assemblages, with two separate lognormal distributions corresponding to the size categories traditionally regarded as macrofauna and meiofauna (Fig. 11.2). The meiofaunal mode occurs at a dry body mass 0.64 mg and the macrofaunal mode at 3.2 mg, with a trough between them at 45 mg. Rather few subsequent studies have attempted to count species numbers across the whole

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8 7 6 5 19

Number of species

4

18 17 16 15

3

14 13 12 11 2

1

10 9

10–1

100

101

102

103

104

Length (mm)

Figure 11.1 Numbers of species in regional species pools of guilds of marine animals divided into size categories on a 1:28 geometric scale. 1 – Tardigrades, Britain (Morgan & King, 1976); 2 – Selective deposit feeding (bactivorous) nematodes, Chile (Wieser, 1959); 3 – Non-selective deposit feeding nematodes, Chile (Wieser, 1959); 4 – Epistrate (diatom) feeding nematodes, Chile (Wieser, 1959); 5 – Carnivorous/omnivorous nematodes, Chile (Wieser, 1959); 6 – Harpacticoid copepods, Norway (Sars, 1911); 7 – Calanoid copepods, Norway (Sars, 1903); 8 – Ostracods, Norway (Sars, 1928); 9 – Gammarid amphipods, Britain (Lincoln, 1979); 10 – Cumaceans, Britain (Jones, 1976); 11 – Mysids, Britain (Tattersall & Tattersall, 1951); 12 – Shrimps and prawns, Britain (Smaldon, 1979); 13 – Filter-feeding bivalves, Britain (Tebble, 1966); 14 – Ophiuroids, Britain (Mortensen, 1927); 15 – Regular echinoids, Britain (Mortensen, 1927); 16 – Irregular echinoids, Britain (Mortensen, 1927); 17 – Flatfish, NW Europe (Wheeler, 1969); 18 – Gadoids, NW Europe (Wheeler, 1969); 19 – toothed whales, Europe (Van den Brink, 1967).

meiofauna–macrofauna size spectrum, but these have confirmed the bimodal species size distribution, with many meiofaunal and many macrofaunal species, but few of intermediate size (Warwick et al., 1986; Warwick & Joint, 1987; Kendall, Warwick & Somerfield, 1997). An intuitive explanation for this follows Schwinghamer’s (1981) explanation for the ataxonomic benthic biomass spectrum concerning the constraint on body size of sediment granulometry.

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24 Number of species

214

Northumberland mud

20

Carmarthen Bay sand

Algoa Bay sand

16 12 8 4 0 2

6 10 14 18 22 26 30

2

6 10 14 18 22 26 30

2

6 10 14 18 22 26 30

X2 geometric weight classes

Figure 11.2 Benthic species-size distributions in subtidal soft-sediment assemblages off NW England (Northumberland), South Wales (Carmarthen Bay) and South Africa (Algoa Bay) showing the conservative bimodal pattern (after Warwick, 1984).

Schwinghamer (1981) found a biomass trough at exactly the same body size as the species body-size trough (between 0.5 and 1 mm equivalent spherical diameter) and argued that this size defines the upper limit of the interstitial meiofauna and is the region of a shift from interstitial to burrowing lifestyles, with a class of intermediate-sized animals capable of neither. This hypothesis, involving the importance of habitat architecture (Holling, 1992), is not only intuitively appealing but is also open to empirical test (Stead et al., 2005). However, the only experimental test on soft-bottom marine benthos is that of Leaper et al. (2001) who found no support for it. Furthermore, this explanation does not bear critical examination based on comparative studies, since the bimodal species body-size distribution is apparent in thixotropic muddy sediments where the interstitial mode is not possible (Warwick, 1984), and also in sediment-free algal habitats where such sedimentary constraints do not exist (Gee & Warwick, 1994). Further, in freshwater sediments, evidence suggests that the meiofauna/ macrofauna dichotomy does not exist. Strayer (1986) found that, in the sediments of Mirror Lake, New Hampshire, USA, both the biomass spectrum and the species size distribution were unimodal, in marked contrast to the marine situation, and this unimodal pattern of taxon richness in body-size classes has also been found in freshwater streams (Stead et al., 2005) (Fig. 11.3). Physical sedimentary constraints are clearly the same in the freshwater and marine situations, but the reproductive characteristics of the species involved are very different. Most shallow-water temperate marine macrobenthos have planktonic larvae, whereas many species in the freshwater benthos are the larval stages of flying insects. The conservative nature of the species bodysize spectrum in marine habitats therefore adds credence to the suggestion that it results from evolutionary adaptations to the spatial and temporal structure of the marine environment, which will affect the regional species pool, rather than ecological constraints imposed by the physical nature of particular habitats. The meiobenthos are considered to be the first metazoans to evolve in the Middle Precambrian, with the Plathelminthes (including Gnathostomulida) and

BODY SIZE AND DIVERSITY IN MARINE SYSTEMS

(a)

Proportion of species (%)

16

4

1

0.25

(b)

Number of taxa

20

15 10

5 0 10–9

10–6 10–3 Body size (g dry weight)

100

Figure 11.3 (a) Species body-size distribution for the benthos of Mirror Lake, New Hampshire, USA (triangles and dotted line) compared with a typical shallow-water temperate marine benthic distribution (dots and solid line) (from Strayer, 1986). (b) Taxon body-size distribution in Lone Oak stream, SE England, drawn on the same x-axis scale as (a) (after Stead et al., 2005). Note the close similarity of the two unimodal freshwater distributions and the contrast with the marine bimodal distribution.

‘Aschelminthes’ (Nematoda, Gastrotricha, Kinorhyncha) being considered the most primitive forms (Boaden, 1989). These all have reproductive adaptations associated with small size: direct benthic development, dispersal as adults, short generation times (<1 year), semelparity, and reaching an asymptotic body size after which growth stops and reproduction commences. It is probable that these early meiofauna had the full range of trophic specializations before the major macrobenthic groups (Annelida, Arthropoda, Mollusca, Echinodermata) appeared. They were, and are, motile forms seeking food particles in a highly discriminate manner. Macrofaunal species have an alternative set of size related life-history and feeding traits: planktonic larval development and dispersal, long generation times (>1 year), iteroparity (usually), and continuing growth between successive spawnings. They may be either sedentary or motile, and feed less selectively on food particles. These contrasting traits are summarized in Table 11.2. Warwick (1984) suggested that the bimodal pattern of species-size distribution is apparent because there is a particular size at which meiofaunal life-history and feeding traits can be optimized, and another for macrofauna traits, compromises either being non-viable or disadvantageous. As size departs in eithes direction (larger or smaller) from these optima, fewer and fewer species

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Table 11.2 Size related biological traits that switch abruptly at about 45 g dry weight in temperate shallow water marine benthos (from Warwick, 1984).

Development Dispersal Generation time Reproduction Feeding Resource partitioning Growth Mobility

Smaller than 45 mg

Larger than 45 mg

Direct benthic As adults Less than one year Semelparous Discriminate use of particles Particle selection (size, shape, quality) Reach asymptotic adult size Motile

Planktonic Planktonic larvae More than one year Iteroparous (usually) Indiscriminate use of particles Spatial segregation and particle size selection Continue growth throughout life Sedentary or motile

are able to coexist. Warwick (1989) went on to suggest that it had been ‘necessary’ for larger animals to evolve a planktonic larva to avoid competition with and predation by the permanent meiobenthos, which constitute a highly efficient consumer unit. Whilst it is difficult to invoke the strength of present-day interactions between the meiobenthos and macrobenthic larvae as evidence for selection pressure in the past, there is strong present-day evidence that the meiobenthos can significantly depress the densities of newly settled macrobenthic larvae. This is mainly by predation but also by competition and disturbance (Bell & Coull, 1980; Watzin, 1983, 1986). Meiobenthic predators can take rather large prey relative to their own body size, even larger than themselves (Bilio, 1967; Straarup, 1970; Watzin, 1985), including the young of traditionally macrobenthic taxa (Fig. 11.4). Eggs produced by macrobenthic species, and consequently the larvae hatching from them, fall exactly in the same size range as the adult meiobenthos (Fig. 11.5), and settle out of the plankton to the bottom at a size corresponding to the position of the trough in the bimodal species body-size distribution (Figs. 11.5 & 11.6). It had already been suggested that the planktotrophic larval phase in macrobenthos is principally a migration for feeding and safety (with dispersal as an inevitable secondary by-product), and that ‘Life-history theories for marine animals cannot ignore a strong historical component stretching back to the origin of the metazoa’ (Strathmann, 1985).

All-animal body-size distributions in integral benthic assemblages The above discussion concerns the diversity of metazoans divided among adult body-size categories. Of course, natural assemblages also comprise the smaller developmental stages of these species that are potentially interacting with the adults. Warwick, Dashfield and Somerfield (2006) explicitly addressed the issue of all-animal size distributions by determining the degree to which infaunal

BODY SIZE AND DIVERSITY IN MARINE SYSTEMS

MEIOFAUNA

LARVAL MACROFAUNA Syllidae <8 setigers Nephtyiidae

Macrostomum beaufortensis

Nereidae <7 setigers Polydora sp. Streblospio benedicti

Turbellarian A

Prionospiop sp. Convoluta sp.

Neochildia fusca

Capitellidae Orbiniidae Cirratuldae

Acoel B

Archiloa wilsoni Clymenella torquata

Other harpacticoid copepods

Terebellidae Oligochaeta <1 mm

Enhydrosoma sp. Nereidae 8–12 setigers

Nematoda 1 mm

Amphipoda Bivalvia (shell broken)

Oligochaeta >1 mm

Figure 11.4 The meiofaunal and young macrofaunal diets of two species of meiobenthic turbellarians, Neochildia fusca and Archiloa wisoni. All animals drawn to scale. Note the large size of many prey items relative to the body size of the predators (after Watzin, 1985).

diversity assemblage structure varied with the mesh sizes of the sieves used to extract the animals from the sediment. Within an apparently homogeneous area of coarse intertidal sand in the Isles of Scilly, UK, samples were extracted using a standard range of five mesh sizes (63, 125, 250, 500, 1000 mm), with the sample areas and distances between samples scaled to the mesh size. All metazoans in each of the sample sets were identified to species level. Diversity and dominance patterns showed a dramatic stepwise change between the 250 mm and 500 mm mesh-size samples, being relatively constant in the <500 mm and >500 mm categories, with diversity higher in the former (Figs. 11.7 & 11.8). This suggested a fractal structure within but not between the <500 mm and >500 mm body-size categories (cf. Schmid & Schmid-Araya, this volume). This clear meiofauna/ macrofauna dichotomy, Warwick et al. (2006) argued, supports the view that the important relationships are those between body size and various biological characteristics such as feeding behaviour, reproductive mode and life history as they are affected by the spatial and temporal structure of the environment.

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(b) Proportion of species Number of species

(a) Proportion of species Number of species

218

0.1 benthic adults

0.1 benthic adults

0.05

0.05

0 10

eggs

0 0

10

20

30

X2 geometric weight class

0 3

Thorson’s polychaete larvae

0 4 Northumberland larvae 0 0

10

20

X2 geometric weight class

Figure 11.5 (a) Histogram of the size distribution of eggs of macrobenthic species that have planktotrophic larvae, compared with a generalized benthic species body-size distribution curve (from Warwick et al., 1986). (b) Histogram of the sizes of the polychaete larvae in Figure 11.6 and for a variety of newly settled macrobenthic larvae off the coast of Northumberland, compared with the adult species body-size distribution curve for the Northumberland station (from Warwick, 1984).

Pelagic assemblages For comparison with benthic species size distributions, Warwick et al. (1986) made a comprehensive collection of pelagic animals at station CS2 in the Celtic Sea, using a range of sampling devices with mesh sizes of 10 mm, 1 mm, 280 mm and 53 mm, and determined the adult body weights of all species in the samples. The centre of the size distribution of pelagic species closely corresponded with the trough in the bimodal benthic curve, with a few species extending as a tail across the macrobenthic size range (Fig. 11.9). Since the larvae of the macrobenthos (the meroplankton) are in the plankton when they occupy the meiobenthic size range, resource partitioning on a size basis between the meroplankton and holoplankton may have been an important evolutionary driving force in determining the pelagic size-distribution pattern (Warwick et al., 1986; Warwick & Joint, 1987).

Effects of pollution and disturbance Disturbed soft-bottom assemblages, and particularly those subjected to organic enrichment, become dominated by a group of species that have become known as ‘pollution indicators’ (Pearson & Rosenberg, 1978). These species are the smallest representatives of the macrofauna, mainly small annelids, and the largest species of the meiofauna, mainly oncholaimid nematodes and harpacticoid copepods of the genera Tisbe and Bulbamphiascus (Table 11.3). The body size of these species falls within the trough between the meiofauna and macrofauna

30

BODY SIZE AND DIVERSITY IN MARINE SYSTEMS

Polydora caeca

Nerine foliosa Pygospio elegans

Magelona papillicornis

Polydora ciliata 1 mm

Lagis koreni Spiophanes bombyx

Lanice conchilega

Figure 11.6 Late stage marine polychaete larvae at the size they begin to settle from the plankton to the seabed (after Thorson, 1946).

Shannon diversity (H’loge)

4.5 4 3.5 3 2.5 2 1.5 63

125

250

500

Sieve mesh size (µm)

1000

Figure 11.7 Species diversity in samples extracted from the sediment using a range of sieve mesh sizes on a sandflat in the Isles of Scilly, UK (after Warwick et al., 2006).

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Cumulative % dominance

100 80 Mesh size (µm)

63 125 250 500 1000

60 40 20 0 1

10

100

1000

Species rank

Figure 11.8 k-dominance curves averaged over all replicates for each mesh size in the same samples as Figure 11.7 (after Warwick et al., 2006).

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Number of species

220

20

benthic

10 pelagic 0 5 Pollution indicators 0 0

10

20

X2 geometric weight class

30

Figure 11.9 Species body-size distribution of the metazoan pelagos (solid histogram) compared with the metazoan benthos (upper curve) at a station in the Celtic Sea. Also shown (dotted histogram) is the size distribution of the ‘pollution indicator’ species listed in Table 11.3 (after Warwick et al.,1986).

adult body-size distributions, and within the size range of adult pelagic animals (Fig. 11.9). In these ‘enrichment communities’ of opportunistic species the meiofauna/macrofauna traits dichotomy (Table 11.2) breaks down; all the species have direct benthic development and are non-selective deposit feeders with approximately the same lifespan. This may also be the reason why the bimodal body-size distribution also breaks down.

Discussion and conclusion The mechanisms usually invoked to explain species size distributions, as with most other attributes of multispecies assemblages, have generally involved local ecological processes; species interactions (resource partitioning, predation, etc.) or environmental constraints (habitat architecture, disturbance, etc.). This chapter advocates the alternative, or additional, view that it is evolutionary processes acting over geological time that shape the structure of the regional species pool,

BODY SIZE AND DIVERSITY IN MARINE SYSTEMS

Table 11.3 Adult dry weight of species that become very abundant in organically enriched habitats. For sources of data see Warwick et al. (1986). Species Annelids Capitella capitata Polydora ciliata*/ligni Streblospio benedicti/shrubsolii* Tubificoides benedeni Ophryotrocha hartmanni Ophryotrocha puerilis Raphidrilus sp. Protodorvillea kefersteini Pholoe minuta Nematodes Metoncholaimus albidus Metoncholaimus scanicus Pontonema spp. Copepods Tisbe spp. Bulbamphiascus imus

Dry weight (mg)

505 125* 188* 306 50 140 158 108 190 12 23 64 12 3

and that the species occurring in any particular location are a more or less random selection from that pool. This would account for the conservative basic patterns encountered in marine habitats, which of course will be modified to some degree by ecological constraints. Whilst the effects of these ecological constraints can be examined experimentally, we cannot do manipulative experiments over evolutionary time and we must rely on so-called ‘natural experiments’, studying comparative situations where the invoked evolutionary mechanisms differ. For example, it would be a good test for the importance of the developmental mode if situations where the benthic/pelagic larval development dichotomy does not exist, e.g. the deep-sea, could be compared. Although no comprehensive size spectra yet exist for the deep sea, the model predicts a unimodal species-size distribution if the developmental mode is the key trait responsible for the size dichotomy.

Acknowledgements The ideas summarized here result from interactions with a large number of colleagues, and financial support from a large number of funding agencies over the course of a long career (resulting in an embarrassing proportion of selfcitations). These are far too numerous to list, but I thank them all. The writing of

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this chapter was done as a contribution to the biodiversity element of the Plymouth Marine Laboratory’s core strategic research programme. It was supported by the UK Natural Environment Research Council (NERC) and the UK Department for Environment, Food and Rural Affairs (DEFRA) through the AMBLE project ME3109, and I acknowledge my position as an honorary fellow of the Plymouth Marine Laboratory.

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Dyar, H. G. (1890). The number of molts of lepidopterous larvae. Psyche, 5, 420–422. Eadie, J. McA., Broekhoven, L. & Colgan, P. (1987). Size ratios and artefacts: Hutchinson’s rule revisited. American Naturalist, 129, 1–17. Etienne, R. S. & Olff, H. (2004). How dispersal limitation shapes species-body size distributions in local communities. American Naturalist, 163, 69–83. Fenchel, T. (1993). There are more small than large species? Oikos, 68, 375–378. Gee, J. M. & Warwick, R. M. (1994). Body-size distribution in a marine metazoan community and the fractal dimensions of macroalgae. Journal of Experimental Marine Biology and Ecology, 178, 247–259. Greene, E. (1987). Sizing up size ratios. Trends in Ecology and Evolution, 2, 79–81. Holling, C. S. (1992). Cross-scale morphology, geometry, and the dynamics of ecosystems. Ecological Monographs, 62, 447–502. Horne, H. S. & May, R. M. (1977). Limits to similarity among coexisting competitors. Nature, 270, 660–661. Hutchinson, G. E. (1959). Homage to Santa Rosalia, or why are there so many kinds of animals. American Naturalist, 93, 117–125. Huxley, J. (1942). Evolution: the Modern Synthesis. New York: Harper. Jones, N. S. (1976). British Cumaceans. Synopses of the British Fauna (New Series) No. 7. London: Academic Press. Kendall, M. A., Warwick, R. M. & Somerfield, P. J. (1997). Species size distributions in Arctic benthic communities. Polar Biology, 17, 389–392.

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Kochmer, J. P. & Wagner, R. H. (1988). Why are there so many kinds of passerine birds? Because they are small. A reply to Raikow. Systematic Zoology, 37, 68–69. Lawton, J. H. & Strong, D. R. (1981). Community patterns and competition in folivorous insects. American Naturalist, 118, 317–338. Leaper, R., Raffaelli, D., Emes, C. & Manly, B. (2001). Constraints on body-size distributions: an experimental test of the habitat architecture hypothesis. Journal of Animal Ecology, 70, 248–259. Lincoln, R. J. (1979). British Marine Amphipoda: Gammaridea. London: British Museum (Natural History). Lorenzen, S. (1978). Postembyonalentwicklung von Steineria- und Sphaerolaimidenarten (Nematoden) und ihre Konsequenzen fu¨r die Systematic. Zoologische Anzeiger, Jena, 200, 53–78. May, R. H. (1986). The search for patterns in the balance of nature: advances and retreats. Ecology, 67, 278–279. Morgan, C. I. & King, P. E. (1976). British Tardigrades. Synopses of the British Fauna (New Series) No. 9. London: Academic Press. Mortensen, T. H. (1927). Handbook of the Echinoderms of the British Isles. London: Oxford University Press. Orme, C. D. L., Quicke, D. L. J., Cook, J. M. & Purvis, A. (2002). Body size does not predict species richness among the metazoan phyla. Journal of Evolutionary Biology, 15, 235–247. Pearson, T. H. & Rosenberg, R. (1978). Macrobenthic succession in relation to organic enrichment and pollution of the marine environment. Oceanography and Marine Biology: an Annual Review, 16, 229–311. Sars, G. O. (1903). An Account of the Crustacea of Norway, Volume 4 – Copepoda, Calanoida. Bergen: Bergen Museum. Sars, G. O. (1911). An Account of the Crustacea of Norway, Volume 5 – Copepoda, Harpacticoida. Bergen: Bergen Museum.

Sars, G. O. (1928). An Account of the Crustacea of Norway, Volume 9 – Ostracoda. Bergen: Bergen Museum. Schwinghamer, P. (1981). Characteristic size distributions of integral benthic communities. Canadian Journal of Fisheries and Aquatic Sciences, 38, 1255–1263. Siemann, E., Tilman, D. & Haarstad, J. (1996). Insect species diversity, abundance and body size relationships. Nature, 380, 704–706. Smaldon, G. (1979). British Coastal Shrimps and Prawns. Synopses of the British Fauna (New Series) No. 15. London: Academic Press. Stead, T. K., Schmid-Araya, J. M., Schmid, P. E. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487. Straarup, B. J. (1970). On the ecology of turbellarians in a sheltered brackish shallowwater bay. Ophelia, 7, 185–216. Strathmann, R. R. (1985). Feeding and nonfeeding larval development and life-history evolution in marine invertebrates. Annual Review of Ecology and Systematics, 16, 339–361. Strayer, D. (1986). The size structure of a lacustrine zoobenthic community. Oecologia, 69, 513–516. Tattersall, W. M. & Tattersall, O. S. (1951). The British Mysidacea. London: The Ray Society. Tebble, N. (1966). British Bivalve Seashells. British Museum (Natural History), London. Thorson, G. (1946). Reproduction and larval development of Danish marine bottom invertebrates. Medd. Komm. Danm. Fisk. -og Havunders, ser Plankton, 4, 1–523. Tietjen, J. H. & Lee, J. J. (1972). Life cycles of marine nematodes. Influence of temperature and salinity on the development of Monhystera denticulata Timm. Oecologia, 10, 167–176. Tietjen, J. H. & Lee, J. J. (1973). Life history and feeding habits of the marine nematode Chromadora macrolaimoides Steiner. Oecologia, 12, 303–314.

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CHAPTER TWELVE

Interplay between individual growth and population feedbacks shapes body-size distributions LENNART PERSSON Umea8 University, Sweden

ANDRE´ M . DE ROOS University of Amsterdam, The Netherlands

Body size in contemporary ecology Body size and variation in body size have formed the focus of many studies in ecology, ranging from the study of individual performance to large-scale communities and ecosystems (Werner & Gilliam, 1984, Gaston & Lawton, 1988, Werner, 1988, Cohen, Johnson & Carpenter, 2003, Brown et al., 2004, Loeuille & Loreau, 2005). This focus is well-founded given the large variation in body size that exists among organisms from micro-organisms to large mammals (Gaston & Lawton, 1988; Werner, 1988). Body size is also the most important trait that affects the performance of individuals. Basic ecological capacities such as foraging rate and metabolic requirements are close functions of body size (Peters, 1983; Kooijmann, 2000; Brown, et al., 2004) affecting, for example, competitive abilities of differently sized organisms (Wilson, 1975; Persson, 1985; Werner, 1994). Body size strongly influences the diet of consumers with mean prey size, but also the variation in the size of prey eaten, increasing with predator size (Wilson, 1975; Werner & Gilliam, 1984; Cohen et al., 2005; Woodward & Warren, this volume; Humphries, this volume). Furthermore, the risk for an organism being preyed upon is heavily influenced by its own body size as well as the body size of its potential predator (Polis, 1988; Werner, 1988; Claessen, De Roos & Persson, 2000). Given its influence on basic individual ecological processes, body size has been an important variable in the investigation of larger ecological entities including communities, food webs and ecosystems. For example, predator–prey size ratios have formed the basis for food-web models such as the cascade model (Chen & Cohen, 2001), and for estimating interaction strengths in food webs (Emmerson & Raffaelli, 2004). Body size has also been the key variable in the analysis of food-web patterns with regard to numerical and biomass abundance at different trophic positions (Cohen et al., 2003; Cohen, this Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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volume). Another example where body size is a key variable is in size spectra analyses of the organization of trophic dynamics among populations of organisms (Kerr & Dickie, 2001; Shin et al., 2005). Finally, during the last decade the ‘metabolic theory of ecology’ (West, Brown & Enquist, 1997; Brown et al., 2004) has become very popular and is heavily founded on body-size variation. This theory has been advanced by its proponents to form a conceptual basis for ecology comparable to that of genetic theory for evolution and to ‘link the performance of individual organisms to the ecology of populations, communities, and ecosystems’ (Brown et al., 2004; Brown, Allen & Gillooly, this volume).

Neglected aspects of body size in contemporary ecology Although body size plays a central role in ecology, an important aspect of body size in many ecological communities has been largely neglected in the theoretical and empirical research mentioned above. In fact, the ecological entities upon which patterns have been analyzed are based on ‘average individuals’ (of different body sizes), an approach that basically is in conflict with a Darwinian view stressing variation among the individual organisms (see De Roos & Persson, 2005a). A major part of observed body-size variation is related to within-species variation, as individuals grow over a substantial part of their life cycle, whereas most contemporary ecological studies restrict their attention to between-species variation. To consider ontogenetic variation among individuals seems essential for any conceptual synthesis, given that the overwhelming majority of the Earth’s taxa exhibit some degree of size/stage structure (Werner, 1988) and the ecological effects of intraspecific variation in body size are well represented in the other chapters of this volume (e.g. Woodward & Warren, this volume; Warwick, this volume). Actually a whole body of theory on ontogenetic development and food-dependent growth of individuals was developed during the 1980s (Sebens, 1982; Werner & Gilliam, 1984; Sebens, 1987; Sauer & Slade, 1987; Ebenman & Persson, 1988), a literature that has been largely neglected by more recent ecological studies on body size. The purpose of this chapter is to give first a short historical overview of studies considering patterns of development and growth in organisms and to link size-dependent individual performance to community patterns. Second, we give an overview of how to progress towards an explicit and rigorous link between individual body size and population and community processes. Our focus will be on how size-dependent interactions shape the dynamics and structure of ecological communities including body-size distributions.

Development and growth – a retrospective overview As already mentioned, considering individual growth and development is important, because the majority of animals exhibit substantial changes in size and/or morphology over their ontogeny (Werner, 1988). Further, for most plant

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species growth and development is a major aspect of their life history. An overview of different animal taxa shows that major changes in body morphology as a result of metamorphosis are present in more than 85% of all taxa (25 of 33 phyla) (Werner, 1988). This pattern largely results because of the very many species of insects. Nevertheless, even if only vertebrates are considered, individuals of 75% of all taxa show substantial growth for much of their lives, which is due to the taxonomic dominance of fish, amphibians and reptiles. Actually, it is only among altricial birds and some mammals where the young are close to the adult body size when they become independent of the parents (Werner, 1988). Scaling constraints and growth patterns It has been suggested that large changes in body size due to ontogenetic development and growth impose a number of constraints on the body morphology of organisms related to physical, chemical and biological processes (Peters, 1983; Calder, 1984; Werner, 1988; Stearns, 1992; Humphries, this volume). When increasing in size, scaling properties – depending on both physical and ecological constraints – will set limits over which size range a particular lifestyle can be exploited (Calder, 1984; Werner, 1988). For example, physical parameters acting on small and large organisms are very different exemplified/illustrated by the effects of different Reynolds numbers on small and large aquatic organisms, respectively (Humphries, this volume). For small organisms, the low Reynolds number means that they swim with friction as the propulsive mode. In contrast, large organisms use the inertia of the water to propel themselves (Werner, 1988). Within the broader limits set on morphology by physical constraints, ecological constraints are also present related to, for example, which prey types an organism with a specific body morphology and size can efficiently utilize (Werner, 1988; Woodward & Warren, this volume). In particular, the morphologies that can evolve to efficiently handle different prey sizes during different parts of ontogenesis are constrained by genetic additative covariance in the genotype (Werner, 1988; Ebenman, 1992). Werner (1988) argued that allometric growth in organisms is only partly sufficient to cope with the different demands on body morphology made during different parts of the life cycle. These constraints imposed by allometric growth therefore result in an ‘allometric scaling problem’ for performance over the life cycle. He argued that, if scaling imposes a problem during the ontogeny, there should be patterns among the variety of life-history strategies by which animals cope with this problem (Cohen, 1985; Werner, 1988). Four particular tactics were discussed by Cohen (1985) and Werner (1988). The first represents organisms that largely avoid the problem of substantial size change by specializing as a very small adult (for example protozoans). The second tactic represents organisms in which the basic (small) trophic apparatus

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remains intact but is multiplied (e.g. coral polyps). The third tactic represents the situation where the adults extensively provide the egg and juvenile with transformable mass (e.g. yolk, maternal fluids, bodies of prey) until the young has reached a size where it can take up the parental lifestyle (birds and mammals). Fourth, the organism may adopt a succession of complex life histories that accommodate the increase in size (insects, amphibians, fish). Here, complex life cycles in the form of metamorphosis represent a way to break up genetic covariances between sizes/stages (Werner, 1988; Ebenman, 1992). One common trait among the two groups (birds and mammals) where the parents provide the egg and juvenile with transformable mass until it can take up the parental lifestyle is endothermy, including a high body temperature (Case, 1979; Stearns, 1992). This observation suggests that the rapid development from juvenile to adult in these groups not only requires the ability to provide eggs/juveniles with extensive amounts of energy, but also the ability to transform that energy rapidly into growth. This leads to the hypothesis that there is a relationship between endothermy and individual growth rate, an assumption that is supported by empirical data, because mammals and birds have a growth rate that is an order of magnitude higher than that of ectotherms such as reptiles and fishes (Ricklefs, 1973; Case, 1979). In summary, species for which individual growth and development plays a smaller role are primarily found among unicellular organisms and endotherms. In other organisms, substantial growth and development after the juvenile becomes independent of its parents is the rule. The different growth patterns observed among different organisms have formed the basis for different classifications of growth types (see Sebens, 1987). Without giving a more detailed description of these classification schemes, they have focused on two aspects of ontogenetic growth: the extent to which growth and development is plastic/indeterminate and hence food dependent, and the extent to which the asymptotic size is fixed or food dependent. In several instances these two aspects of growth have been mixed. For example, Stearns (1992) defined determinate growth as the situation where individuals do not grow in size after maturation. This definition of determinate growth is in our opinion not satisfactory, as it totally neglects whether growth up to maturation is food dependent or not. As considered above, ontogenetic growth and development take very different forms in different groups of taxa. Food-dependent growth over ontogeny can be continuous, as in fish and plants, or discrete where the development time between stages is food dependent, as in many invertebrates. We argue that it is food-dependent development per se that forms one dividing line for how ontogenetic development will affect individual performance, population and community processes and the biomass structures.

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Individual-level formulations for how individuals grow – linkage to community patterns The main message to be drawn from the above overview is that ontogenetic growth and development are characteristic of many organisms on Earth and that individual performance over ontogeny is constrained by both physical and ecological factors. At a broad scale, organisms showing substantial growth after becoming independent of their parents and those that do not can be separated along the endothermy–ectothermy gradient. At the same time, the different growth patterns described above are limited to broad categories, and a more quantitative link between individual performance and growth, with its consequences for community attributes such as body-size patterns, is therefore needed. A number of attempts were also undertaken during the 1980s to link individual body-size dependent performance and the dynamics of ecological communities. First, the scaling of foraging rate and metabolism with body size was used to determine the competitive ability of differently sized organisms and to predict niche shifts over ontogeny based on energy maximization (Mittelbach, 1981; Werner & Gilliam, 1984; Werner, 1988). Second, as the risk of being eaten is also a function of body size, the literature on individual size-dependent performance also came to include the effects of predation using optimal control theory (Werner & Gilliam, 1984). This individual-based framework using explicit body-size scalings of different rates was quite successfully applied to predict and understand the distribution of species and size classes within and between systems, primarily in freshwater fish communities (Mittelbach, 1981; Werner, 1986; Persson, 1988). Implicitly this approach assumed that community patterns could be predicted from individual-level traits ignoring population-level dynamics and feedbacks. An exception is the study by Hamrin and Persson (1986) on population cycles in cisco (Coregonus albula) where the population dynamics were explained from size-dependent foraging and metabolic rate including feedbacks on the resource. Modelling methods to address the dynamics of size-structured dynamics (Sinko & Streifer, 1967) were already being discussed at this time (Werner & Gilliam, 1984). However, more complete modelling formulations to address size-structured dynamics were first developed during the second half of the 1980s (Metz & Diekmann, 1986; De Roos et al., 1990) and their efficient use in ecological theory started first in the 1990s, which is the focus of the rest of this chapter (De Roos et al., 1990; Persson et al., 1998; Claessen, De Roos & Persson, 2000).

Developments of an explicit link from individual body size to population dynamics Brown et al. (2004) envisage metabolic theory to link the performance of individual organisms to the ecology of populations, communities and ecosystems.

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This might be true for some elements of the hierarchy from individuals to ecosystems, but a number of key elements, especially at the level of populations, are inadequately considered. Although we agree that there are constraints on ecological performance, such as individual metabolic rate, population maximum growth rate and ecosystem turnover as a function of body size (Brown et al., 2004), this theory addresses how ecological interactions shape body-size distributions in ecological communities only to a limited extent. Moreover, given that ontogenetic development is a major feature in most organisms, the effect of ontogeny on the development of body-size distributions is also a major aspect to take into account. In the following, we briefly describe a modelling framework that (i) explicitly links individual-level processes, including bodysize scaling, to population-size distributions and, (ii) considers ontogenetic development. We will subsequently discuss how food-dependent development rate gives rise to both dynamical and structural patterns not present in unstructured theory and how this shapes body-size distributions. It will become evident that body size in different ecological configurations is both an input to (by determining individual performance) and outcome of (as a result of population feedbacks) ecological interactions. Modelling framework The modelling approach we consider are physiologically structured population models (PSPMs) (Metz & Diekmann, 1986; De Roos et al., 1990) referred to as i-state distribution models. They are based on two different state concepts, the individual or i-state and the population or p-state. The i-state represents the state of the individual in terms of a collection of characteristic physiological traits, such as size, age and energy reserves, while the p-state is the frequency distribution over space of all possible i-states. The model formulation process consists of deriving a mathematical description of how individual performance (growth, survival, reproduction) depends on the physiological characteristics of the individual and the condition of the environment (i-state description). Handling the population-level (p-state) dynamics is subsequently just a matter of bookkeeping of all individuals in different states without making any further model assumption at this level (Fig. 12.1). The core of PSPMs is thus the individual state and the modelling of the individual life history. The derivation of the PSPM proceeds by writing down the equations describing the i-state dependent processes of energy gathering (attack rate, digestive capacity), metabolism, energy channelling between somatic and gonad growth and survival (generally a function of energy status and size-dependent mortality from predators) (see De Roos et al., 1990 and Persson et al., 1998 for examples). Energy allocated into gonad tissue may be spent continuously or discretely constrained by, for example, season. Bookkeeping provides the link from the individual to the population level, which also includes calculations of the impact of the total population on its

INDIVIDUAL GROWTH AND BODY SIZE

Individual Life History

Modelling

Environmental condition (e.g. food density)

Reproduction

Growth

Bookkeeping

Survival

Individual state (e.g. size)

Dynamics of population abundance and composition

Ecological interactions

Figure 12.1 Schematic representation of the philosophy behind the framework of physiologically structured population models. Based on the state of the individual and the environmental condition, we can model foraging rate, growth, survival and reproduction of the individual, while the population state is merely a bookkeeping of all individuals in all i-states.

environment. The change in the environment resulting from this impact represents the population feedback on individual life history and/or behaviour (Fig. 12.1). In a consumer-resource system, for example, the population influence on consumer life history operates through an increased or decreased density of resource, which affects individual growth, mortality and reproduction. In addition to i- and p-states, an environmental (E) state is defined, which in the consumer-resource system is the resource. In a system including predators of the consumer, the E-state also includes all potential predators on a consumer of a specific i-state. Ontogenetic development – dynamical aspects As discussed above, the size scalings of foraging and metabolic rate were recognized as basic variables to determine the competitive ability of differently sized individuals (Mittelbach, 1981; Lundberg & Persson, 1993; Werner, 1994). We extend this individual-level argumentation to analyze its populationlevel consequences using two case studies, a size-structured consumer-resource and a cannibalistic system, with the purpose of showing how size-structured dynamics may induce temporal variation in body-size distributions. For a consumer-resource model, the body-size scalings of foraging rate (attack rate, digestive capacity) and metabolism have been shown to have major effects on the population dynamics observed (Persson et al., 1998). Combining the size scaling of attack rate, digestive rate and metabolic rate allows us to calculate

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Figure 12.2 Changes in the numbers of young-of-the-year (dotted black lines), juveniles from an age of one year (solid grey lines) and adult (black solid thick lines) consumers and resource levels in the two types of cohort cycles discussed in the text. Left panels: cohort cycle driven by recruiting individuals. When a strong cohort is born, it almost immediately depresses the resource to low levels and out-competes older cohorts. The pattern repeats itself when the dominating recruiting cohort matures and gives rise to a new strong reproductive pulse. Right panels: cohort cycle driven by larger juveniles. When a strong cohort is born it causes a decrease in the resource for several years driving new cohorts to starvation death (vertical dotted grey lines) despite that adult reproduction is present for several years (years 2–4).

the resource level that differently sized individuals need to just meet maintenance (critical resource density, Persson et al., 1998). If the critical resource density increases monotonically with body size, cohort cycles driven by competitively superior recruiting cohorts will prevail (Fig. 12.2). In contrast, when critical resource density at first decreases with body size but increases thereafter, cohort cycles driven by larger individuals will occur (Fig. 12.2). Finally, in a narrow parameter range where critical resource density is relatively independent of body size, equilibrium conditions with many coexisting size cohorts will prevail (Persson et al., 1998). The different dynamics observed can thus be predicted from the form of the critical resource-density function. The cycle length of the resulting cohort cycles, which are driven by cohort interactions is, in contrast to predator–prey cycles, set by the time it takes individuals to reach maturation (generation time  cycle length). A literature review shows that single generation cycles (37% of all cycling populations) are as

INDIVIDUAL GROWTH AND BODY SIZE

common as traditional predator–prey cycles (38% of all cycling populations) among fluctuating populations (Murdoch et al., 2002). Together with another type of stage-based dynamics, delayed-feedback cycles (25% of all cycling populations), size/stage-based cycles thus are the dominant type of cycle observed in populations. Moreover, predator–prey cycles are found almost exclusively in specialist predators. Two further things can be stated about size-dependent consumer-resource dynamics. First, the observed size scalings of foraging rate and metabolism (that determine the competitive ability of differently sized individuals) suggest that cyclic dynamics should dominate over equilibrium dynamics, with the consequence that the body-size distributions of consumer populations will vary over time. Second, cohort (‘single species’) cycles are common in many species systems (Murdoch et al., 2002), suggesting that intraspecifically driven cycles cannot be ignored in many species systems. Typical examples of cohort-dominated cycles include population oscillations in Daphnia and planktivorous fish (McCauley et al., 1999; Persson et al., 1998). For planktivorous fish, estimated critical-resource demands show that these cycles are recruit-driven with an observed cycle length of 2–5 years. For shorter cycles (2–3 years), age cohorts may coexist and a cycling in growth rates of the different age cohorts is observed (Hamrin & Persson, 1986; Cryer, Peirson & Townsend, 1986; Townsend, Sutherland & Perrow, 1990). For longer cycles, strong age cohorts become more dominant and major shifts in size distributions can be observed over the years due to growth of dominant age cohorts (Fig. 12.3) (Sanderson et al., 1999). Cannibalism represents an extension of consumer-resource interactions to include predation among consumers. Because many cannibals share a common resource with their victims, the latter may subject the cannibals to severe exploitative competition for this shared resource (Polis, 1988; Persson, 1988; Polis, Myers & Holt, 1989). Experiments and field data, particularly on cannibalistic fish, show that a positive cannibalistic attack rate is constrained between a lower boundary below which the cannibal does not encounter a victim because of difficulties in seeing it, and an upper boundary above which the escape ability of victims and gape-size constraints prevents cannibalism (Claessen et al., 2000, Juanes, 2003). Analyses of the dynamics of cannibalistic systems show that three aspects of the size scaling of the cannibalistic attack function are important in determining population dynamics and cannibal-size distributions. The maximum victim/cannibal size ratio has less effect on population dynamics, but a strong effect on the ultimate size that an individual reaches and thereby the size distribution of the cannibal population (Claessen et al., 2002). In contrast, the overall rate by which the cannibalistic attack rate increases with cannibal size and the lower victim/cannibal size ratio have major effects on population dynamics and therefore on the degree of temporal variation in size distributions of cannibalistic populations (Claessen et al., 2000, 2002).

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Figure 12.3 (a) Growth (mean  1 SD) of two dominating cohorts of yellow perch (Perca flavescens) born in 1980 and 1985, respectively. (b) Shift in the size distribution of yellow perch from 1988 to 1992 as a result of growth of the dominating cohort born in 1985 (data from Sanderson et al., 1999).

Three different dynamical outcomes can be found: (i) low-amplitude/fixed-point dynamics, where cannibals control victims by inducing a high mortality on them, (ii) high-amplitude cohort cycles of the kind discussed above, in which victims outcompete cannibals before the latter can start cannibalizing, and (iii) a dynamics involving a mix of the previous two. Studies of cannibalistic perch (Perca fluviatilis) populations show that this species with a relatively high minimum victim–cannibal size ratio agrees with theoretical expectations and undergoes shifts in dynamics between a ‘stunted’ cannibal-driven phase and a phase driven by inter-cohort competition resulting in dramatic shifts in size distributions (Fig. 12.4b). The phases are also characterized by very different life-history trajectories with a periodic appearance of giant individuals (Fig. 12.4a). In conclusion, the two examples (consumer-resource and cannibalistic interactions) used here to illustrate the implications of size-structured interactions on dynamics show that different size scalings of individual rates have strong influences on distribution of body sizes over time. As the dynamics of species such as fish, feeding near the top of food web, feed back on lower trophic components, the changes in size distribution at these higher trophic positions will also cascade down to cause shifts in overall size distribution of the food web (Cryer et al., 1986; Shiomoto et al., 1997; Persson et al., 2003).

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Ontogenetic development and community structure Analyses of the dynamics of consumer-resource and cannibalistic systems show how different body-size scalings impact population dynamics and temporal changes in body-size distributions. Size-structured dynamics in these systems also have the potential to result in alternative states, which, particularly in cannibalistic systems, may result in very different size distributions (Claessen & De Roos, 2003). An extension of physiologically structured population models to more complex trophic configurations will further increase the likelihood of alternative states. In the following, we discuss alternative states and body-size distributions of populations exemplified by tritrophic food chains and tritrophic configurations with life-history omnivory. Since the classical paper by Brooks and Dodson (1965) it is generally accepted that size-dependent predation by top predators has a strong structuring impact on prey size distributions. Size-dependent predation in combination with fooddependent development in prey has the potential to lead to alternative stable states with vastly different size distributions of the prey (De Roos & Persson, 2002). In the tritrophic food chain studied by De Roos and Persson (2002), two

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alternative states were found under otherwise identical conditions, one consumer-resource, the other a predator-consumer-resource state. It is noteworthy that the invasion boundary of the predator occurred at a higher productivity level than its persistence boundary and, similarly, the harvesting persistence boundary for the predator was positioned at higher harvesting levels than the invasion boundary, making these systems prone to catastrophic collapses. The mechanistic explanation behind this catastrophic behaviour of the system is that a predator selecting small size classes of the consumer will increase the development rate of the remaining consumers into larger adult size classes, leading to increased population fecundity of the consumer and, therefore, counter-intuitively to an increased number in individuals of the size class that the predator feeds on (Fig. 12.5a) (De Roos & Persson, 2002). This overcompensatory effect has been termed an emergent Allee effect as it, in contrast to other mechanisms accounting for Allee effects, is purely based on exploitation of resources. The emergent Allee effect is also present if the predators select the largest size classes in the consumer population (De Roos, Persson & Thieme, 2003b; De Roos & Persson, 2005b). Size-structured dynamics in tritrophic food chains have also been shown to lead to the possibility of predator facilitation, where one predator may allow

Figure 12.5 (a) Size distributions of the consumer species in the absence (black bars) and presence (white bars) of size-selective predators in the tritrophic model with size structure in the consumer population. (b) Size structure of the char population in Takvatnet in 1985 and 1998 (data from Klemetsen et al., 2002).

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the invasion of another predator by altering the size structure of the consumer (De Roos & Persson, 2005b). The emergent Allee effect may be one explanation for the collapse and lack of recovery that has been observed in stocks of marine top predators (Carscadden, Frank & Leggett, 2001; De Roos & Persson, 2002). In agreement with model predictions, capelin, the main prey fish of cod, has been observed to show decreased per capita fecundity and mean size following the collapse of the North Atlantic cod (Carscadden et al., 2001). A large-scale removal of a fish stock in the Norwegian Lake Takvatn provides another example suggesting alternative states induced by the emergent Allee effect. At the beginning of the study, the population of the numerically dominant fish species (Arctic char) was stunted, with very few individuals growing larger than 25 cm (Fig. 12.5b) (Klemetsen et al., 2002). Following the removal of more than 70% of the Arctic char during the late 1980s, individual growth rate increased drastically, leading to a shift towards larger individuals in the size distribution that still persists (Fig. 12.5b). Despite the reduction of the Arctic char population, population fecundity increased substantially to more than six times the original population fecundity, thus showing strong elements of an overcompensatory effect. Following the reduction in char numbers, its main predator, brown trout, which was very rare at the start of the experiment, has increased in numbers by 30 times. Thus, the data for both predator and prey all support the contention that the dynamics of this system may involve an emergent Allee effect. The trait that individuals grow over their life cycle will affect the dominant interaction they experience between competitive and predatory interactions resulting in life-history omnivory (Werner & Gilliam, 1984; Lasenby, Northcote & Fu¨rst, 1986; Persson, 1988; Wilbur, 1988). For size-structured omnivorous (intraguild predation) systems, food-dependent development has been shown to reduce the scope for coexistence between top predator and intermediate consumer compared to unstructured models or structured models where transitions between stages is not food (or density) dependent (van de Wolfshaar, 2006). In systems with life-history omnivory where the top predator competes with the intermediate consumer at small sizes (, effect) but preys on it at larger sizes (þ, effect), model results and field data suggest that very different size distributions of the predator and prey will develop depending on environmental conditions (for example, productivity). Modelling results suggest that the growth of young (young-of-the-year) top predators will generally be slower in the presence of the intermediate consumer than in its absence, showing an interspecific competitive effect of the intermediate consumer on juvenile predators (Figs. 12.6a, b). In contrast, the effects on the growth of larger size classes of the top predator can be qualitatively different, with both an increase as well as a decrease in the maximum size of the top predator in the presence of the intermediate consumer compared with in its

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Figure 12.6 Above: model predictions of size distributions of top predator (TP) where the maximum size achieved is increased (a) or decreased (b) in the presence of the intermediate consumer compared with when the intermediate consumer is absent (arrows TP alone). In both cases the sizes of one-year-old (OYO) top predators are smaller in the presence of the intermediate consumer than in its absence (arrows OYO) (from van de Wolfshaar, 2006). Below: different size distributions of perch in moderately productive Lake N. Bolmen (c) and highly productive Lake So¨vdeborg (d) (data from Persson, 1983).

absence (Figs. 12.6a, b) (van de Wolfshaar, 2006). Varying size distributions of perch (top predator) populations coexisting with roach (Rutilus rutilus) (intermediate consumer) have also been observed and attributed to the relative strength of predatory and competitive interactions, respectively (Figs. 12.6c, d) (Persson, 1983; Bystro¨m, Persson & Wahlstro¨m, 1998). The empirical relationship between intermediate consumer abundance and size distribution and top predator abundance and size distribution is presently under investigation. To summarize, size-dependent multispecies interactions exemplified in the tritrophic food chain and in systems with life-history omnivory potentially cause substantially different body-size distributions of communities. Furthermore, size-dependent dynamics clearly affect the stability properties of ecological communities and promote the presence of alternative states. This

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suggests that an explicit consideration of the dynamics of size-dependent interactions may be essential to understand and predict body-size distributions in many systems.

Extensions to more complex configurations The results presented above show that size-dependent processes have important implications for the dynamics and structure of ecological communities. Sizestructured interactions may promote the likelihood of alternative states in terms of both species composition (presence/absence) as well as size distributions of coexisting species. Still, the model complexity and parameter richness of the consumer-resource model considered above that forms the basis for many of the results discussed here, will limit the extent to which these models can be expanded to multispecies configurations. Since many of the questions raised in the body-size literature deal with multi-species systems, there is a need for simpler modules that can handle more speciose systems but still incorporate essential aspects of the individual’s life history, especially food-dependent growth. Recently, a model-building block based on stages, termed a ‘structured biomass community module’ has been developed that accounts for fooddependent development and maturation (De Roos et al., unpublished). This modelling approach parallels the bioenergetics population models developed by Yodzis and Innes (1992) for non-structured populations. Compared with the consumer-resource model considered above, the dimensionality of the system is heavily reduced to a two-stage (juveniles, adults) model. Both juvenile and adult consumption is assumed to follow a Type II functional response with a maximum ingestion rate Imax and a half saturation constant H. The net production per unit of biomass for adult ( a) and juveniles (vj), respectively, is given by: R va ¼ qImax HþR T R T vj ¼  Imax HþR

(12:1)

q represents the difference between adults and juveniles in time spent foraging on the resource. It is assumed that ingestion and metabolic rate scale linearly with body mass. Ingested energy is assimilated with an efficiency , and assimilated energy is first used to cover maintenance T. The net energy left is transformed into consumer biomass. For a system with juveniles (J) investing all their net energy into growth and adults (A) investing all their net energy into reproduction, the dynamics of the system takes the following form:

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dJ ¼ aþ A þ j J   jþ J  J J dt dA þ ¼ va A  v þ a A þ  v j J  A A dt dR R ¼   R  ðImax J þ qImax AÞ dt HþR

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Juvenile biomass increases through recruitment (aþ A) and growth in biomass ( jJ) and decreases due to maturation to the adult stage ( jþ J) and mortality (JJ). Adult biomass increases through maturation of juveniles ( jþ J) and decreases due to mortality (AA). aþ A can only take positive values and ensures that no reproduction in adults takes place if resource levels are too low to sustain maintenance. Similarly,  jþ J ensures that no maturation takes place if resource levels are too low.  is resource productivity and  resource turn-over rate. The maturation function  is dependent on juvenile mortality, newborn and adult size, and the net production per unit body mass of juveniles,  j. The structured biomass community model is derived through the formulation of a physiologically structured population model and also yields the same equilibrium results as the latter. Analyses show that the multiple equilibria resulting from the emergent Allee effect, emergent facilitation and ontogenetic niche shifts are also present in this more aggregated biomass community model (De Roos et al., unpublished). With a body-size perspective, this more aggregated module thus has the potential to allow an investigation of size-structured induced shifts in body-size distributions in many species systems.

Conclusions As evident in our retrospective overview, growth and development is a major feature of many organisms on Earth, hence the implications of this for individual, population, community and ecosystem processes can hardly be neglected. This circumstance has also been recognized in the most recent body-size literature (Woodward et al., 2005; Woodward & Warren, this volume). As discussed in this chapter, growth and development take different forms in different organisms, but one dividing line can be seen along the ectothermy–endothermy gradient. Theoretical studies suggest that a critical element giving rise to the various size-dependent patterns is food-dependent development per se and not whether organisms continue to grow in somatic size over their whole life period (De Roos et al., 2003b; De Roos et al., unpublished). That is, whether individuals continue to grow in somatic tissue or allocate all their net energy into reproduction after maturation is not a factor affecting the presence of, for example, the emergent Allee effect. The recent body-size literature has emphasized the need to document sizedependent interactions at the level of individuals, with the main purpose of reducing biases in estimates of predator/prey (parasitoid/host) ratios (Cohen

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et al., 2005). The investigation of individual size scaling of foraging rates in particular, was a significant area of research 20 years ago including the development of individual level models (Werner & Gilliam, 1984). The development of the framework of physiologically structured population models with its two-level (individual, population) representation has made it possible formally to connect size-dependent individual-level processes to the population level, which, in turn, has allowed us to start to answer questions about the effects of body-size scaling for population and community dynamics and its feedbacks on body-size distributions. The insights gained so far from these analyses concern both dynamical aspects and equilibrium properties. As an example of the former, studies of size-structured consumer-resource systems show that cohort cycles are the most common outcome of consumerresource interactions (Persson et al., 1998). Furthermore, these cohort cycles are not restricted to systems with few species but are also present in manyspecies systems; hence the non-equilibrium dynamics resulting from cohort dynamics cannot be ignored in a food-web context (Murdoch et al., 2002). Correspondingly, the presence of temporal variation in body-size distribution is increasingly recognized in the body-size literature (Stead et al., 2005; Woodward et al., 2005). Studies of multitrophic systems show that size-dependent processes will give rise to alternative equilibrium states with major ramifications for overall bodysize distributions (De Roos & Persson, 2002; De Roos et al., 2003a). Given the common observation of food-dependent development in organisms, we argue that approaches not incorporating food-dependent development may have a limited capacity to yield both understanding of, and useful predictions, about the dynamics and structure of ecological communities. A major challenge for the future is to develop approaches that allow the analyses of more complex configurations in terms of the number of species present, but still encompass major processes resulting from ontogenetic development (De Roos et al., unpublished). Such approaches should also make it possible to provide new insights about the community dynamics based on a relatively limited number of intraspecific size-scaling parameters along the lines of the body-size based trophic dynamic models developed for interspecific interactions by Yodzis and Innes (1992).

Acknowledgements We thank the organizers for inviting us to the British Ecological Society meeting on the effects of body size in aquatic systems. The research based on which this overview was written has been supported by the Swedish Research Council and the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning to L. Persson, and the Netherlands Organization for Scientific Research to A. M. De Roos.

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Polis, G. A. (1988). Exploitation competition and the evolution of interference, cannibalism, and intraguild predation in age/size-structured populations. In Size-Structured Populations – Ecology and Evolution, ed. B. Ebenman and L. Persson. Berlin: Springer, pp. 185–202. Polis, G. A., Myers, C. & Holt, R. (1989). The ecology and evolution of intraguild predation: potential competitors that eat each other. Annual Review in Ecology and Systematics, 20, 297–330. Ricklefs, R. E. (1973). Patterns of growth in birds. II. Growth rate and mode of development. Ibis, 115, 177–201. Sanderson, B. L., Hrabik, T. R., Magnuson, J. J. & Post, D. D. (1999). Cyclic dynamics of a yellow perch (Perca flavescens) population in an oligotrophic lake: evidence for the role of intraspecfic interactions. Canadian Journal of Fisheries and Aquatic Sciences, 56, 1534–1542. Sauer, J. R. & Slade N. A. (1987). Size-based demography of vertebrates. Annual Review in Ecology and Systematics, 18, 71–80. Sebens, K. P. (1982). The limits to indeterminate growth: an optimal model applied to passive suspension feeders. Ecology, 63, 209–222. Sebens, K. P. (1987). The ecology of indeterminate growth in animals. Annual Review in Ecology and Systematics, 18, 371–407. Shin, Y. J., Rochet, M., Jennings, S., Field, J. G. & Gislason, H. (2005). Using size-based indicators to evaluate ecosystem effects of fishing. ICES Journal of Marine Science, 62, 384–396. Shiomoto, A., Tadokoro, K., Nagasawa, K. & Ishida, Y. (1997). Trophic relations in the subArctic North Pacific ecosystem: possible feeding effect from pink salmon. Marine Ecology Progress Series, 150, 75–85. Sinko, J. W. & Streifer, W. (1967). A new model for age-size structure of a population. Ecology, 48, 910–918. Stead, T. K., Schmid-Arya, J. M., Schmid, P. E. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487.

Stearns, S. C. (1992). The Evolution of Life Histories. Oxford: Oxford University Press. Townsend, C. R., Sutherland, W. J. & Perrow, M. R. (1990). A modelling investigation of population cycles in the fish Rutilus rutilus. Journal of Animal Ecology, 59, 469–485. van de Wolfshaar, K. E. (2006). Population persistence in the face of size-dependent predation and competition interactions. PhD thesis, University of Amsterdam. Werner, E. E. (1986). Species interactions in freshwater fish communities. In Community Ecology, ed. J. Diamond and T. J. Case. New York: Harper & Row, pp. 344–358. Werner, E. E. (1988). Size, scaling and the evolution of complex life cycles. In Size-Structured Populations – Ecology and Evolution, ed. B. Ebenman and L. Persson. Berlin: Springer, pp. 60–81. Werner, E. E. (1994). Ontogenetic scaling of competitive relations: size-dependent effects and responses in two Anuran larvae. Ecology, 75, 197–231. Werner, E. E. & Gilliam, J. F. (1984). The ontogenetic niche and species interactions in size-structured populations. Annual Review in Ecology and Systematics, 15, 393–425. West, G. B., Brown, J. H. & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276, 122–126. Wilbur, H. M. (1988). Interactions between growing predators and growing prey. In SizeStructured Populations – Ecology and Evolution, ed. B. Ebenman and L. Persson. Berlin: Springer, pp. 157–172. Wilson, D. S. (1975). The adequacy of body size as a niche difference. American Naturalist, 109, 769–784. Woodward, G., Ebenman, B., Ernmerson, M. et al. (2005). Body size in ecological networks. Trends in Ecology and Evolution, 20, 402–409. Yodzis, P. & Innes, S. (1992). Body size and consumer resource dynamics. American Naturalist, 139, 1151–1175.

CHAPTER THIRTEEN

The consequences of body size in model microbial ecosystems OWEN L . PETCHEY University of Sheffield

ZACHARY T . LONG University of North Carolina at Chapel Hill Virginia Institute of Marine Science

PETER J . MORIN Rutgers University

Introduction Patterns in the sizes of coexisting organisms have always intrigued ecologists (Hutchinson, 1961). Some kinds of regularities are well known for some systems (Sheldon, Prakash & Sutcliffe, 1972), and are less appreciated or rediscovered for others (Enquist & Niklas, 2001; Cohen, Jonsson & Carpenter, 2003). One example of this kind of pattern is the apparent constancy of total biomass within different size fractions of organisms living in aquatic communities (Sheldon, et al. 1972; Cyr, 2000; Kerr & Dickie, 2001; Cohen et al., 2003; Sheldon, Sutcliffe & Paranjape, 1977; Tilman et al., 2001; Mulder et al., 2005). Essentially, over many orders of magnitude of organism size, any particular size class holds about the same total biomass of organisms per unit volume. The result is an inverse relationship between the log of organism size and the log of organism abundance per unit volume, with a slope of 1. The apparent constancy of this relationship has even led some workers to suggest, tongue in cheek, that it could be used to estimate the population size of some organisms that have proven to be notoriously difficult to observe, once assumptions about their average size were made (Sheldon & Kerr, 1972, 1973). Whether or not the elusive Loch Ness Monster (to which these calculations were rather whimsically applied) actually exists, it appears that the total biomass of organisms in some habitats is fixed by certain features of the habitat, most likely the abundance of incoming energy and nutrients that drive productivity (Sheldon et al., 1977; Cyr, 2000; Kerr & Dickie, 2001; Cohen et al., 2003; Mulder et al., 2005). A recent flurry of research on the allometry of metabolism seeks to explain such patterns mechanistically as a consequence of the ways that organisms capture and transport energy and material (Brown, 2004). It is worth noting that none of these patterns suggest that diversity, the number of different organisms that total biomass is divided among, should necessarily influence the total standing stock of biomass supported by a particular environment and its energetic regime. Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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Independently of this line of inquiry, ecologists have suggested that the total biomass of particular subgroups of organisms, plants for instance, can increase as the diversity of organisms within that group increases (Hector et al., 1999; Tilman et al., 2001). For this pattern to square with the pattern of constant total biomass observed in natural systems, one of several things must hold. (i) Natural communities may be at the maximum diversity that a particular habitat will support – and the communities where diversity-dependent biomass increases are seen must be below that level of diversity. (ii) An increase in the diversity and biomass within a particular size fraction of the community will produce a corresponding increase in the biomass of size fractions in the remainder of the community – an interesting but little explored phenomenon. Some of the work that we describe here was initially conceived and conducted to evaluate critiques of early biodiversity experiments, specifically to determine whether what are now known as selection effects caused by the chance occurrence of larger organisms can explain patterns of increased biomass in more diverse systems. While it seems likely that such transient effects could arise as a consequence of initial conditions, the size invariance of productivity and biomass noted above make it seem unlikely that such differences would persist for long in communities after population densities of organisms respond and adjust to the availability of energy and nutrients. To address these ideas we first ask if diversity per se can change the size–population abundance relationship within communities and among experiments. Second, we ask whether communities initially constructed of organisms of very different size would rapidly converge in biomass. Finally, we investigate the consequences of body size for an ecosystem-level process: whole community metabolism. Specifically, we test the hypothesis that the metabolism of a given biomass will depend on whether the biomass is divided up among lots of small individuals or just a few large ones. Why investigate these consequences using data from model microbial ecosystems? Microbial microcosms can contain organisms with a wide range (about seven orders of magnitude) of organism size. The organisms used in our microcosms also fill a wide range of trophic roles, including photoautotrophs, decomposers, primary consumers and secondary consumers. This allowed us to evaluate effects of size across multiple trophic levels, thereby extending the analysis beyond primary producers (Duffy, 2002; Petchey et al., 2004). Additionally, these organisms have generation times ranging from hours to days. This allows for rapid population dynamics, such that an experiment encompassing many generations of population dynamics can take place in a few weeks. Properly testing the predictions of allometric theory may require multiple generations because it may take many generations for changes in population sizes due to thinning or density compensation to occur, so that initial conditions, transient dynamics, and potential selection effects may be less important. We could also limit the effect of the environment on abundance and yield by holding environmental conditions

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

constant (Gillooly et al., 2001; Savage et al., 2004). Conversely, controlled manipulation of environmental conditions, particularly temperature, allows investigation of how it alters the consequences of body size.

Methods General methods The analyses presented here draw on data from four experiments that share much methodology in common. In all, experimental communities were 240–250 ml glass or pyrex jars each containing 100 ml of nutrient medium (1 litre of well water, 0.55 g Carolina Biological Supply Protozoan Pellet, and 2–6 wheat seeds) housed in incubators at 188C unless otherwise stated below. This medium was first autoclaved and then inoculated with three or four species of bacteria (Serratia marcescens, Bacillus subtilus, B. cereus and sometimes Proteus vulgaris). To this basal food-web level were added various combinations of the protist (algae, ciliates and sarcodines) and small metazoans (rotifers) that were kept in laboratory stock cultures. Bacterivores and autotrophs were typically added before predators and herbivores, to allow resources to grow to levels that could sustain consumers. The experiments lasted six or seven weeks and were sampled between two and six times. All analyses are of only the last week of collected data. Sampling involved swirling the microcosms to homogenize the distribution of organisms, removal of first 0.3 ml and then potentially 5 ml of media. The number of individuals of each species was recorded in the smaller volume and if some species were not observed the larger volume was searched. Autotrophs were sampled by a third method: enumeration using a haemocytometer, with a minimum detection threshold of approximately 104 ml1. All counts were transformed into number of individuals per ml to give the population density of each species in each community. Cell size (mass here) was estimated from linear dimensions of up to ten cells of each species and the rough shape of the cells (Wetzel & Likens, 1991). Transformation of the linear dimensions to volume, and assumption of 1 mm3 ¼ 1 milligram resulted in the mass of each cell and is reported in milligrams here. Some variation in cell size occurs during the growth of protist populations and can also result from changes in environmental conditions that occur during an experiment (e.g. depletion of available resources) or from experimental treatments (e.g. a cool versus warm environment). Though here we ignore this intraspecific variation in cell mass, it seems unlikely that it could invalidate the analyses of many orders of magnitude of interspecific variation in cell mass presented. Choice of species One might argue that studying the consequences of body size in communities with artificial body-size distributions is meaningless. We do not believe this is the case. First, all of the species in our laboratory stocks potentially co-occur in natural aquatic communities and so are not necessarily evolutionarily and ecologically

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naı¨ve to each other. Consequently, the community and ecosystem properties that emerge result from similar ecological interactions as might occur in natural systems. Second, in each of the four experiments analyzed, the species present in particular communities were selected at random from the laboratory pool. The frequency distribution of body sizes in this pool is approximately log-normally distributed (unpublished data). It therefore seems unlikely that we have biased body-size distributions by choice of particular species. However, extinctions often occur during an experiment and alter community composition (Weatherby, Warren & Law, 1998; McGrady-Steed & Morin, 2000). Presumably this change in composition results from ecological interactions and influences body-size distributions and their consequences. Third, because the experiments are long relative to the generation time of the organisms, great changes in population size occur. For example, a bacterivores species may initially occur at ten individuals per ml, but in a week have multiplied to thousands of individuals per ml. So although cellsize distributions are somewhat constrained, population densities, population biomasses and ecosystem process rates are emergent. Description of the four experiments and data sets

Experiment 1 This experiment was designed to address two questions (Long & Morin, 2005). First, whether diversity or the size of dominant species affects ecosystem functioning, and second, how effects changed in importance through time. Food webs were assembled using two size fractions (small species or large species) and two levels of diversity (four or nine species) using autotrophic and heterotrophic species of protist and small metazoan. The two size fractions of organisms differed in average cell mass by approximately two orders of magnitude. There were two different community compositions in the low diversity food webs. The resulting six food webs were replicated five times. Population densities were measured once a week for each of the six weeks of the experiment. Experiment 2 The experiment was designed to investigate the relationship between biodiversity and ecosystem functioning and the variability of ecosystem functioning, and is described in detail elsewhere (McGrady-Steed, Harris & Morin, 1997). There were 10 different communities with from 3 to 31 autotrophic and heterotrophic species of protists and small metazoans distributed among multiple trophic levels. There were five replicates of each community, and population densities were recorded at least once a week for six weeks. Experiment 3 This experiment was designed to examine the effects of environmental warming on ecological communities (Petchey et al., 1999). There were four different

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

communities (two compositions at two diversity levels) and an environmental warming treatment (constant temperature or warmed). Five replicates of each treatment combination made a total of 40 microcosms. Population densities were sampled in the second and sixth week of the experiment.

Experiment 4 This experiment tested the insurance hypothesis: that biodiversity stabilizes aggregate community and ecosystem properties (Petchey et al., 2002). There were four diversity levels (two, four, six, and eight species) and four compositions at each level. This is the only experiment that contained a single trophic level of protist species (bacterivores). In addition, there were three environmental variability treatments (constant temperature, fast temperature fluctuations and slow temperature fluctuations). Population densities and CO2 flux were estimated in the second and sixth week of the experiment. Population consequences of body size We analyzed the relationship between cell mass and population size within and across the four experiments using three separate analysis of covariance models. In all analyses, data points were averages of the values of a species across the replicates of each treatment combination in which it occurred. That is, there is only one data point per species per treatment combination. All analyses included log 10 abundance as the response variable, and log 10 body size as a continuous explanatory variable. The first model included three data sets (Experiments 1, 2, 3) but only constant temperature regimes. The explanatory variables were trophic group (categorical, five levels, autotroph, bacterivores, herbivores, omnivores, predators), experiment (categorical, three levels, 1, 2, 3) and species richness (continuous). The second model included only the data set from Experiment 3 and explanatory variables were environment (categorical, two levels, constant temperature and higher temperature) and species richness (continuous). The third model included only the data set from Experiment 4 and explanatory variables of environment (categorical, three levels, constant temperature, fast varying temperature, slow varying temperature) and species richness (continuous). Significant interaction terms between body mass and another explanatory variable would indicate that variables affect the population consequences of body size. All interaction terms were initially included and backwards elimination by Akaike Information Criterion (AIC) and F-test were used to find the minimum adequate model (Crawley, 2002). Community consequences of body size Food webs that receive similar amounts of energy should reach similar levels in total biomass, regardless of differences in organism size found among different food webs (Damuth, 1981, 1987; Brown & Gillooly, 2003; Brown, 2004; Mulder

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et al., 2005). If this occurs, distinct food webs that experience similar abiotic conditions should fall on the single constant yield line described by log Ntotal ¼ log b  log Maverage, where Ntotal is the total number of individuals in a community, Maverage is the average mass of an individual in a community, and b reflects environmental influences like resource supply rates and temperature. The slope of 1 means that a community containing cells twice the average mass of those in another community will contain half the number of individuals. Consequently, differences in the mass of individuals are accompanied by opposite and perfectly compensatory changes in the number of individuals. To test this hypothesis we used the same three analyses as described earlier except: log 10 Ntotal was the response variable, log 10 Maverage was the continuous explanatory variable, datapoints were communities (rather than species), and there was no ‘trophic group’ categorical variable. Ecosystem consequences of body size Metabolic rate scales with individual mass0.75 (Peters, 1983; Damuth, 1987; West, Brown & Enquist, 1997) and consequently lots of small individuals should have higher total metabolism than just a few large ones, even if they represent the same amount of total biomass. Of course, the microbial communities that we analyze are composed of a mixture of small or large individuals, so we predict community metabolism from the size and abundance observed for each of the species in the community. This prediction is compared with observed flux of CO2, a measure of whole community metabolism. Observed ecosystem level CO2 flux was estimated using a closed-circuit microrespirometer (Micro-oxymax, Columbus Instruments, OH, USA). This measures the CO2 concentration in the gas above the liquid in the sealed culture vessels at multiple discrete times, and flux can be calculated from these measures. Concentrations were measured during at least an eight-hour period and flux averaged across that. Can the total biomass or body sizes of the organisms in the community in a particular vessel predict ecosystem-level CO2 flux? To test this we assumed that CO2 flux is proportional to community metabolism (CM) and this is the sum of the metabolism of all the individuals in the community. We limit the analyses to the data from the constant temperature replicates of the only experiment that included only heterotrophic species (Experiment 4). The other three experiments all contained autotrophs. If the individuals are grouped into species, community metabolism is the sum of the species’ metabolisms, where a species’ metabolism is the sum of the metabolisms of the individuals of that species:

CM ¼

s X i¼1

Ni  Mi ;

(13:1)

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

where Ni is the number of individuals of species i, Mi is the metabolism of an individual of species i, and s is the number of species in the community. An individual’s metabolism is related to its body size by allometry such that Mi ¼ b  B0:75 ; i

(13:2)

were Bi is the body size of species i and b is a constant converting mass to energy per second. Consequently, CM ¼ b

s X

Ni  B0:75 i

(13:3)

i¼1

This prediction for community metabolism (CO2 flux) was compared to the explanatory power of total biomass using linear regression by ordinary least squares.

Results Population consequences of body size – results In each of the three analyses of the relationship between cell mass and population density (the mass–density relationship), cell mass was very strongly and relatively linearly related to population size (Figs. 13.1, 13.2 and 13.3). However, the slope differed greatly between the first two analyses and the third analysis (0.93, 0.95 and 0.52, respectively) (Tables 13.1, 13.2 and 13.3). Communities in the third analysis contained only one trophic level, while all of the communities in the first and second contained species at several trophic levels. However, effects of trophic group on the mass-density relationship within the first two analyses were inconsistent with this between analysis difference. In the first, slopes differed between trophic groups, with the slope becoming shallower from autotrophs, to bacterivores, to omnivores (Table 13.1). In the second analysis, trophic group had a marginally significant effect on the intercept (but not the slope), with bacterivores having the steepest slope and omnivores the shallowest (Table 13.2). The species richness of the community had a significant negative effect on the intercept of the mass–density relationship in analysis one (Figure 13.1, Table 13.1). This is a signature of density compensation, in which populations within less species-rich communities are on average denser than when in richer communities (McGrady-Steed & Morin, 2000; Petchey et al., 2002); density compensation can occur because species compete for similar resources and are therefore somewhat redundant. Density compensation was not evident in analysis two or three where there was no significant effect of species richness on the slope or intercept of the mass–density relationship (Figs. 13.2 and 13.3, Tables 13.2 and 13.3). Perhaps surprisingly, there was no evidence that environment conditions altered the slope or intercept of the mass–density relationship. In analysis

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(b) 2 species 6 species 10 species 14 species 18 species

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Figure 13.1 Size-abundance relationship for analysis one, which tests for influence of (a) species richness, (b) species trophic position, and (c) experiment on the slope of relationship.

two, the 12 8C difference in temperature between normal and warmed communities had no significant effect (Fig. 13.2, Table 13.2), and in analysis three there was no apparent effect of the different temporal patterns of temperature variation (Fig. 13.3, Table 13.3). Community consequences of body size – results The slope of the relationship between total density and mean cell mass was 0.93 in analysis one (Fig. 13.4), 0.81 in analysis two (Fig. 13.5) and 0.35 in analysis three (Fig. 13.6). Again, results were therefore more similar in communities that contained species from multiple trophic levels (analyses one and two) compared with communities containing only one trophic level. The exponent for all communities in analysis one was not different from unity, indicating that the

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

(b) 2 species 6 species 10 species 14 species

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Low temperature High temperature 6

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Figure 13.2 Size-abundance relationship for analysis two, which tests for influence of (a) species richness, (b) species trophic position, and (c) environmental temperature on the slope of the relationship.

communities reside on the constant yield line and total biomass was not a function of the size distribution of individuals. However, the slopes in analysis two and three were significantly less than unity, indicating that communities containing larger individuals contained greater total biomass. Species richness tended to increase the intercept of the relationship between average mass and total density in both analysis one and three (Figs. 13.4 and 13.6; Tables 13.4 and 13.6). This indicates that more speciose communities contain greater total biomass than less rich communities and has been observed directly in these communities before (McGrady-Steed & Morin, 2000; Petchey et al., 2002). This could result from a variety of mechanisms, including complementarity among species and more probabilistic processes (Loreau et al., 2001).

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Table 13.1 Summary of analysis one of the population consequences of body size on population density, the response variable. M ¼ body mass, S ¼ species richness, T ¼ trophy, TB ¼ bacterivores, TO ¼ omnivores. M:T ¼ interaction term between M and T. * ¼ p < 0.05; ** ¼ p < 0.01; *** ¼ p < 0.001. Analysis of variance (ANOVA) table

M S T M:T Residuals

Df

Sum sq

Mean sq

F value

Pr(>F)

1 1 2 2 186

482.36 4.34 8.35 5.26 111.43

482.36 4.34 4.17 2.63 0.60

805.1509 7.2508 6.9687 4.3883

<2.2e  16*** 0.007734** 0.001207** 0.013734*

Coefficients

(Intercept) M S TB TO M:TB M:TO

Estimate

Std. error

t value

Pr(>|t|)

0.84994 0.92967 0.04101 0.22936 1.25460 0.13027 0.43899

0.42476 0.06802 0.01331 0.50877 0.54686 0.09105 0.14999

2.001 13.668 3.081 0.451 2.294 1.431 2.927

0.04685* <2e  16*** 0.00237** 0.65265 0.02290* 0.15420 0.00385**

2 species 4 species 6 species 8 species

4 3 2

Log10(Density per ml)

(b)

(a)

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Constant Fast variation Slow variation

4 3 2 1

1

–7

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Log10(Cell mass (mg))

–2

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–5 –4 –3 Log10(Cell mass (mg))

Figure 13.3 Size-abundance relationship for analysis three, which tests for influence of (a) species richness, (b) environmental variability on the slope of the relationship.

–2

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

Table 13.2 Summary of analysis two of the population consequences of body size on population density, the response variable. M ¼ body mass, T ¼ trophy, TB ¼ bacterivores, TO ¼ omnivores. ANOVA table

M T Residuals

Df

Sum sq

Mean sq

F value

Pr(>F)

1 2 181

625.23 5.25 142.27

625.23 2.62 0.79

795.4230 3.3367

<2e  16*** 0.03775*

Coefficients Estimate 1.38488 0.94759 0.26031 0.24933

(Intercept) M TB TO

Std. error 0.27125 0.04251 0.14711 0.24332

t value 5.105 22.291 1.769 1.025

Pr(>|t|) 8.3e  07*** <2e  16*** 0.0785 0.3069

Table 13.3 Summary of analysis three of the population consequences of body size on population density, the response variable. M ¼ body mass. ANOVA table

M Residuals

Df

Sum sq

Mean sq

F value

Pr(>F)

1 173

123.164 89.290

123.164 0.516

238.63

<2.2e  16***

Coefficients

(Intercept) M

Estimate

Std. error

t value

Pr(>|t|)

0.15208 0.52241

0.16945 0.03382

0.898 15.448

0.371 <2e  16 ***

There was an interaction between this effect and ‘experiment’ in analysis one: there was no biomass increase due to species richness in the warming experiment data. Analysis two showed a significant three-way interaction between average mass, species richness and environment, indicating that the slope of the relationship depended on the interaction of species richness and environmental temperature. In the warming experiment, the large and directional changes in average cell mass that occurred when warmed communities lost their large top predator

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(b)

2 species 6 species 10 species 14 species 18 species

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Figure 13.4 Relationships between total density and average cell size of the individuals in a community in analysis one, coded by (a) species richness and (b) experiment.

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(b) 2 species 6 species 10 species 14 species

7.0

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Log10(Average cell mass (mg))

Figure 13.5 Relationships between total density and average cell size of the individuals in a community in analysis two, coded by (a) species richness and (b) temperature.

species suggest that analysis of covariance (ANCOVA) may not be the most appropriate method of analysis, because of covariation between explanatory variables. Ecosystem consequences of body size – results Predicted community metabolism was positively related with total community biomass (Fig. 13.7a). However, there were three unusual communities with greater than 1 mg biomass per ml of media (this equates to about 0.1% of the culture volume occupied by organisms), while the remaining communities

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

Table 13.4 Summary of analysis one of the community consequences of body size on total community biomass. The response variable is total community density. M ¼ body mass, S ¼ species richness, E ¼ Experiment 1, E2 ¼ Experiment 2, E3 ¼ Experiment 3. ANOVA table

M S E S:E Residuals

Df

Sum sq

Mean sq

F value

Pr(>F)

1 1 2 2 93

82.631 3.085 3.058 0.828 5.610

82.631 3.085 1.529 0.414 0.060

1369.7640 51.1433 25.3445 6.8662

<2.2e  16*** 1.923e  10*** 1.638e  09*** 0.001655**

Coefficients

(Intercept) M S E2 E3 S:E2 S:E3

Estimate

Std. error

t value

Pr(>|t|)

0.37009 0.91873 0.12799 0.13487 0.74098 0.06112  0.12586

0.24455 0.03881 0.05476 0.23196 0.28869 0.05607 0.05855

1.513 23.670 2.337 0.581 2.567 1.090 2.150

0.1336 <2e  16*** 0.0216* 0.5624 0.0119* 0.2786 0.0342*

(a)

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Log10(Density per ml)

4.5 4.0 3.5 2 species 4 species 6 species 8 species

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–6.0

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–4.5

Log10(Cell mass (mg))

–4.0

–6.5

–6.0

–5.5 –5.0 –4.5 –4.0 Log10(Cell mass (mg))

Figure 13.6 Relationships between total density and average cell size of the individuals in a community in analysis three, coded by (a) species richness and (b) environmental fluctuations. Arrows show the communities in Fig. 13.3 that have unusually high (>1 mg ml1) total biomass.

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Table 13.5 Summary of analysis two of the community consequences of body size on total community biomass. The response variable is total community density. M ¼ body mass, S ¼ species richness, E ¼ environmental warming treatment, Ew ¼ warmed. ANOVA table

M S E M:S M:E S:E M:S:E Residuals

Df

Sum sq

Mean sq

F value

Pr(>F)

1 1 1 1 1 1 1 32

11.0975 0.0022 0.2561 0.1847 0.1634 0.0432 0.2138 0.8428

11.097 0.0022 0.2561 0.1847 0.1634 0.0432 0.2138 0.0263

421.3570 0.0843 9.7256 7.0116 6.2034 1.6387 8.1185

<2.2e  16*** 0.773437 0.003829** 0.012466* 0.018131* 0.209700 0.007601**

Coefficients

(Intercept) M S Ew M:S M:Ew S:Ew M:S:Ew

Estimate

Std. error

t value

Pr(>|t|)

0.53928 0.91835 0.13457 10.74478 0.02363 1.44316 1.03664 0.14428

1.76310 0.2545 0.24425 2.88291 0.03724 0.39465 0.35082 0.05064

0.306 3.608 0.551 3.727 0.635 3.657 2.955 2.849

0.761685 0.001039** 0.585502 0.000749*** 0.530111 0.000909*** 0.005827** 0.007601**

contained less than 0.1 mg per ml (Fig. 13.7a). While the positive relationship between biomass and predicted metabolism persisted among the communities with less than 1 mg per ml, there were also communities with very similar total biomass but different predicted metabolism (Fig. 13.7b). That two communities with equal total biomass have very different levels of metabolism must result from differences in the size distributions between those communities. Higher metabolism for a given biomass results if a community contains mostly small individuals in contrast to communities that contain mostly large individuals. Across all of the communities, total biomass and predicted metabolism explained very similar amounts of variation in observed metabolism (measured by respirometry) (Figs. 13.7c & 13.e). They both explained about 45% of the variation in observed metabolism and were both significant at p ¼ 0.01. Analyzing on the communities with less than 1 mg per ml revealed different results. Here, total community biomass had very little explanatory power

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

Table 13.6 Summary of analysis three of the community consequences of body size on total community biomass. The response variable is total community density. M ¼ body mass, S ¼ species richness. ANOVA table

M S Residuals

Df

Sum sq

Mean sq

F value

Pr(>F)

1 1 69

3.2283 2.8076 9.9136

3.2283 2.8076 0.1437

22.469 19.541

1.109e  05*** 3.575e  05***

Coefficients

(Intercept) M S

Estimate

Std. error

t value

Pr(>|t|)

1.62628 0.37154 0.12205

0.39459 0.07407 0.02761

4.121 5.016 4.421

0.000103*** 3.93e  06*** 3.58e  05***

(Fig. 13.7d, r2 ¼ 0.08, p ¼ 0.38) while predicted community metabolism explained 35% of the variance in observed community metabolism and was marginally significant (p ¼ 0.04).

Discussion Population consequences of body size – discussion Brown and Gillooly (2003) hypothesize that the slope of the relationship between body size and population abundance will be shallower when measured across species that share a common resource pool (e.g. with an exponent of 0.75) and steeper when species acquire resources from different sources, in particular, when species occupy multiple trophic levels and therefore forage on each other (e.g. with an exponent of 1). The inefficiency of energy transfer from a lower to higher trophic level means that less energy is available to species at the higher level, and consequently their abundance should be lower relative to their biomass. We found some support for this hypothesis, but there was also evidence that was inconsistent with this idea. Analyses of communities that contained multiple trophic levels (analysis one and two) revealed much steeper mass–density relationships than in the communities that contained only species that consumed bacteria (analysis three). This is consistent with the hypothesis. In contrast, analyses of mass–density relationships within communities (i.e. within analysis one and two), did not consistently show that species at higher trophic levels (classed as omnivores here) had lower intercepts (and the same slope) as species at lower trophic levels (the bacterivores). We are uncertain about what

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(b) 4

Predicted CO2 flux

Predicted CO2 flux

(a)

3 2 1 0

1.5 1.0 0.5 0.0

0.0

0.4

0.8

1.2

0.00

Community biomass (d)

r2 = 0.48; p = 0.004

4.0

3.0

2.0 0.0

0.4

0.8

3.0

2.5

2.0

1.2

0.0

(f)

Observed CO2 flux

4.0

3.0

2.0 1

2

3

Predicted CO2 flux

0.04

0.08

Community biomass

r2 = 0.43; p = 0.008

0

0.08

r2 = 0.08; p = 0.38

Community biomass (e)

0.04

Community biomass

Observed CO2 flux

Observed CO2 flux

(c)

Observed CO2 flux

260

4

r2 = 0.35; p = 0.04 3.0

2.5

2.0

0.0

0.5

1.0

1.5

Predicted CO2 flux

Figure 13.7 Relationships between total community biomass, total community metabolism and predicted community metabolism (measured as CO2 flux). The left column of graphs contains all available data, the right column excludes the three communities with very high biomass that are obvious in (a). The explanatory power (r2) and statistical significance of linear regression is given for the lower four graphs only.

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

caused this difference in results between the two levels of comparison (between communities versus within communities). It is possible that classification of the species as bacterivores and omnivores is too simplistic and that accounting for more fine-scale differences in their trophic strategies would change the results of within-community level analyses. It is also possible that some of our findings can be explained by processes that are not included in classic allometric theory, such as the effect body size has on the diets of consumers, and therefore their potential sources of energy (Marquet, Navarette & Castilla, 1995; Carbone & Gittleman, 2002; Loeuille & Loreau, 2006). Theory predicts that equilibrium abundances will be lower at higher temperatures (Allen, Brown & Gillooly, 2002; Brown, 2004). Our results are not consistent with theory, because there are no significant effects of environmental temperature in analysis two. Though the analysis of covariance should be interpreted with caution, because of incomplete overlap of explanatory categories on the covariate axis, there was no indication that population density (given body mass) was lowered by a warming event of greater than 10 8C. The explanation for this difference between theoretical expectation and experimental result seems to be that the theory assumes no change in resource supply rate accompanies a change in temperature (Brown & Gillooly, 2003). In our experiments the resources are bacteria, which decompose the organic matter present in the ecosystem. It seems likely that increasing temperatures will increase rates of decomposition, bacterial production and resource supply rates to the protist species. If the scaling of bacterial production with temperature is the same as the scaling of consumer metabolism with temperature, there should be no decrease in equilibrium abundance with increases in temperature. A factorial experimental manipulation of temperature and resource supply rates could separate the effects of both on the population level consequences of body size, but this experiment remains to be done. Community consequences of body size – discussion Links between biodiversity and ecosystem functioning have been alternatively interpreted as consequences of traits of dominant species or diversity per se. Some aspects of functioning (such as productivity or total community biomass) may increase with diversity because more diverse communities may by chance contain larger species, and not because of mechanisms associated with diversity. However, allometric theory predicts that communities receiving the same amount of energy will eventually support the same total amount of biomass, regardless of organism size. Thus, the size of dominant organisms may determine functioning early in community development, but with enough time thinning or increases in density may eliminate size-specific influences on functioning. These hypotheses were supported in a recently published experimental manipulation of body-size distributions in microbial microcosms (Long &

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Morin, 2005). Early in the experiment, total community biomass was lower in communities containing species with small individuals than in communities containing larger individuals. However, after 25–50 generations, there were no detectable differences between the biomass of the two types of community. The results of the analyses presented suggest that certain ecological differences among communities and experiments might affect the relationship between individual size and density, so that the total biomass of all communities is not equal, even if energy supply to the communities is. The first two analyses showed much greater levels of biomass equivalence than the third, in which communities with larger individuals tended to have greater total biomass. One finding that is recovered in our analyses is that communities with greater numbers of species tend to have greater total biomass than those with fewer species (McGrady-Steed & Morin, 2000; Petchey et al., 2002; Hooper et al., 2005). Data in Fig. 13.7 also clearly show that factors other than energy supply must influence total community biomass, because there are three communities with nearly an order of magnitude greater biomass than others. Ecosystem consequences of body size – discussion For a subset of the communities in one of the experiments (Experiment 3) there was evidence that the size distribution of individuals influenced community metabolism, as measured by the amount of CO2 produced by a community during a fixed time. Communities that contained many small individuals tended to have higher metabolism than communities with fewer individuals. It is perhaps surprising that any significant relationships between biomass and community metabolism, and predicted and observed metabolism, were detected considering that a major taxonomic component of the microcosms was completely ignored (the bacteria). Their small size might suggest a very large contribution to community metabolism and future analyses would benefit from taking their size and abundance into account. The evidence was equivocal, however, and further studies are needed to test the robustness and generality of the importance of size distributions for community metabolism. In general, the analyses presented above should be considered preliminary in nature and can perhaps be best used to make recommendations for future experiments. These could include predictions based on the size distribution of individuals within species, as opposed to the assumption made here that all individuals of the same species are the same mass. Furthermore, experiments could manipulate the size distribution of species (and thereby individuals) present in different communities (e.g. Long & Morin, 2005). Here, communities were assembled mostly from species with small sized individuals, or mostly from species with large sized individuals. We did not analyze Long and Morin’s (2005) data in this context because their communities contained photoautotrophs and including their contribution to

CONSEQUENCES OF BODY SIZE IN MODEL MICROBIAL ECOSYSTEMS

community metabolism would have required additional model complexity. This could be included in future models that predict ecosystem process rates from the size and abundance of organisms at multiple trophic levels. Closing remarks This volume contains many valuable contributions towards the understanding of the ecological consequences of body size that use a range of methodologies, including observations of natural systems, experiments with natural systems, theoretical modelling and experiments with artificial ecosystems. We present examples of the last approach, using new analyses of data from our published experiments. These analyses have demonstrated effects of body size at three levels of organisation, and how these effects can be altered by community properties such as trophic complexity and species richness. We have illustrated the utility of experimental microbial systems for evaluating allometric theories of community structure and metabolism, and shown that patterns based on observations across many natural systems readily emerge in experimental systems where attributes such as organism size and trophic complexity are subject to rigorous experimental control. These results also point to an important role for biodiversity in influencing community biomass and metabolism that remains incompletely integrated into allometric theories of community and ecosystem properties. Discrepancies between the predictions of allometric theory and our findings could be due to any of many properties of real organisms, for example, evolution can produce a mass–density relationship (Loeuille & Loreau, 2006). Integration of biodiversity, trophic structure and evolution remains an important challenge for ecologists working at the interface of population, community and ecosystem ecology.

Acknowledgements Jill McGrady-Steed kindly made the data from her experiment available in electronic format. Those data and others were originally collected with the support of the US NSF under grant 9806427 to PJM and Timothy Casey. Discussion with participants of the British Ecological Society Special Symposium on Body Size and the Organisation and Function of Aquatic Ecosystems, and the comments of two anonymous reviewers improved the content of this manuscript. OLP is a Royal Society University Research Fellow.

References Allen, A. P., Brown, J. H., & Gillooly, J. F. (2002). Global biodiversity, biochemical kinetics, and the energy-equivalence rule. Science, 297, 2545–1548. Brown, J. H. (2004). Toward a metabolic theory of ecology. Ecology, 85, 1771–1789.

Brown, J. H. & Gillooly, J. F. (2003). Ecological food webs: high-quality data facilitate theoretical unification. Proceedings of the National Academy of Sciences of the United States of America, 100, 1467–1468.

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Carbone, C. & Gittleman, J. L. (2002). A common rule for the scaling of carnivore density. Science, 295, 2273–2276. Cohen, J. E., Jonsson, T. & Carpenter, S. R. (2003). Ecological community description using the food web, species abundance, and body size. Proceedings of the National Academy of Sciences of the United States of America, 100, 1781–1786. Crawley, M. J. (2002). Statistical Computing. An Introduction to Data Analysis using S-Plus. Chichester: John Wiley & Sons, Ltd. Cyr, H. (2000). Individual energy use and the allometry of population density. In Scaling in Biology, ed. J. H. Brown and G. B. West. Oxford: Oxford University Press, pp. 267–295. Damuth, J. (1981). Population density and body size in mammals. Nature, 290, 699–700. Damuth, J. (1987). Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy use. Biological Journal of the Linnean Society, 31, 193–246. Duffy, J. E. (2002). Biodiversity and ecosystem function: the consumer connection. Oikos, 99, 201–219. Enquist, B. J. & Niklas, K. J. (2001). Invariant scaling relations across tree-dominated communities. Nature, 410, 655–660. Gillooly, J. F., Brown, J. H., West, G. B., Savage, V. M. & Charnov, E. L. (2001). Effects of size and temperature on metabolic rate. Science, 293, 2248–2251. Hector, A., Schmid, B., Beierkuhnlein, C. et al. (1999). Plant diversity and productivity experiments in European grassland. Science, 286, 1123–1127. Hooper, D. U., Chapin, F. S., Ewel, J. J. et al. (2005). Effects of biodiversity on ecosystem functioning: a consensus of current knowledge. Ecological Monographs, 75, 3–35. Hutchinson, G. E. (1961). The paradox of the plankton. The American Naturalist, 95, 137–145.

Kerr, S. R. & Dickie, L. M. (2001). The Biomass Spectrum. NewYork: Columbia University Press. Loeuille, N. & Loreau, M. (2006). Evolution of body size in food webs: does the energy equivalence rule hold? Ecology Letters, 9, 171–178. Long, Z. T. & Morin, P. J. (2005). Effects of organism size and community composition on ecosystem functioning. Ecology Letters, 8, 1271–1282. Loreau, M., Naeem, S., Inchausti, P. et al. (2001). Biodiversity and ecosystem functioning: current knowledge and future challenges. Science, 294, 804–808. Marquet, P. A., Navarette, S. A. & Castilla, J. C. (1995). Body size, population density, and the energetic equivalence rule. Journal of Animal Ecology, 64, 325–332. McGrady-Steed, J. & Morin, P. J. (2000). Biodiversity, density compensation, and the dynamics of populations and functional groups. Ecology, 81, 361–373. McGrady-Steed, J., Harris, P. M. & Morin, P. J. (1997). Biodiversity regulates ecosystem predictability. Nature, 390, 162–165. Mulder, C., Cohen, J. E., Seta¨la¨, H., Bloem, J. & Breure, A. M. (2005). Bacterial traits, organism mass, and numerical abundance in the detrital soil food web of Dutch agricultural grasslands. Ecology Letters, 8, 80–90. Petchey, O. L., McPhearson, P. T., Casey, T. M. & Morin, P. J. (1999). Environmental warming alters food-web structure and ecosystem function. Nature, 402, 69–72. Petchey, O. L., Casey, T. J., Jiang, L., McPhearson, P. T. & Price, J. (2002). Species richness, environmental fluctuations, and temporal change in total community biomass. Oikos, 99, 231–240. Petchey, O. L., Downing, A. L., Mittelbach, G. G. et al. (2004). Species loss and the structure and functioning of multitrophic aquatic ecosystems. Oikos, 104, 467–478.

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Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge: Cambridge University Press. Savage, V. M., Gillooly, J. F., Brown, J. H., West, G. B. & Charnov, E. L. (2004). Effects of body size and temperature on population growth. American Naturalist, 163, E429–E441. Sheldon, R. W. & Kerr, S. R. (1972). The population density of monsters in Loch Ness. Limnology and Oceanography, 17, 796–798. Sheldon, R. W. & Kerr, S. R. (1973). The Loch Ness Monster: reply to comments of C. H. Mortimer. Limnology and Oceanography, 18, 345–346. Sheldon, R. W., Prakash, A. & Sutcliffe, W. H. (1972). The size distribution of particles in the ocean. Limnology and Oceanography, 17, 327–340. Sheldon, R. W., Sutcliffe, W. H. & Paranjape, M. A. (1977). Structure of pelagic food-chain

and relationship between plankton and fish production. Journal of the Fisheries Research Board of Canada, 34, 2344–2353. Tilman, D., Reich, P. B., Knops, J. et al. (2001). Diversity and productivity in a long-term grassland experiment. Science, 294, 843–845. Weatherby, A. J., Warren, P. H. & Law, R. (1998). Coexistence and collapse: an experimental investigation of the persistent communities of a protist species pool. Journal of Animal Ecology, 67, 554–566. West, G. B., Brown, J. H. & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276, 122–126. Wetzel, R. G. & Likens, G. E. (1991). Limnological Analyses, 2nd edn. New York: Springer-Verlag.

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CHAPTER FOURTEEN

Body size, exploitation and conservation of marine organisms SIMON JENNINGS Centre for Environment, Fisheries and Aquaculture Science (CEFAS)

JOHN D . REYNOLDS Simon Fraser University, Burnaby

Introduction Aquatic ecologists and conservationists have long been obsessed with trying to understand links between body size, exploitation and conservation (e.g. Adams, 1980; Dickie, Kerr & Schwinghamer, 1987a). There are several reasons for this interest. First, at the individual level, fisheries management for both vertebrate and invertebrate populations tries to minimize the mortality of smaller individuals, in order to increase the probability that individuals have reproduced before they are caught (Jennings, Kaiser & Reynolds, 2001a). Even if other management methods are used, practically every stock assessment that has ever been done on an indeterminately growing species has included size as a key input parameter. Second, at the population level, large-bodied species have life-history traits that lead to slow rates of population turnover, with clear implications for productivity, resilience and recovery potential (Hutchings, 2001; Denney, Jennings & Reynolds, 2002; Reynolds et al., 2005; Goodwin et al., 2006). Third, at the community level, predator–prey relationships are strongly linked to size (Cohen et al., 1993; Woodward & Warren, this volume; Persson & De Roos, this volume), leading to the potential for understanding how fishing mortality may have wider ecosystem impacts through food-web dynamics (Dickie et al., 1987a). At the population level, studies of the effects of exploitation have long focused on the direct effects of fishing mortality on a single stock, and this is often a pragmatic response to limited information on the indirect effects of mortality on one species affecting other species in the ecosystem (Hilborn & Walters, 1992). However, renewed concerns about the environmental impacts of fishing have encouraged new research on fishing effects on communities and ecosystems, where an understanding of the direct and indirect effects of mortality, and the capacity to partition them, is essential. Since the structure of aquatic food webs is often strongly size based, we hope to show that understanding interactions between body size and exploitation provides the basis for describing and managing the effects of fishing. Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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In this chapter we consider linkages between body size, exploitation and aquatic conservation at all three scales: individuals, populations and communities. Our aim is to understand, from first principles of metabolic scaling rules and life histories, how population and community dynamics are linked to the sizes of individuals. Although much of the research that has been done in this field has focused on fish as the main animals caught, a nice feature of working with body-size distributions at the community level is their continuity from primary producers to top predators, which often transcend taxonomic boundaries (e.g. Warwick, this volume).

Setting: the magnitude of fishing effects Some brief highlights of the state of aquatic biodiversity can make for depressing reading. The Food and Agriculture Organization of the United Nations (FAO) (2005) report on the state of the world’s fisheries points out that 52% of the world’s stocks are fully exploited, 17% are over exploited, 7% depleted and 1% recovering. The proportion of stocks that are over-exploited, depleted and recovering has increased from 10% in the mid 1970s to 25% in the early 1990s. World marine fisheries catches levelled out in the late 1980s, with fluctuations since then driven by changes in some highly productive areas in the Pacific (Watson & Pauly, 2001; FAO, 2005). This limit to marine catches has occurred in spite of a continuing increase in fishing effort and efficiency. When we break these global figures down to the level of specific populations, we can identify many reductions in abundance over the past two to three decades. A review of data from 232 exploited fish populations revealed a median maximum rate of decline of 83% from known historical levels (Hutchings & Reynolds, 2004). Over half (58%) the populations declined by more than 80%. Note that these are maximum declines, based on time series of at least ten years, and the timeseries usually began well after the onset of fishing. The declines are also much greater than those associated with taking a large sustainable yield from these populations. Even if fishing mortality can be substantially reduced, some stocks, in particular those of bottom dwelling fishes, do not show recovery if they have been pushed to very low abundance (Hutchings, 2001, 2002; Hutchings & Baum, 2005). There is evidence for extinction of some populations of fishes and other marine species. Dulvy, Sadovy and Reynolds (2003) compiled a list of 133 cases of local, regional or global extinctions of marine species. Of these, 55 cases involved fishes, while the rest included birds, mammals and invertebrates. This is a preliminary assessment: we still know very little about the status of the vast majority of aquatic organisms. Indeed, 80% of the extinctions were discovered through historical comparisons rather than real-time detections, with a median 53-year lag between disappearance and the reporting of

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that disappearance. Thus, the near-extinction of the common skate, Dipturus batis, from the Irish Sea was brought to the world’s attention only several decades after the decline had occurred (Brander, 1981). As we scale up from populations to communities, the principal effects of fishing on size and species composition are well known. Both spatial comparisons between areas subject to different fishing intensities and temporal comparison within areas where fishing effort has increased over time, indicate broadly predictable effects. As fishing mortality rises, the mean size of individuals in the community falls, and species with larger body sizes form a smaller proportion of community biomass. Since larger species and individuals often, but not exclusively, feed at higher trophic levels, so changes in size structure are often paralleled by a reduction in the trophic level of the community – an effect dubbed ‘fishing down the food web’ by Pauly et al. (1998). While much of the theory and data on fishing effects refers to target species, we have also learned a great deal in the past 20 years about impacts of fishing gear on the seabed (Kaiser & de Groot, 2000). Impacts on bottom fauna are most severe in habitats that do not naturally receive much disturbance. As we will see below, we can use the same body of theory developed for linking body size, life histories and responses to mortality for predicting the responses of benthic invertebrate species and communities to trawling disturbance.

Size-related responses to exploitation The responses of populations and communities to human activities depend on interactions between the extrinsic mortality rate and the intrinsic aspects of the species’ biology that affect population growth rates. Body size plays a key role in both elements of vulnerability. Fisheries are selective, typically targeting the large-bodied, high-value individuals and species that are favoured for consumption and sale. Even when fisheries do not deliberately pursue larger individuals and species, there will still be higher mortality for such animals because they are often caught as by-catch due to their greater likelihood of being retained by gears such as trawls. While there are a few notable exceptions to the rule of larger animals being more vulnerable to capture, such as gill nets and traps that select individuals and species of intermediate size, almost all population-based assessments show that large size classes suffer higher mortality. There is clear evidence for the size-relatedness of fishing effects in populations and communities. Thus, in one early study, we compared trends in the abundance of populations of the same species that had different maximum sizes, after accounting for differences in fishing mortality. Populations with larger maximum sizes consistently showed greater rates of decline in response

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to mortality (Jennings, Reynolds & Mills, 1998). In a second study, using a phylogenetic comparative approach to account for relatedness, we compared trends in pairs of species of different body size. In eight out of nine comparisons, the larger species declined more in abundance during a period of increasing fishing mortality (Jennings, Greenstreet & Reynolds, 1999). There are many other recent examples of trends in abundance that can be related to body size (Reynolds, 2003). The overall trend of targeting large species has had the same impacts on large, profitable prey on land as in the water (Reynolds & Peres, 2006). Thus, we have seen the sequential loss of species from the largest to the smallest, in groups as diverse as whales in the Southern Ocean, abalones along the coasts of western North America, and primates in the Brazilian Amazon. The effects of fishing on communities are a consequence of interactions between the direct and indirect effects of fishing. The direct effects are due to mortality on component populations and tend to result in a reduction in the mean size of animals in the community. The indirect effects are due to the changes in predator–prey relationships which occur when predator and/or prey abundance changes. Direct and indirect effects usually result in a reduction in the mean body size of animals in the community and a decrease in the proportion of animals with larger body size (Shin et al., 2005). Fishing effects on communities have often been reported in terms of changes to the slope of abundance (y) vs. body mass (x) relationships, otherwise known as size spectra. The slopes of size spectra tend to become steeper with increased fishing (Bianchi et al., 2000; Duplisea & Kerr, 1995; Gislason, 2002; Pope et al., 1988; Rice & Gislason, 1996). Intercepts were often reported to increase as the slope declined, but this could have been a real effect or a statistical artefact resulting from the correlation between intercept and slope. To avoid this, Daan et al. (2005) re-scaled size spectra to the midpoint size class and expressed midpoint heights rather than intercepts. Results suggested that changes in the spectrum can be driven both by the loss of large fish and proliferation of small fish as their larger predators are depleted (Daan et al., 2005). The physical impacts of fishing gears also cause size-selective mortality. When trawl gears are towed across the seabed they may kill differentially many larger and more fragile animals, as small ones may be pushed aside by the pressure wave in front of the gear (Gilkinson et al., 1998). The larger species are also less able to withstand a given rate of mortality. As a result, benthic communities in trawled areas comprise smaller individuals and species (Kaiser et al., 2000), and the slopes of benthic invertebrate size spectra become steeper in more heavily trawled areas (Jennings et al., 2002; Warwick, this volume).

Linking body size, life histories and population dynamics Rates of metabolism, the biological processing of energy and materials, are systematically related to body size and ultimately correlate with the life histories

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of animals and their responses to exploitation. Relationships between metabolism and size are further modified by chemical composition and temperature (Brown et al., 2004). These factors consequently drive most other biological rates and timings, such as lifespans and growth (Gillooly, 2000; Gillooly et al., 2001, 2002; Brown, Allen & Gillooly, this volume; Atkinson & Hirst, this volume). The combined effect of body size and temperature on individual wholeorganism metabolic rate has been approximated as: I ¼ i0 M0:75 eE=kT

(14:1)

Where I is individual metabolic rate, i0 is a normalization constant, M is body mass, T is temperature (Kelvin), E is the activation energy of metabolism and k is Boltzmann’s constant. Since the mass-specific rate of metabolism (R) is 1/M, R will scale with M as R / M0:25 eE=kT

(14:2)

This demonstrates that large organisms must require more resources and flux them more slowly than smaller ones (Brown et al., 2004). Not surprisingly, intrinsic rates of increase and production scale similarly, and turnover time as the inverse of production; approximately W0.25. Changes in resource requirements with size will limit the resources available for allocation to life histories, and species have evolved many ways of allocating these limited resources to maximize reproductive output. In a former British Ecological Society symposium, Law (1979) described the Darwinian demon, an organism in which all the problems of maximizing reproductive output had been solved. This animal began reproducing immediately after birth, producing large numbers at frequent intervals as it got older. It experienced no mortality and its capacity for dispersal and finding mates knew no bounds. Of course, as Law pointed out, no such animal exists because of trade-offs. Thus, species have followed a wide diversity of paths through these trade-offs in arriving at the combinations of life-history traits that we see today and which maximize individual fitness (Atkinson & Hirst, this volume). Relationships among traits can be described with invariants, which reflect general life-history patterns among species after removing the dimensions of mass and time (Charnov, 1993). Examples of invariants are relationships between size at maturity and maximum size, lifespan and age at maturity, natural mortality and growth rate (Beverton, 1992). Two aspects of life histories, which result from trade-offs, are critical in determining the response of a population to additional mortality: the intrinsic rate of increase and the strength of compensation. The intrinsic rate of natural increase is often denoted rmax, to make it clear that this is the maximum rate that populations could achieve in the absence of density dependence, which we can usually expect to apply to small populations that are far from their carrying

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capacity. There is a strong theoretical literature that links body size to rmax, through links with key components of rmax such as age at maturity and natural lifespan (Roff, 1992). The strength of compensation, or density dependence, indicates how the production of recruits (juvenile fish at a specified age) per spawner changes with the abundance of spawners. Since the abundance of recruits can be measured at different ages for different populations, estimates of population-specific mortality in subsequent years can be used to express recruits per spawner in a consistent way for comparative purposes: as spawners per spawner (Myers, Mertz & Fowlow, 1997).

Population dynamics and responses to mortality Intrinsic rates of increase Species with high rmax will have fast population turnover, and should therefore be better able to compensate for increased mortality due to fishing. This has been suggested by a variety of theoretical analyses, which have focused on body size as well as its correlated life-history traits, such as age at maturity and natural lifespan (Adams, 1980; Stokes, McGlade & Law, 1993). The prediction that large-bodied species should decline more quickly when exposed to a given rate of fishing mortality has been upheld in many studies of marine fishes in both tropical and temperate waters (reviewed by Reynolds, 2003). Many of these studies have included comparisons between closely related species, to avoid ‘apples and oranges’ comparisons between species that differ greatly in other aspects of behaviour or life histories (Harvey & Pagel, 1991). The prediction that large-bodied species should have lower recovery potential has also been upheld in comparative studies of marine invertebrates (Fenchel, 1974) and fishes (Denney et al., 2002). For example, Denney et al. (2002) measured the slope at the origin of recruitment plotted against adult stock size for fish populations in the northeast Atlantic. This provided a practical metric for rmax, the number of spawners produced per spawner in the absence of density dependence (Myers et al., 1997), which could be plotted against various life-history traits. Body size was negatively related to rmax, the implication being that, all else being equal, small-bodied species should be able to bounce back from small population size faster than larger ones. When the length-based measures of body size reported by Denney et al. (2002) are converted to mass (Maxwell & Jennings, 2005), it is notable that the slope of the relationship between log10 spawner per spawner and log10 maximum body mass does not significantly differ from the M0.25 scaling of intrinsic rate and body mass predicted from theory (Eq. (14.2); Savage et al., 2004). Density dependence The strength of density dependence is critical for determining the ability of populations to compensate for increased mortality. Yet, by definition, rmax and

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the surrogates used to measure it, such as the slope at the origin of a spawnerrecruitment relationship, apply to small populations in the absence of density dependence. For example, if the population follows a logistic growth pattern, the rate of change in number of individuals per unit time, dN/dt, will depend on population growth rate r and the carrying capacity, K.   dN N ¼ rN 1  (14:3) dt K Only at the smallest population size will r ¼ rmax. Cynics might argue that this is the case for the majority of fisheries today, so we need go no further! Even in heavily fished populations, however, we cannot completely ignore densitydependent interactions between individuals, predator–prey relationships and other aspects of ecology and behaviour that may determine intrinsic aspects of vulnerability. These features of biology translate the conceptually simple rmax into realized population growth rates. Recently, Goodwin et al. (2006) have examined relationships between density dependence and life history. They used stock-recruitment curves to measure the compensation ratio of a population (Fig. 14.1). The compensation ratio (CR; Goodyear, 1977) was defined as: CR ¼

Maximum recruit survivalðÞ Recruit survival at SSBF¼0

(14:4)

Where a is the slope at the origin of a spawner–recruit relationship and SSBF¼0 is the spawning stock biomass at equilibrium in the absence of fishing. Goodwin et al. (2006) demonstrated that large-bodied species with low maximum rates of increase and long generation times tended to have strong compensation. Their results help us to understand how populations respond to fishing. Those populations with small body size and low spawners per recruit in the absence of fishing (SPRF¼0) have weak density-dependence and high annual production. At the outset α SF=0 Recruit abundance (R)

272

Spawner abundance (S)

Figure 14.1 A spawner–recruit relationship where  is the maximum recruits per spawner at low population size and SF¼0 is equilibrium spawner abundance in the absence of fishing. The relationship between maximum recruits per spawner and recruit survival at SF¼0 defines the compensation ratio. After Goodwin et al. (2006).

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of fishing even low fishing mortality could rapidly deplete these populations since they would show little compensatory response. However, they would show high resilience to extinction at very low abundance. Conversely, populations with strong density-dependence have a greater initial compensatory reserve, but can collapse owing to low resilience once they reach low abundance.

Communities and their responses to mortality Size-based structuring of marine communities To understand and predict how fishing affects communities, it is necessary to know how communities are structured in the absence of fishing. Strong sizebased structuring is ubiquitous in marine ecosystems (Sheldon, Prakash & Sutcliffe, 1972) and trophic level increases more or less continuously with body size (Fry & Quinones, 1994). Why food webs of this type have evolved in aquatic environments when many terrestrial webs have clear trophic levels is not clear. Loeuille and Loreau (2005) recently explored one possibility, based on a model where food webs evolve from a single ancestor and assuming that adaptation acts on body size, which has a well-established impact on metabolism and interactions between organisms. Based on parameters defined at the organism scale, the model predicts emergent properties at the food-web scale. If niche width and competition intensity are small then distinct trophic levels evolve. When niche width or competition intensity are large then clear trophic levels do not emerge, consistent with patterns seen in many aquatic food webs. One feature of many marine species is their large scope for individual growth. Thus, individuals of most species begin life as larvae feeding at the base of food chains, but can end life as large terminal predators. Size-based predation and the large scope for growth in aquatic animals are significant because, at least over the course of a species’ life cycle, body size will be a better indicator of trophic level than species identity (see Woodward & Warren, this volume). This observation provides a compelling reason to adopt size rather than species-based analysis of aquatic food webs; treating small individuals of a large species as functionally equivalent to large individuals of small species (Kerr & Dickie, 2001). While such size-based analyses are necessarily simplifications, they provide an excellent means of understanding the development of size structure and assessing the effects of mortality (Jennings, 2005; Persson & De Roos, this volume). Attempts to model the processes that lead to the emergence of size spectra have included simple models based on fundamental ecological principles (Kerr & Dickie, 2001; Brown & Gillooly, 2003) and detailed process-based models of predator–prey interactions (Shin & Cury, 2004). Almost all models are underpinned by the recognition that the scaling of metabolism with body size determines the energy requirements of animals in different size classes. The time-averaged slopes of abundance–body mass relationships in size-based food webs are principally determined by the availability of energy to animals in

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each size class (Kerr & Dickie, 2001). Availability of energy at size, and hence the scaling of abundance and body mass, can be predicted by extending the theory of energetic equivalence that applies to communities that share energy. For these communities, such as phytoplankton using sunlight, numerical abundance (N) typically scales with body mass (M) as M0.75. Since the scaling of individual metabolic rate and body size can be approximated as Mþ0.75 (Eq. (14.1)), the rate of energy use is expected to be independent of body size (Damuth, 1981), a prediction that has since been referred to as energetic equivalence (Nee et al., 1991). In the case of phytoplankton communities, for example, the sunlight energy used by plankton cells in a size class is the same as in any other size class (Li & Charnov, 2001). Food chains are not characterized by the sharing of energy, but by larger predators eating smaller prey. Thus the availability of energy falls with size and trophic level (Ware, 2000). The rate at which available energy falls will depend on the efficiency of energy transfer and the number of predator–prey interactions that transfer energy from small to large body-size classes. The latter depends on the ratio of the mean predator size to mean prey size (PPMR), which in most aquatic ecosystems ranges from 100 to 1000:1 by mass (Cushing, 1975). Cyr (2000) and Brown and Gillooly (2003) proposed that knowledge of PPMR and transfer efficiency (TE) could be used to predict the changes in energy available to animals of different body sizes in a complete size spectrum and hence the slope. Their analysis helped to explain the remarkable consistency in the observed slopes of size spectra (Boudreau & Dickie, 1992). This is because PPMR and TE place significant constraints on the slope of abundance–body mass relationships and because PPMR and TE are remarkably consistent in different ecosystems (Jennings, 2005). Brown and Gillooly’s (2003) analysis, as further developed in Brown et al. (2004), was based on a series of trophic levels, each of which extended over a range of body sizes. In most aquatic communities trophic level actually rises continuously with body size (Jennings et al., 2002). Jennings and Mackinson (2003) formalized the approach of Brown and Gillooly (2003) for application to such a community, and showed that the method provided good predictions of the slope of the size spectrum. These methods for predicting the slope of size spectra are helpful in understanding the size structure of communities and for providing a baseline for assessing the relative effects of exploitation. However, they do not allow prediction of the consequences of various levels of exploitation. To achieve this, models that account for the growth and mortality of individuals are required. This is the interface between understanding the dynamics of populations and understanding how population dynamics contribute to community structuring. Describing and predicting responses to mortality It can be difficult to link changes in fishing mortality to changes in the slopes of size spectra empirically, because mortality data for communities are hard to

BODY SIZE AND EXPLOITATION

obtain. However, available evidence suggests that the slopes respond principally to fishing rather than to other drivers such as temperature. Blanchard et al. (2005), for example, considered the effects of fishing and climate variation on size-based metrics, including slope of the size spectrum, in the Celtic Sea. Their analysis suggested that size-based metrics responded clearly to the effects of fishing in variable environments, reflecting the ubiquity of size-based processes in defining community structure and responses to mortality. This is consistent with theory. While temperature will have a marked effect on rates of biomass turnover and energy flux in the spectrum (Eqs. 14.1 & 14.2), TE and PPMR are largely temperature independent. Much work on size spectra has focused on fishing effects on fish communities, but benthic invertebrate communities are also directly impacted by bottom fishing gears such as trawls and show strong size-based responses to fishing. Comparisons among areas subject to different levels of trawling disturbance have shown that the frequency of bottom trawling disturbance in the central North Sea had a greater effect on the size structure of the fauna in a soft-sediment benthic community than other environmental variables such as sediment particle size and depth (Duplisea et al., 2002). Size spectra became steeper and their heights decreased with increased trawling disturbance. As a result, the total production of infaunal invertebrates fell with increasing trawling disturbance while relative production of the infaunal community rose significantly. The increases in relative production were largely attributable to the dominance of smaller animals in the trawled community and did not compensate for the loss of biomass and production of larger animals (Jennings et al., 2001b). Differences between the slopes of size spectra in exploited communities and those that are predicted for unexploited communities can be used to assess the effects of fishing on abundance in different ecosystems. In addition, given wellestablished scaling relationships between body size and biological properties, the size spectrum can be parameterized to estimate the effects of fishing on production (P) or turnover time. To assess the overall effects of fishing on the North Sea fish community, Jennings and Blanchard (2004) attempted to compare a theoretical abundance–body mass relationship for the unexploited North Sea with an abundance–body mass relationship estimated from contemporary data (Fig. 14.2). The slope of the unexploited size spectrum was predicted from PPMR and TE (using the methods introduced above under Size-based structuring of marine communities) since there was little evidence that either parameter was affected by exploitation to the same extent as biomass (B). By comparing the unexploited theoretical and observed size spectra they predicted that the scaling of B with M had changed from M0.10 (unexploited) to M1.0 (exploited). This suggested that the current biomass of large fishes weighing 4–16 kg and 16–66 kg was 97.4% and 99.2%, respectively, lower than would be expected in the absence of fisheries exploitation. The mean

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(a) 6

Trophic level

5

4

3 1

2

3

4

5

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Trophic level (b)

4.0

4.2

4.4

4.6

4.8

5.0

5.2

1 TE = 0.150

Biomass (log10)

276

TE = 0.125 0

TE = 0.100

–1

–2 1

2

3 Body mass (log10)

4

5

Figure 14.2 The relationship between trophic level, as estimated with nitrogen stable isotope analysis, and body mass for North Sea fishes in 2001 (a); 95% confidence intervals for the mean reflect among-site variation, and the slope of this relationship implies a mean predator–prey mass ratio (PPMR) of 390:1. Predicted slopes of abundance–body mass relationships for the unexploited community (b) were calculated from PPMR and estimates of transfer efficiency (TE) of 0.100–0.150. The observed slope of the abundance–body mass relationship in 2001 is shown with a broken line. From Jennings and Blanchard (2004).

turnover time of the exploited community (1/P:B) was almost twice as fast as that of the unexploited community, falling from 3.5 to 1.9 years. Comparisons such as these are useful for comparing the magnitude of fishing effects in different ecosystems and for assessing the relative impacts of fishing on a range of community and ecosystem properties. However, such static descriptions cannot be used to guide management and to modify fishing to achieve desirable community structures, such as those that provide good yields of target species while ensuring that large and vulnerable species do not go extinct.

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Models of the effects of varying fishing mortality on the slope of size spectra have focused on the various processes that lead to changes in slope, specifically: (1) the differential reduction in the abundance of larger species that are more vulnerable to a given rate of mortality, (2) within-population changes in mean body size and life history due to the direct effects of fishing on the population, (3) genetic changes in life history and (4) predator–prey relationships in the community that result in proliferation of small species and individuals that are better able to tolerate a given rate of fishing mortality and benefit from depletion of their predators. Responses (1) and (2) are governed by the links between body size, life histories and response to mortality that we considered above. Existing theoretical models that describe the structure of size spectra and their response to fishing have principally focused on (1), (2) and (4) (e.g. Boudreau et al., 1991; Dickie, Kerr & Boudreau, 1987b; Kerr, 1974; Thiebaux & Dickie, 1993). Response (3) is arguably as important as the others in the medium- to long-term and there is a developing body of theory and empirical observation at the population level that would allow genetic effects to be addressed (Law, 2000; Law & Stokes, 2000; Heino & Godo, 2002). Some recently published modelling results suggest that the effects may not be intuitive due to the interplay between the selection caused by fishing and changes in predation pressure on different size classes (Thygesen et al., 2005; Persson & De Roos, this volume). In models of fishing effects on community size structure, the capacity to partition the direct and indirect effects of fishing and to understand how they interact is critical in providing insight into the effects of fishing. Gislason and Rice (1998) used a combination of existing length-based fishery models and multispecies models to predict the slopes and intercepts of size spectra for a community consisting of 11 fish species that account for much of the fisheries production in the North Sea. Fishing mortality increased the slope of the size spectrum. Building on this approach, Pope et al. (2006) generalized the model for a community of species defined by their maximum body sizes (asymptotic length L1 as defined in the von Bertalanffy growth model, in 10 cm length classes from 10 cm to 130 cm). We discuss this model in a little detail, as it gives important insights into the links between size-based population and community responses to fishing and could provide a basis for predicting and managing the impacts of fishing on size-based communities. For each species (S), the number (N) surviving from one length class (L) to the next, where successive length classes are denoted 1 and 2 was given as:  NL2;S ¼ NL1;S

L1 ðSÞ  L2 L1 ðSÞ  L1

ZðL1;SÞ kðSÞ (14:5)

based on the fisheries assessment method of length cohort analysis (Jones, 1974), where Z(L1,S) is the total mortality rate (y1) at length L1 for the species and k is the Brody growth parameter from the von Bertalanffy growth model

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that reflects the rate of growth towards asymptotic length (L1). One limitation of the application of this approach was that the assumption of a fixed relationship between L1 and growth rate, means that the modelled rates of growth persist regardless of the level of available resources. The average number of fish  L1;S ) in the L1 length group by species is given by: per year (N  L1;S ¼ ðNL1;S  NL2;S Þ=ZðL1; SÞ N

(14:6)

 L1;S may then be summed across species at each length group L from 10 to The N  L;# : Consistent with standard practice 130 cm to give the overall size spectrum N in multispecies fishery models, the components of Z considered were fishing mortality rate (F), non-predation natural mortality rate M1 and predation mortality rate M2. Thus: Z ¼ F þ M1 þ M2

(14:7)

Predation mortality was set proportional to the sum of the power of biomass in larger size classes, modified by a size-preference function. Maturity was based on life-history invariants. Once mature, fishes produced recruits in proportion to their total abundance and length. A power term in the spawner–recruit relationship provided compensation, the density dependent reduction in recruitment at high spawner abundance that we discussed previously. The slope of the size spectrum for fishes from 20–100 cm was broadly linear and became increasingly steep as a function of fishing mortality. Density dependent controls, due to predation mortality and the extent of compensation in the spawner–recruit relationship, were key mechanisms in maintaining the slope. When compensation exerted strong control, the model suggested that the role of fishing quickly dominated the effect of predation. The model also provided insights into the relative role of predation mortality and fishing in different size classes, building on the observations of Dickie (1976) who demonstrated that: (1) the ratio of biomass at successive trophic levels must be independent of sizes of individuals and, (2) the ratio of biomass at successive trophic levels is the ecological efficiency (ratio of food intake at two successive trophic levels) corrected by the ratio of predation rates. Thus Dickie (1976) showed that predation rate must be relatively higher at lower trophic levels, and that a given amount of fisheries yield from a lower trophic level is a much smaller proportion of predation mortality rate than at a higher trophic level. The Pope et al. (2006) model suggests that the reduction in the biomass of larger species and individuals in the community leads to the proliferation of smaller individuals. Using a method developed by Daan et al. (2005) to assess changes in the abundance of fishes in different size classes over time, there have now been three empirical demonstrations of increases in the steepness of size

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spectra being partially driven by the proliferation of fish in smaller size classes: for the North Sea (Daan et al., 2005), Fijian reefs (Dulvy et al., 2004) and the Celtic Sea (Blanchard et al., 2005) (Fig. 14.3). The model of Pope et al. (2006) suggests that the relationship between the strength of compensation in the spawner–recruit relationship and body size play an important role in controlling the extent of prey release. The Pope et al. (2006) size-based model is an important development because they have captured the dynamics of individual species within the size spectrum,

(a) 0.4

Relative change in biomass

0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 2

4

6

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Body mass class (log2) (b) 0.4

Relative change in biomass

0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 20

30

40

Body mass class (cm)

50

60

Figure 14.3 Relative changes in biomass as a function of body size across (a) a temporal gradient in multispecies fishing mortality in the Celtic Sea and (b) a spatial gradient in fishing effort on Fijian reefs. Both examples show evidence for prey release following predator depletion. Data from Blanchard et al. (2005) and Dulvy et al. (2004).

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1

Spawner biomass (log10)

280

0

10 cm

–1 20 cm

–2

30 cm

–3

50 cm 70 cm

–4 0.0

130 cm

0.5

1.0 1.5 2.0 2.5 Fishing mortality

3.0

Figure 14.4 The effects of fishing mortality on the relative abundance of fishes as a function of their maximum potential size. From Pope et al. (2006).

by associating species identity with a maximum length. This allows the model to be used to predict the proportion of species with different ultimate body sizes that ‘populate’ any size class in the spectrum (Fig. 14.4). In the same way that Cohen, Jonsson and Carpenter (2003) and Cohen (this volume) uniquely linked species identity, body mass and abundance in a new approach to conventional food-web analysis, the Pope et al. (2006) approach attempts to bring species identity into size-based models and provides the basis for starting to investigate links between community processes and the diversity and persistence of populations. Size-based models have also been used to predict fishing effects on benthic invertebrate communities. In benthic communities, the structure of the size spectrum is driven more by competition rather than predation, since the animals present in many size classes often share the same energy sources (Warwick, this volume). Duplisea et al. (2002) developed a competition-based model to assess the effects of size-selective mortality due to trawling disturbance on the size-structure of the benthic community. By applying size-related mortality, they showed that fishing increased the slope of benthic size spectra, consistent with empirical observation.

Conclusions There are clear links between the metabolic processes that drive rates of living and dying, life histories, and the structure and function of populations and communities. Thus body size and body-size distributions, as easily measured attributes of individuals, populations and communities, can provide significant insight into responses to exploitation. It seems fitting that fisheries ecologists have made many contributions to the development and testing of theory that links body size, exploitation and conservation, since this reinvigorates a long but intermittent history of fisheries science contributing to wider ecological thinking (Frank & Leggett, 1994; Shuter & Abrams, 2005). Indeed,

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some of the most influential scientists working on the development of fisheries assessment methods were responsible for theoretical developments that proved fundamental in understanding life histories (Beverton & Holt, 1957, 1959). While fisheries scientists have consistently been aware of links between population biology and the ecosystem, the politics and practicalities of management have led to the development of management systems that were dominated by the assessment of single populations. This approach was accepted by most management agencies from the 1960s to the present, but two events in recent years have provided a strong driver for moving toward management systems that also focus on communities and ecosystems. First, there has been near universal commitment within international fora that fisheries must be managed in an ecosystem context to take account of conservation concerns (Sinclair & Valdimarsson, 2003). Second, there have been major advances in the development of food-web theory that may have management applications, and in the development of connected theory that helps to formalize many of the observed relationships between individual, population and community processes (Brown & Gillooly, 2003; Cohen et al., 2003; Brown et al., this volume; Cohen, this volume). The changing drivers for management, and these new developments in ecology, suggest that theoretical development should reinvigorate the development of new management and assessment methods.

Acknowledgements We thank Nick Goodwin for providing the materials to prepare Fig. 14.1 and Julia Blanchard and Nick Dulvy for providing data to prepare Fig. 14.3.

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Gilkinson, K., Paulin, M., Hurley, S. & Schwinghamer, P. (1998). Impacts of trawl door scouring on infaunal bivalves: results of a physical trawl door model/dense sand interaction. Journal of Experimental Marine Biology and Ecology, 224, 291–312. Gillooly, J. F. (2000). Effect of body size and temperature on generation time in zooplankton. Journal of Plankton Research, 22, 241–251. Gillooly, J. F., Brown, J. H., West, G. B., Savage, V. M. & Charnov, E. L. (2001). Effects of size and temperature on metabolic rate. Science, 5538, 2248–2250. Gillooly, J. F., Charnov, E. L., West, G. B., Savage, V. M. & Brown, J. H. (2002). Effects of size and temperature on developmental time. Nature, 417, 70–73. Gislason, H. (2002). The effects of fishing on nontarget species and ecosystem structure and function. In Responsible Fisheries in the Marine Ecosystem, ed. M. Sinclair & G. Valdimarsson. CAB International, Wallingford, pp. 255–274. Gislason, H. & Rice, J. C. (1998). Modelling the response of size and diversity spectra of fish assemblages to changes in exploitation. ICES Journal of Marine Science, 55, 362–370. Goodwin, N. B., Grant, A., Perry, A. L., Dulvy, N. K. & Reynolds, J. D. (2006). Life history correlates of density-dependent recruitment in marine fishes. Canadian Journal of Fisheries and Aquatic Sciences, 63, 494–509. Goodyear, C. P. (1977). Assessing the impact of power plant mortality on the compensatory reserve of fish populations. In Proceedings of the Conference on Assessing the Effects of Power Plant Induced Mortality on Fish Populations, ed. W. Van Winkle. New York: Pergamon Press, pp. 186–195. Harvey, P. H. & Pagel, M. D. (1991). The Comparative Method in Evolutionary Biology. Oxford: Oxford University Press.

Heino, M. & Godo, O. R. (2002). Fisheries-induced selection pressures in the context of sustainable fisheries. Bulletin of Marine Science, 70, 639–656. Hilborn, R. & Walters, C. J. (1992). Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertaincy. New York: Chapman and Hall. Hutchings, J. A. (2001). Influence of population decline, fishing, and spawner variability on the recovery of marine fishes. Journal of Fish Biology, 59 (Supplement A), 306–322. Hutchings J. A. (2002). Life histories of fish. In Handbook of Fish Biology and Fisheries. Vol. 1., ed. P. J. B. Hart and J. D. Reynolds. Oxford: Blackwell Publishing, pp. 149–174. Hutchings, J. A. & Baum, J. K. (2005). Measuring marine fish biodiversity: temporal changes in abundance, life history and demography. Philosophical Transactions of the Royal Society B, 360, 315–338. Hutchings, J. A. & Reynolds, J. D. (2004). Marine fish population collapses: consequences for recovery and extinction risk. Bioscience, 54, 297–309. Jennings, S. (2005). Size-based analysis of aquatic food webs. In Aquatic Food Webs: An Ecosystem Approach, ed. A. Belgrano, U. M. Scharler, J. Dunne and R. E. Ulanowicz. Oxford: Oxford University Press, pp. 86–97. Jennings, S. & Blanchard, J. L. (2004). Fish abundance with no fishing: predictions based on macroecological theory. Journal of Animal Ecology, 73, 632–642. Jennings, S. & Mackinson, S. (2003). Abundancebody mass relationships in size structured food webs. Ecology Letters, 6, 971–974. Jennings, S., Reynolds, J. D. & Mills, S. C. (1998). Life history correlates of responses to fisheries exploitation. Proceedings of the Royal Society: Biological Sciences, 265, 333–339. Jennings, S., Greenstreet, S. P. R. & Reynolds, J. D. (1999). Structural change in an exploited fish community: a consequence of differential fishing effects on species with

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contrasting life histories. Journal of Animal Ecology, 68, 617–627. Jennings, S., Kaiser, M. J. & Reynolds, J. D. (2001a). Marine Fisheries Ecology. Oxford: Blackwell Science. Jennings, S., Dinmore, T. A., Duplisea, D. E., Warr, K. J. & Lancaster, J. E. (2001b). Trawling disturbance can modify benthic production processes. Journal of Animal Ecology, 70, 459–475. Jennings, S., Pinnegar, J. K., Polunin, N. V. C. & Warr, K. J. (2002). Linking size-based and trophic analyses of benthic community structure. Marine Ecology Progress Series, 226, 77–85. Jones, R. (1974). Assessing the long-term effects of changes in fishing effort and mesh size from length composition data. ICES CM 1974, pp. 33–47. Kaiser, M. J. & de Groot, S. J. (eds.) (2000). The Effects of Fishing on Non-Target Species and Habitats: Biological, Conservation and SocioEconomic Issues. Oxford: Blackwell Science. Kaiser, M. J., Ramsay, K., Richardson, C. A., Spence, F. E. & Brand, A. R. (2000). Chronic fishing disturbance has changed shelf sea benthic community structure. Journal of Animal Ecology, 69, 494–503. Kerr, S. R. (1974). Theory of size distribution in ecological communities. Journal of the Fisheries Research Board of Canada, 31, 1859–1862. Kerr, S. R. & Dickie, L. M. (2001). The Biomass Spectrum: a Predator-Prey Theory of Aquatic Production. New York: Columbia University Press. Law, R. (1979). Ecological determinants in the evolution of life histories. In Population Dynamics, ed. R. M. Anderson, B. D. Turner and L. R. Taylor. Oxford: Blackwell Scientific Publications, pp. 81–103. Law, R. (2000). Fishing, selection and phenotypic evolution. ICES Journal of Marine Science, 57, 659–668. Law, R. & Stokes, T. K. (2000). Evolutionary impacts of fishing on target populations. In

Marine Conservation Biology: the Science of Maintaining Biodiversity, ed. L. Crowder and E. Norse. Island Press. Li, B. L. & Charnov, E. L. (2001). Diversity-stability relationships revisited: scaling rules for biological communities near equilibrium. Ecological Modelling, 140, 247–254. Loeuille, N. & Loreau, M. (2005). Evolutionary emergence of size-structured food webs. Proceedings of the National Academy of Sciences, 102, 5761–5766. Maxwell, D. & Jennings, S. (2005). Power of monitoring programmes to detect decline and recovery of rare and vulnerable fish. Journal of Applied Ecology, 42, 25–37. Myers, R. A., Mertz, G. & Fowlow, P. S. (1997). Maximum population growth rates and recovery times for Atlantic cod Gadus morhua. Fishery Bulletin, 95, 762–772. Nee, S., Read, A. F., Greenwood, J. J. D. & Harvey, P. H. (1991). The relationship between abundance and body size in British birds. Nature, 351, 312–313. Pauly, D., Christensen, V., Dalsgaard, J., Froese, R. & Torres, F. (1998). Fishing down marine food webs. Science, 279, 860–863. Pope, J. G., Stokes, T. K., Murawski, S. A. & Idoine, S. I. (1988). A comparison of fish size composition in the North Sea and on Georges Bank. In Ecodynamics: Contributions to Theoretical Ecology, ed. W. Wolff, C. J. Soeder and F. R. Drepper. Berlin: Springer Verlag, pp. 146–152. Pope, J. G., Rice, J. C., Daan, N., Jennings, S. & Gislason, H. (2006). Modelling an exploited marine fish community with 15 parameters – results from a simple size-based model. ICES Journal of Marine Science, 63, 1029–1044. Reynolds, J. D. (2003). Life histories and extinction risk. In Macroecology, ed. T. M. Blackburn and K. J. Gaston. Oxford: Blackwell Publishing, pp. 195–217. Reynolds, J. D. & Peres, C. A. (2006). Overexploitation. In Principles of Conservation Biology, ed. M. Groom, G. Meffe and

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R. Carroll. Massachusetts: Sinauer, Sunderland. Reynolds, J. D., Dulvy, N. K., Goodwin, N. B. & Hutchings, J. A. (2005). Biology of extinction risk in marine fishes. Proceedings of the Royal Society London, B, 272, 2337–2344. Rice, J. & Gislason, H. (1996). Patterns of change in the size spectra of numbers and diversity of the North Sea fish assemblage, as reflected in surveys and models. ICES Journal of Marine Science, 53, 1214–1225. Roff, D. A. (1992). The Evolution of Life Histories: Theory and Analysis. New York: Chapman & Hall. Savage, V. M., Gillooly, J. F., Brown, J. H., West, G. B. & Charnov, E. L. (2004). Effects of body size and temperature on population growth. American Naturalist, 163, 429–441. Sheldon, R. W., Prakash, A. & Sutcliffe, W. H. (1972). The size distribution of particles in the ocean. Limnology and Oceanography, 17, 327–340. Shin, Y. J. & Cury, P. (2004). Using an individualbased model of fish assemblages to study the response of size spectra to changes in fishing. Canadian Journal of Fisheries and Aquatic Sciences, 61, 414–431. Shin, Y.-J., Rochet, M.-J., Jennings, S., Field, J. & Gislason, H. (2005). Using size-based indicators to evaluate the ecosystem effects

of fishing. ICES Journal of Marine Science, 62, 384–396. Shuter, P. J. & Abrams, B. J. (eds.) (2005). Building on Beverton’s legacy: life history variation and fisheries management. Canadian Journal of Fisheries and Aquatic Sciences, 62, 725–902. Sinclair, M. & Valdimarsson, G. (2003). Responsible Fisheries in the Marine Ecosystem. Rome: FAO. Stokes, T. K., McGlade, J. M. & Law, R. eds. (1993). The Exploitation of Evolving Resources. Berlin: Springer-Verlag. Thiebaux, M. L. & Dickie, L. M. (1993). Structure of the body size spectrum of the biomass in aquatic ecosystems: a consequence of allometry in predator-prey interactions. Canadian Journal of Fisheries and Aquatic Sciences, 50, 1308–1317. Thygesen, U. H., Farnsworth, K. D., Anderson, K. H. & Beyer, J. E. (2005). How optimal life history changes with the community sizespectrum. Proceedings of the Royal Society B, 272, 1323–1331. Ware, D. M. (2000). Aquatic ecosystems: properties and models. In Fisheries Oceanography: An Integrative Approach to Fisheries Ecology and Management, ed. P. J. Harrison and T. R. Parsons. Oxford: Blackwell Science, pp. 161–194. Watson, R. & Pauly, D. (2001). Systematic distortions in world fisheries catches. Nature, 414, 534–536.

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How body size mediates the role of animals in nutrient cycling in aquatic ecosystems ROBERT O . HALL , JR . University of Wyoming, USA

BENJAMIN J . KOCH University of Wyoming, USA

MICHAEL C . MARSHALL University of Wyoming, USA

BRAD W . TAYLOR University of Wyoming, USA

LUSHA M . TRONSTAD University of Wyoming, USA

Introduction Aquatic ecosystems have been fertile ground for understanding the extent to which animals can alter nutrient cycling. Although animals have been included in ecosystem models for years (for example, Teal, 1962), it is only more recently that investigators have looked at animals, either as individuals, single species, or assemblages, as agents regulating nutrient cycling (Kitchell et al., 1979; Meyer, Schultz & Helfman, 1983; Grimm, 1988; Jones & Lawton, 1995). A recent review details how animals can affect nutrient cycling in freshwater ecosystems (Vanni, 2002), but the next step is to understand the controls on which animals are important regulators of nutrient dynamics in ecosystems. One controlling factor is determined by attributes of the animals themselves, such as their body size. Animals can regulate nutrient cycling directly or indirectly (Kitchell et al., 1979; Vanni, 2002). Direct regulation is the transformation and transportation of nutrients by animal ingestion, egestion, production and excretion. For example, animal excretion can constitute the largest source of plant-available nitrogen (N) within an ecosystem (Hall, Tank & Dybdahl, 2003) and animals can move nutrients between habitats (Meyer et al., 1983). Perhaps more common are indirect controls, whereby animals alter nutrient cycling by changing the biomass, production or distribution of the plants or microbes that take up nutrients. For example, predatory fish can regulate phosphorus (P) dynamics or nitrogen retention via a trophic cascade (Elser et al., 1998; Simon et al., 2004). Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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In this paper we consider only direct effects of animals on nutrient cycling, because predicting indirect effects in food webs contains much more uncertainty (Wootton, 1994). A point mentioned by Vanni (2002), that we expand on here, is the role of body size in controlling the degree to which animals contribute to ecosystem nutrient fluxes. Body size may control animal-mediated nutrient cycling by three main mechanisms. First, small animals have higher metabolism and, therefore, higher mass-specific excretion rates (Wen & Peters, 1994; Brown, Allen & Gillooly, this volume). Thus, total biomass being equal, an assemblage with small animals may have higher animal-mediated nutrient fluxes than one with large animals. Second, as body size increases, allometric variation in structural tissue (e.g. P-rich bone) may alter ratios of excreted nutrients. Third, large animals have larger home ranges and are more likely to migrate long distances, so nutrient translocation by animals may also be a function of body size. In this chapter we first address how body size controls nutrient fluxes in the context of the first two mechanisms described above by using published and unpublished data to examine the relationship between nutrient excretion and body size. We also consider the spatial and temporal translocation of nutrients by animal movements as a function of body size. In the second part of the chapter we apply these findings to address how ecosystem-level nutrient cycling will change as a function of variation in animal body size. In short, we know excretion can vary as a function of body size, but does this variation matter in ecosystems? We explore other factors that affect animal-mediated nutrient cycling, such as variation in the biomass of animal assemblages and their taxonomic composition, so that we can compare their influence to the effects of body size. Lastly, predators, especially humans, may alter the size structure of animal assemblages, and we consider how loss of large-bodied organisms may indirectly alter nutrient cycling (see also Jennings & Reynolds, this volume).

Body size and nutrient excretion Rates Aquatic animals excrete N and P in mostly mineral forms which are readily taken up by microbes. The primary form of N is ammonium, which is excreted via the gut in insects, or diffuses across the integument and gills of other animals. Animals primarily excrete P in the form of PO43 . Nutrient excretion rates vary with body size. In general, excretion rates (E) scale allometrically with body mass (M): E ¼ aMb

(15:1)

where a and b are constants (Huxley, 1932; Peters, 1983; Wen & Peters, 1994; Gillooly et al., 2001). For most aquatic animals, the relationship has an exponent b < 1 indicating that excretion rates increase at a rate less than isometric with

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increasing body size (Wen & Peters, 1994). For example, individual ammonium excretion rates for stream invertebrates, from at least 18 taxonomic orders, scale to the 0.85 power of body mass (Fig. 15.1), implying that larger taxa excrete at a lower rate for their size than smaller taxa. The mechanism for the less than proportional increase in excretion rate is probably linked to metabolism, which scales as the 3/4 power of body size (Brown et al., 2004; Brown et al., this volume). However, for many specific groups of animals, b can be higher or lower than 3/4. For example, b ¼ 0.67 for N and 0.54 for P in zooplankton (Wen & Peters, 1994), whereas macroinvertebrates (Fig. 15.1) have higher values. However, body size is not the sole factor controlling variation in animal excretion rate. It is worth considering the influence of other variables, that may alter or interact with the effects of body size, on animal-mediated nutrient cycling in aquatic ecosystems. For example, temperature influences metabolic processes, such as excretion rate (Peters, 1983; Fukuhara & Yasuda, 1989; Zhuang, 2005). Metabolic theory (Gillooly et al., 2001; Brown et al., 2004; Brown et al., this volume) provides a mechanistic framework for incorporating the effects of both temperature and body size on excretion rate. Fed animals have higher excretion rates than unfed animals (Gardner & Scavia, 1981; Grimm,

Figure 15.1 Ammonium excretion rates increase less than proportionally with body size (b < 1) for many benthic stream invertebrate taxa, indicating that larger invertebrates excrete ammonium at a lower rate per mg of body mass than do smaller invertebrates. The regression line (log10 [excretion rate] ¼ 1.057 þ 0.853log10 [mean individual body mass]; n ¼ 320, r2 ¼ 0.381, 95% CI on b [0.776  0.937]) was estimated using type II, reduced major axis linear regression (Bohonak & van der Linde, 2004). Data points were gathered using identical methods on field-caught animals from six streams and represent total excretion rates computed from one or more similarly-sized individuals of the same taxon within the same incubated container (Hall et al., 2003; R. O. Hall, unpublished data; Koch, 2005; M. C. Marshall, unpublished data).

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1988), probably because of active metabolism of recently digested and assimilated N compounds. The use of fed or unfed animals may have contributed to the variability in Fig. 15.1 and make studies where methods differ less comparable. Taxonomic differences can also explain some of the variation in invertebrate nutrient excretion rates (Wen & Peters, 1994). For example, Conroy et al. (2005) found taxonomic differences in excretion rates of P, but not of N, between two species of mussels in the genus Dreissena. Interestingly, in contrast to nearly all other freshwater invertebrate taxa studied to date, N and P excretion rates for Dreissena increase disproportionately with body size (b ¼ 1.379), such that larger individuals excrete nutrients at a higher mass-specific rate than do smaller individuals (Conroy et al., 2005). The mechanisms behind this relationship are unclear, although it highlights the importance of recognizing taxonomy in studies of animal-mediated nutrient cycling. To examine taxonomic and size variation in excretion rates among fishes, we compared published fish excretion rates of individuals (n ¼ 156 for P and 163 for N) and species means (n ¼ 30 species for P and N) among freshwater representatives of 14 families, including Anostomidae, Aspredinidae, Catostomidae, Cetopsidae, Characidae, Characidiidae, Cichlidae, Clupeidae, Curimatidae, Loricariidae, Parodontidae, Pimelodidae, Salmonidae and Trichomycteridae (Schaus et al., 1997b; Gido, 2002; Vanni et al., 2002; Andre, Hecky & Duthie, 2003; B. J. Koch, unpublished data). Individual rates are the excretion of a single fish (many individuals in a species were measured) and species means were calculated by averaging the excretion and size of all the individuals in that species. All studies measured ammonium, but Schaus et al. (1997a) and Andre et al. (2003) measured soluble reactive P, Vanni et al. (2002) estimated total dissolved P, while Gido (2002) measured total reactive P. We converted wet mass to dry mass by assuming dry mass was 25% of wet mass (Schaus et al., 1997a; Gido, 2002; Andre et al., 2003), or used measured values directly (Vanni et al., 2002; B. J. Koch, unpublished data). Excretion of individuals within a species scaled with body size similarly, and were higher or lower than the species means (Table 15.1). The P excretion of three species scaled less than 1 (Table 15.1; Fig. 15.2a), meaning that the massspecific excretion rates declined with increasing size. However, N excretion of species showed greater variability (b < 1, b ¼ 1, b > 1), indicating that both size and taxonomy influence rates (Table 15.1; Fig. 15.2b). When fish species means were considered, excretion scaled proportionally with dry mass (that is b  1; Table 15.1, Figs. 15.2c, d). These data cannot disentangle the relative contribution of phylogeny vs. size because they are not independent. However, comparing species means to individual species, we can conclude that fish scale similarly to each other. Additionally, measurements were collected by different researchers under different conditions, which may cause high variation in excretion rates among all fishes.

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Table 15.1 Reduced major axis regression estimates for nitrogen and phosphorus excretion (log10 g N or P fish1 h1) and size (log10 dry mass, g) in five groups of fish (see Fig. 15.2). Data for Mbuna Cichlidae, Carpiodes carpio, Ictiobus bubalus and Dorosoma cepedianum estimates are excretion rates from individual fish within a taxon. We also calculated the mean excretion rate and mean size of 30 fish species taken from Gido (2002); Vanni et al. (2002); Andre et al. (2003); Schaus et al. (1997b); and Koch (unpublished data) and regressed mean excretion rate on mean body size. The bootstrapped 95% confidence intervals of the exponents are in parentheses. Taxa

Nitrogen n

Mbuna* Cichlidae Carpiodesx carpio Ictiobusx bubalus Dorosomayx cepedianum Species means

Intercept Exponent

Phosphorus r2

n

Intercept Exponent

r2

40 2.04

0.759 (0.664–0.886) 0.769 37 0.975

0.886 (0.567–1.24)

10 2.96

0.789 (0.525–1.06)

0.770 10 1.39

0.733 (0.543–0.848) 0.875

16 2.27

0.983 (0.764–1.43)

0.633 16 0.803

0.568 (0.347–0.906) 0.301

93 2.13

1.14 (1.04–1.24)

0.883 93 1.40

0.921 (0.844–0.997) 0.781

30 2.41

0.953 (0.851–1.05)

0.930 30 0.916

1.07 (0.903–1.32)

x

Gido (2002) Andre et al. (2003) y Schaus et al. (1997b) *

The relative importance of taxonomy, body size and temperature in controlling nutrient excretion rates is only just beginning to be explored, and adequately testing the interactions among these factors will require richer data sets and resolved molecular phylogenies. In addition, determining the basis of taxonomic variation in excretion rates remains a challenge. Body nutrient composition and diet may both play roles. Given that ammonium excretion rates for stream invertebrates are higher for fed than unfed animals (Grimm, 1988), predators, which feed sporadically, may have more variable excretion rates over time than continuously feeding grazers and detritivores. Stoichiometric differences in animal nutrient use might also drive taxonomic variation (Elser & Urabe, 1999). Predators, with relatively N-rich diets, may have higher N excretion rates than other feeding groups. Understanding when to account for taxonomic variation and when body size alone is sufficient for studies of animal-mediated nutrient cycling is central to predict successfully the role of animals in the nutrient dynamics of aquatic ecosystems.

0.176

0.831

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Figure 15.2 Phosphorus (a, c) and nitrogen (b, d) excretion rates (mg P or N fish1 h1) versus dry mass (g) for individual fish of several taxa (a, b) and means of 30 fish species (c, d) from the literature (Schaus et al., 1997b; Gido, 2002; Vanni et al., 2002; Andre et al., 2003; B. J. Koch, unpublished data). See Table 15.1 for regression coefficients.

Ratios of N and P Not only will the amount of N and P excreted by animals be important in ecosystem nutrient cycling, but the ratio of these nutrients may also drive microbial assemblage structure and productivity (Elser et al., 1988). Nutrient ratios in food sources, animal composition and excretion (that is, ecological stoichiometry) have received much attention in aquatic ecology (Sterner & Elser, 2002). Stoichiometric theory predicts that the N:P in excretion is a positive function of the N:P of ingested food, and a negative function of the N:P requirement of the consumer (Sterner, 1990). Data show that the link between N:P in the zooplankton body and excreted N:P is not nearly as strong as the link with the N:P of their food (Elser & Urabe, 1999); that is, most of the variance in excreted N:P is accounted for by variation in the food. Few analyses show how body size drives the N:P in excretion in animals; indeed, there is little information on animal C:N:P content solely as a function of body size (Sterner & Elser, 2002). One hypothesis might be that aquatic animals should increase their N:P content as size increases, because increased size should lead to decreased demand for P as growth rate declines (Elser et al., 1996). Given higher body N:P, big animals should have lower excreted N:P than small ones. However,

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this effect may be hidden by phylogeny and allometric constraints, as taxonomy correlates with body size because large animals are often vertebrates that have high P storage in bone apatite, and presumably a high N:P in excreta. Data on aquatic animals suggest that excreted N:P increases with body size. Wen and Peters (1994) showed that log N excretion rate (mg N/d) increased more steeply with body mass than did excreted P for zooplankton. The difference in the exponents is 0.13, which corresponds to the exponent for N:P of excretion vs. body mass. Thus the N:P of excretion increases with body mass, suggesting that mechanisms other than growth rate control the relationship of excreted N:P with body size. Data from some vertebrates also suggest increases in the N:P excreted with body size. Excretion N:P in fishes and amphibians from a Piedmont stream in Venezuela was positively related to body size, which agrees with qualitative predictions based on a decreasing body N:P with increasing body mass in vertebrates (Vanni et al., 2002). For example, bony-scaled armoured catfishes (Loricariidae) had particularly low body N:P and therefore high N:P in excretion (Vanni et al., 2002). Tadpoles (families Bufonidae and Ranidae) had low excreted N:P; because they do not have ossified bones (low skeletal demand for P). These studies, although few, suggest that not only will body size determine the rates of nutrient regeneration, but it will also determine the ratio of these nutrients, with the data so far suggesting mostly increasing N:P with body size. Mechanisms for this increase are unclear, and certainly vary across taxa. For example, vertebrates will have proportionally more bone as their size increases (Sterner & Elser, 2002), which will increase P demand (lowering P excretion) with body size.

Body size and nutrient translocation Aquatic animals can alter nutrient cycling by moving nutrients from one location to another, thus subsidizing the receiving habitat (Kitchell et al., 1979; Vanni, 2002). In some instances this nutrient movement is between habitats within an ecosystem such as, for example, benthic feeding fish that excrete nutrients in the pelagic zone (Vadeboncoeur, Vander Zanden & Lodge, 2002) or haemulid grunts that feed in seagrass beds at night and rest above coral heads during the day, where they release nutrients that stimulate coral growth (Meyer et al., 1983). In other cases, animals move nutrients between ecosystems on a daily basis; e.g. ocean-foraging river otters (Lontra canadensis) excrete nutrients in discrete locations in terrestrial habitat (Ben-David et al., 2005). Less mobile or small-sized animals may actually concentrate nutrients at high levels in localized areas (Reinertsen et al., 1986). In contrast, Pacific salmon (Onchorhynchus spp.) transport nutrients from the ocean to rivers via an annual long-distance spawning migration (Gende et al., 2002). The degree of movement will be determined in part by the speed at which animals move and the behavioural

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constraints on their home range. Both of these controls on movements should scale with body size. The distance moved by aquatic animals will depend on their body size because swimming speed scales with animal body size (Peters, 1983). For a given time travelled, a big animal can migrate further than a small one. Over large size ranges, an animal’s Reynolds number constrains movement (e.g. zooplankter versus a salmon). Small animals (e.g. rotifers) move very slowly because their short length confers a low Reynolds number, and therefore viscous forces are much higher than inertial forces. Within fishes that have high Reynolds numbers, swimming speed scales at about M0.14 (Weihs, 1977) assuming M / length2.6 (Peters, 1983). These modelled swimming speeds include both Reynolds number effects plus allometric scaling of swimming force and metabolic costs. Animals with lower Reynolds numbers have a steeper positive relationship between body mass and swimming speed, probably because of the more pronounced effects of viscous forces at small sizes. Swimming speed in diving beetles (Dytiscidae), increases as M0.36 (Nachtigall, 1977) assuming M / L2.5 (Benke et al., 1999). Thus, the decline in swimming speed for small animals probably decreases more quickly with body size than it does for fish. Behavioural constraints on home-range size and migration will also control nutrient movement by animals. Home range scales with body size in mammals at roughly M1 (Jetz et al., 2004). Home-range sizes of fishes are similar to mammals, scaling as M1.1, while insects and crustaceans are at M0.7 and molluscs at M0.55 (Alimov, 2003). Given that distance moved will scale as the squareroot of area, distance moved for fishes should then scale as approximately M0.5. This rate of increase with body size in the actual distance moved by animals is higher than that for speed alone, because home range is determined by many more attributes than is speed. These include, for example, resource requirements and interactions with conspecifics (Jetz et al., 2004). Animals that transport substantial nutrients among habitats are likely to be large, as in Pacific salmon (Gende et al., 2002), river otters (Ben-David et al., 2005), and the longdistance migratory fish, sapuara (Semaprochilodus kneri) (Winemiller & Jepsen, 2004). It is important to consider the strong effect of behaviour; the much smaller sapuara migrates long distances along rivers, and therefore transfers nutrients much further than does the coastal river otter. Coral reef fishes are large enough to travel long distances, but many stay in one spot on the reef all their lives. Thus, while large animals are more likely to move nutrients, behavioural characteristics also control this distance.

Consequences of size-varying nutrient cycling Variation in body-size distributions Because excretion rates typically increase less than proportionally with animal body size, variation in size distributions can partially control animal-driven

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nutrient mineralization and storage in ecosystems. Here we ask to what degree does variation in animal size distribution regulate nutrient mineralization? Researchers have described a wide variety of biomass-size distributions (also called size spectra) for aquatic animal assemblages, including flat or smooth, uni-, bi- and poly-modal, and step or asymptotic functions. Size distributions can vary considerably in space and time within and among aquatic habitats (Hanson, Prepas & Mackay, 1989; Stead et al., 2005), complicating generalizations (see Warwick, this volume). The diversity of methods in body-size estimations (for example, Morin & Nadon, 1991; Ramsay et al., 1997; Baca & Threlkeld, 2000) and analytical techniques, such as different sieve or size classes, further complicate size-spectra summaries (Cyr & Pace, 1993; Robson, Barmuta & Fairweather, 2005). However, when only the invertebrate portions of published aquatic assemblage spectra are included (that is, smaller and larger portions excluded), clearer patterns of shape categories emerge. Most size spectra have biomass peaks that are skewed left, meaning larger animals generally account for most of the total biomass, even though they may be outnumbered by smaller ones. Size distributions in lakes vary as a function of habitat. Studies that include multiple habitat types within the same lake suggest that pelagic and littoral assemblages tend to have bimodal distributions of invertebrates (Hanson et al., 1989; Cyr & Pace, 1993; Rasmussen, 1993) and polymodal distributions when fishes are included (Gaedke, 1992), whereas profundal (and sublittoral) distributions tend to be unimodal (Hanson et al., 1989). The magnitude and locations of biomass peaks and troughs also vary among habitats within lakes; littoral habitats have peaks at larger body sizes. For example, the two biomass maxima for littoral habitats tended to occur between 1–4 mg and 64–256 mg wet mass (Rasmussen, 1993), whereas the two peak densities of pelagic zooplankton occurred between 0.044–0.125 mg and 2.0–11.3 mg dry mass for small and large animals, respectively (Cyr & Pace, 1993). Streams generally have unimodal biomass size distributions (Cattaneo, 1993; Bourassa & Morin, 1995; Mercier et al., 1999; Schmid, Tokeshi & Schmid-Araya, 2002). Body-size maxima, as equivalent to a spherical diameter, were between 2–4 mm in streams (Cattaneo, 1993), and the average individual biomass increased slightly with increasing trophic status from 24–40 mg dry mass in oligotrophic to urban eutrophic streams, respectively (Bourassa & Morin, 1995). Overall, although unimodality is robust across many streams, total biomass can vary by an order of magnitude (for example, Bourassa & Morin, 1995) suggesting possible dramatic differences in animal driven nutrient fluxes within a stream system. Estimating nutrient flux from biomass size distributions Animal assemblages with different size distributions should have different nutrient supply rates to ecosystems, all else being equal. To illustrate this

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Figure 15.3 (a–c) Representative animal size spectra from three littoral ecosystems: (a) Lake Brome, (b) Lake Waterloo, (c) Lake Bromont (Rasmussen, 1993). Total biomass (mg dry mass m2) has been normalized to 1000 mg dry mass m2 for the three communities. Size classes are Log2 (mg dry mass). (d–f) Modelled P fluxes (mg P m2 h1) supplied by excretion for the three assemblages, assuming a negative relationship between mass-specific excretion rate and body size. Total nutrient flux varies nearly two-fold for the three communities (60, 115 and 104 mg P m2 h1 for panels d, e and f, respectively) and the shapes of nutrient flux distributions changed relative to size spectra.

point we used data-capturing software to extract published size spectra from plots. We gathered three representative aquatic animal size spectra: a bimodal distribution with proportionally more large individuals (Fig. 15.3a), a strongly peaked bimodal distribution (Fig. 15.3b) and a unimodal distribution (Fig. 15.3c, Rasmussen, 1993). We assumed dry mass was 25% of wet mass (Feller & Warwick, 1988) and normalized the literature spectra data to have equivalent total biomasses (1000 mg dry mass m2) while preserving the same distribution shape in the original data sets. For each of these three animal assemblages, we then calculated the P flux supplied by excretion for each size class (Figs. 15.3d–f ), using a negative relationship between mass-specific excretion rate and body size (mg P mg dry mass1 h1 ¼ 0.0954[dry mass](0.541); Wen & Peters, 1994). While this analysis accounts for variation in animal excretion rate due to body size, it does not incorporate the effects of potentially different temperatures or taxonomic composition among animal assemblages. Nevertheless, despite total biomass being the same for the three communities, total nutrient flux (cumulative area of rectangles) from each of the three animal communities is not equivalent, varying by almost a factor of two in this example (60, 115 and 104 mg P m2 h1 for Figs. 15.3d, e & f, respectively). Furthermore, the shapes of the

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nutrient flux distributions differ from their respective biomass size spectra. For example, although larger animals comprise most of the total biomass in Fig. 15.3a, small- and medium-sized animals supply the bulk of the nutrient flux from this assemblage (Fig. 15.3d). Thus the size spectra of animal communities have important consequences on the supply and cycling of nutrients, and those size classes that contribute most to total assemblage nutrient flux are not necessarily the most biomass-rich size classes in the assemblage. Predator control of prey body size and nutrient cycling The well-known impact of predators on prey size structure may alter nutrient cycling in aquatic ecosystems. Fish predators can decrease average size of prey by eating large zooplankton (for example, Brooks & Dodson, 1965; Li, Wetterer & Hairston, 1985) and large benthic invertebrates in lakes (Blumenshine, Lodge & Hodgson, 2000). Alternatively, planktonic invertebrate predators, such as Chaoborus, select small zooplankton (for example, Dodson, 1974), increasing average prey body size. In streams, predatory invertebrates, fish and mammals tend to consume the largest individuals of their prey (Quinn & Kinnison, 1999; Allan, 2001; Woodward & Warren, this volume). In addition to changes in size structure via consumptive effects, the presence of predators can alter prey-size distribution simply through non-consumptive effects, such as chemical cues (for example, Tollrian, 1995; Peckarsky et al., 2002) and excretion (Ramcharan, France & McQueen, 1996). Simultaneous to their effects on body size, predators can also affect prey physiology by increasing the allocation of nutrients to structural cells, (for example, Lively, 1986; Vanni, 1987; Crowl & Covich, 1990; Stibor, 1992; Barry, 1994; Arendt & Wilson, 2000; Dahl & Peckarsky, 2002), which may change the composition of consumer-mineralized nutrients. Altered size structure of the prey assemblage may change nutrient cycling, because mass-specific excretion rate decreases with increasing animal size. Additionally, body size affects the nutrient ratios at which animals excrete. Changes in excretion N:P can alter the supply of the nutrient that limits primary producers. Elser et al. (1988) suggest that phytoplankton communities are more likely P-limited when the zooplankton assemblage includes large-bodied individuals and N-limited when the zooplankton assemblage is mainly small-bodied individuals. Understanding how changes in the size structure of prey can affect nutrient cycling is not straightforward, because predators can simultaneously alter prey abundance and biomass, and regenerate nutrients by consuming prey. Bartell (1981) modelled P cycling under differing levels of predation using previously published data on zooplankton size and biomass in lakes, and a mass-specific excretion model for zooplankton. Nutrient fluxes from zooplankton did not always increase when the assemblage switched from large-bodied to the

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small-bodied individuals that have greater mass-specific excretion rates. In fact, P fluxes either remained similar, increased or decreased when lakes were altered from low to high planktivore abundance, depending on changes in total zooplankton biomass. However, nutrients may be more available in lakes with abundant zooplanktivorous fish, because smaller zooplankton turn P over faster than larger-bodied zooplankton (Henry, 1985). In addition to zooplankton, fish can also be an important source of nutrients to primary producers. Some studies have reported that the nutrient flux from zooplankton is much larger than fluxes from fish (Ramcharan et al., 1996), while others found the reverse (Vanni & Findlay, 1990; Carpenter et al., 1992). Boers, Vanballegooijen & Uunk (1991) showed that the main P source switched from zooplankton to fish as planktivore biomass increased. Regardless of which animal supplies more nutrients, their body size can affect nutrient cycling. To illustrate how size structure can change nutrient supply and demand we use lakes with low and high planktivorous fish abundance. In lakes with low planktivore abundance, both large and small zooplankton may be present (Fig. 15.4a), but the assemblage is mainly composed of small zooplankton when planktivores are abundant (solid line, Fig. 15.4c). Compensatory increases in the number of small zooplankton may result when fish are present (dashed line, Fig. 15.4c); however, most studies show an overall decrease in total zooplankton biomass (for example, Vanni & Findlay, 1990). When the density of planktivorous fish is low (that is, both large and small zooplankton are present), zooplankton excrete at a range of N:P ratios (grey line is N; black line is P; Figure 15.4b); however, zooplankton excrete at a lower N:P ratio when planktivorous fish are abundant (causing N to be potentially limiting). Based on modelling by Bartell (1981), changes in zooplankton size structure may either increase, decrease or not change lake nutrient fluxes (Fig. 15.4d), depending on compensatory changes in assemblage biomass. In contrast to planktivorous fish, planktonic-invertebrate predators selectively consume small zooplankton, resulting in a large-bodied prey assemblage excreting at a high N:P ratio. Depending on biomass, prey nutrient fluxes could change in either direction but may cause P to be limiting. The effect of predators on zooplankton body size in temperate lakes is well known; however, to our knowledge no studies have investigated how shifts in body size of stream invertebrates could alter nutrient cycling. Because stream predators selectively consume large-bodied prey, similar to planktivores feeding on zooplankton, we suggest that a decline in N:P mineralization and an increase in mineralization rates may hold for streams. However, even with the advances in methods to estimate pools and fluxes of nutrients in streams, the effects of predators on prey body size and nutrient cycling has not been investigated, even though in certain cases stream invertebrates can be an important source of ammonium (Grimm, 1988; Hall et al., 2003; Koch, 2005).

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Figure 15.4 Harvesting and predators can alter the size structure of their prey, which can change nutrient cycling. (a) In an assemblage with low harvesting or planktivore density (plankton-eating fish), large animals persist but the small animals are most abundant. (b) Nitrogen (grey line) and phosphorus (black line) mass-specific excretion rates are inversely related to body size, thus smaller animals excrete at a lower N:P than larger animals. (c) When harvesting or planktivore density is high, only small animals will be abundant, which may cause compensatory increases in density (dashed line). (d) Nutrient cycling by the small-bodied assemblage may result in compensatory increases, decreases or no change in nitrogen and phosphorus supply by animals, but nutrient ratios will probably be altered.

The effect of harvesting-induced changes in animal size structure on nutrient cycling Harvesting by humans affects the size structure of aquatic animal assemblages, and these altered size distributions may affect the rates and types of nutrients mineralized by animals (Jennings & Reynolds, this volume; Persson & De Roos, this volume). Similar to many other animals, humans selectively harvest large individuals and species (Pauly et al., 1998; Jackson et al., 2001; Roy et al., 2003; Allan et al., 2005). Size-selective harvesting can substantially change species composition and food-web structure (for example, removal of predators), leading to fishing down the food web – a process by which larger species, often predators, with slower growth rates are successively removed from the assemblage, leaving smaller species with faster growth rates (and thus higher massspecific nutrient excretion) that occupy lower trophic levels (Pauly et al., 1998; Welcomme, 1999). In addition, size-selective harvesting can decrease body size indirectly, by causing earlier maturation at smaller sizes via rapid evolutionary

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change or increased resource availability that accelerates growth and decreases time to maturity of the remaining individuals (Trippel, 1995). Taken together, human harvesting generally decreases or eliminates the biomass of large animals from an ecosystem (Myers & Worm, 2003; Allan et al., 2005; Ward & Myers, 2005). There are several mechanisms by which harvest-induced changes in animal body size may alter the role of aquatic animals in mineralizing nutrients. Foremost, size-selective harvesting results in the loss of large-bodied individuals and species with high excretion rates per individual, but low mass-specific excretion. There are also important differences in the ratios at which limiting nutrients, such as N and P, are released by animals of different size (Wen & Peters, 1994; Schindler & Eby, 1997; Sterner & Elser, 2002; Vanni et al., 2002). As a result, the removal of large individuals may disproportionately reduce the amount of N relative to P supplied by animal assemblages (Fig. 15.4a, b), assuming there is no compensatory increase in abundances of smaller individuals or species (solid line; Fig. 15.4c). If there are compensatory increases in abundance of smaller individuals or species (dashed line; Fig. 15.4c) with higher massspecific mineralization rates, then the total supply of nutrients by the assemblage experiencing harvesting may equal or surpass the amount supplied by the assemblage before harvesting (Fig. 15.4d). In addition, because home-range size and migration distance increases with body size (Brown, 1995; Alimov, 2003; Jetz et al., 2004), reduced body size due to harvesting could also decrease the spatial scale over which nutrients are distributed by animals. This impact has been realized; harvesting of large, migratory salmon may have decreased marine nutrient loads to inland rivers, potentially lowering their productivity (Thomas et al., 2003). Moreover, the larger animals, which are often the first and most intensely harvested, generally have longer lifespans and more stable population cycles than the smaller, short-lived species that are less frequently harvested. Therefore, the removal of large, long-lived animals could increase the fluctuations of nutrients mineralized by animal populations. Overharvesting of large animals is a hallmark of all aquatic environments (Myers & Worm, 2003; Allan et al., 2005). However, surprisingly little is known about how the removal of larger animals alters the type or supply rate of nutrients mineralized by animal assemblages and, more importantly, whether such changes in nutrients are large enough to alter ecosystem-level processes. In the Baltic sea, Hjerne and Hansson (2002) estimated the removal of N and P in fish biomass by harvesting to be 1.4–7% of the total nutrient load, although the nutrient loss due to decreased mineralization by fish was not quantified. Although information is available on how predators can mediate nutrient mineralization rates by altering the size-structure of their prey, the process and long-term effects of harvesting by humans are likely to be very different. Humans typically remove the biomass of the largest animals, rarely switch

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prey until populations are severely reduced or regulatory restrictions are imposed, and harvest at maximal rates, which are often supported by external factors such as economic subsidies. In freshwater, species removals for biomanipulation (Horppila, 1998; Tarvainen, Sarvala & Helminen, 2002), and declines in introduced species, affect nutrient fluxes (Kraft, 1993); however, few studies have documented the direct effects of size-selective harvesting on nutrient fluxes. One reason is the mismatch in the data that are available on nutrient mineralization rates and harvesting rates of aquatic animals between marine and freshwater ecosystems. There are comparatively better data on catch size and body size of marine animals (Pauly et al., 1998; Myers & Worm, 2003; Ward & Myers, 2005) than freshwater animals (Allan et al., 2005), whereas there are more empirical data on nutrient regeneration rates for freshwater animals (Sterner & Elser, 2002). In marine systems, it may be useful to apply bioenergetic models to estimate the amount and type of nutrients lost from these systems as a result of having removed 80% of the large predatory fish biomass (Myers & Worm, 2003). Predicting the effects of harvesting-induced changes in body size on nutrient cycling is a new challenge that could improve our understanding of the role of animals in ecosystem functioning, and provide urgently needed guidance for managing and restoring these systems.

The next steps? Given that animals can often be important regenerators, storers and transporters of nutrients in ecosystems (Kitchell et al., 1979; Gende et al., 2002; Vanni, 2002; Koch, 2005), body size may be the single most important trait of the animals themselves in controlling these processes. There are plenty of avenues in which to explore further the role of body size in conjunction with other animal attributes (for example, phylogeny), and ecosystem processes. Below we give some of these examples. 1.

2.

3.

Taxonomic identity probably determines a large fraction of variation in excretion rates, and taxonomy covaries with body size. To what degree does size alone determine nutrient excretion rates? Can we integrate size and phylogeny to improve predictions of nutrient excretion rate? Body size allows us to examine how traits of animals impact ecosystem processes, but we cannot forget that the attributes of the ecosystems themselves will, in part, determine the impact. For example, plant nutrient demand, disturbance and hydrologic flushing rates are certainly important. How important is animal assemblage structure relative to physical controls and plant/microbial demand for nutrients? We can only speculate as to the potential role of many fisheries on changes to nutrient cycling. Some are well known (for example, salmon), but most are unknown (for example, groundfish stocks). These human-induced

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changes present an opportunity to examine how changes in aquatic animal assemblages affect ecosystem processes and may provide the means to compare the relative importance of direct versus indirect effects of assemblage and size structure on nutrient cycling.

Acknowledgements Mike Vanni, Emidio Andre, Keith Gido and Maynard Schaus kindly provided tables of their published data for analysis. Two anonymous reviewers provided useful comments on an earlier draft of this manuscript. Financial support was provided by National Science Foundation; Environmental Protection Agency; and the Juneau Pacific Northwest Research Station, USDA Forest Service.

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Stead, T. K., Schmid-Araya, J. M., Schmid, P. E. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487. Sterner, R. W. (1990). The ratio of nitrogen to phosphorus resupplied by herbivores – zooplankton and the algal competitive arena. American Naturalist, 136, 209–229. Sterner, R. W. & Elser, J. J. (2002). Ecological Stoichiometry. Princeton: Princeton University Press. Stibor, H. (1992). Predator induced life-history shifts in a fresh-water cladoceran. Oecologia, 92, 162–165. Tarvainen, M., Sarvala, J. & Helminen, H. (2002). The role of phosphorus release by roach Rutilus rutilus (L.) in the water quality changes of a biomanipulated lake. Freshwater Biology, 47, 2325–2336. Teal, J. M. (1962). Energy flow in the salt marsh ecosystem of Georgia. Ecology, 43, 614–649. Thomas, S. A., Royer, T. V., Minshall, G. W. & Snyder, E. (2003). Assessing the role of marine derived nutrients in Idaho streams. In Nutrients in Salmonid Ecosystems: Sustaining Productivity and Biodiversity, ed. J. G. Stockner. Bethesda, Maryland: American Fisheries Society, pp. 41–55. Tollrian, R. (1995). Predator-induced morphological defenses: costs, life history shifts, and maternal effects in Daphnia pulex. Ecology, 76, 1691–1705. Trippel, E. A. (1995). Age at maturity as a stress indicator in fisheries. Bioscience, 45, 759–771. Vadeboncoeur, Y., Vander Zanden, M. J. & Lodge, D. M. (2002). Putting the lake back together: reintegrating benthic pathways into lake food web models. Bioscience, 52, 44–54. Vanni, M. J. (1987). Effects of nutrients and zooplankton size on the structure of a phytoplankton community. Ecology, 68, 624–635.

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Welcomme, R. L. (1999). A review of a model for qualitative evaluation of exploitation levels in multi-species fisheries. Fisheries Management and Ecology, 6, 1–19. Wen, Y. H. & Peters, R. H. (1994). Empirical models of phosphorus and nitrogenexcretion rates by zooplankton. Limnology and Oceanography, 39, 1669–1679. Winemiller, K. & Jepsen, D. B. (2004). Migratory neotropical fish subsidize food webs of oligotrophic blackwater rivers. In Food Webs at the Landscape Level, ed. G. A. Polis, M. E. Power and G. R. Huxel. Chicago: University of Chicago Press, pp. 115–132. Wootton, J. T. (1994). Predicting direct and indirect effects: an integrated approach using experiments and path analysis. Ecology, 75, 151–165. Zhuang, S. (2005). The influence of body size and water temperature on metabolism and energy budget in Laternula marilina Reeve. Aquaculture Research, 36, 768–775.

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CHAPTER SIXTEEN

Body sizes in food chains of animal predators and parasites JOEL E . COHEN Rockefeller and Columbia Universities, New York

Introduction Food chains in which animal predators are bigger than their animal prey are called predator chains; those in which the consumers are smaller are called parasite chains (Elton, 1927; Hutchinson, 1959, p. 147). The purpose of this chapter is to display and test empirically some consequences, for predator chains and parasite chains, of assuming that the average mass of a consumer species (predator or parasite) is related to the average mass of its animal resource species (prey or host) by a power law with an exponent less than 1. In 1858, as part of his development of the theory of evolution, Wallace (1858, p. 54) noted that animal predators are generally larger and less numerous than their prey. Among the many echoes of Wallace’s remark, Elton (1927) observed anecdotally that animal predators weigh more than their prey in terrestrial food chains, Hutchinson (1959) analyzed some of the theoretical consequences of predators weighing more than their prey, and Sheldon, Prakash and Sutcliffe (1972) and others posited that marine animal predators outweigh their marine animal prey (see also Humphries, this volume; Woodward & Warren, this volume). Only recently have body sizes been studied empirically in parasite chains (Memmott, Martinez & Cohen, 2000; Leaper & Huxham, 2002) and parasitoid chains (Cohen et al., 2005). The study of parasitoid chains (e.g. Rott & Godfray, 2000; Memmott et al., 2000) appears not to have been considered by Elton (1927) and Hutchinson (1959). Predator and parasite chains are not the only possibilities observed in nature. Other relations between mass and feeding arise from social hunting and metaphoetesis. Among animals that hunt socially (such as wolves and army ants), the aggregate mass of the hunting group may be a more appropriate index of size than the mass of an individual predator. In animals where mass or feeding habit or both change dramatically with the stage of the life cycle (as in many insects and fishes), it is misleading to represent the masses of all stages by a typical adult Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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mass (Hutchinson, 1959; Cohen et al., 2005). Hutchinson (1959) called a change in diet with changing stage of the life cycle metaphoetesis. When Christine Mu¨ller measured the body lengths of individual aphid hosts and of their parasitoid wasp consumers (Cohen et al., 2005, raw data available online), one nymphal aphid Capitophorus carduinis parasitized by a male wasp Aphidius matricariae was longer than the wasp when the wasp emerged from its aphid host, while another nymphal aphid Capitophorus carduinis parasitized by a male wasp Aphidius matricariae was shorter than the wasp when the wasp emerged from its aphid host. Both aphids were found on the same plant species Cirsium palustre. Even controlling for the life stage of the aphid, for the sex of the parasitoid wasp, and for the plant, the ordering of body sizes may differ from one consumer–resource pair of individuals to another. This single instance is illustrative of the variability in the relationship of host and parasitoid body length found in many comparable observations. In most real food webs, predator chains and parasite chains are tightly interwoven because animal predators of almost all sizes support viruses, bacteria and other microscopic and macroscopic parasites. The analysis here of the typical patterns of predator chains and parasite chains makes no claim to cover all kinds of food chains. The relation between the average masses of animal predator species and the average masses of animal prey species has been approximated empirically as a power law (Schoener, 1968; Peters, 1983, p. 277; Ve´zina, 1985; Warren & Lawton, 1987). The power law also applies to individual body masses of aphids and parasitoid wasps (Cohen et al., 2005), but the theoretical implications parallel to those derived here for species-average masses remain to be studied. The analysis below predicts, first, that in predator chains, there is an upper limit to the mass of possible predators and prey; and that this upper limit is independent of the number of trophic links in the chain and independent of the mass of the smallest prey. Conversely, in parasite chains, there is a lower limit to the mass of the smallest host and parasite; this limit is independent of the number of trophic links in the chain and independent of the mass of the largest host. A second consequence is that, in a predator chain, the ratio of predator mass to prey mass decreases according to a power law, with an exponent one less than that for predators and prey masses, as the trophic level and the mass of the prey increase. (In a single food chain in which no species occurs more than once, the trophic level of a species may be unambiguously defined as the number of links between it and the basal species in the chain; thus the basal species has trophic level 0, its consumer has trophic level 1, and the top species in a chain of n trophic links and n þ 1 species has trophic level n.) Conversely, in a parasite chain, the ratio of parasite mass to host mass increases as the trophic level of the host increases (and the mass of the host decreases).

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This theoretical and exploratory analysis of body sizes and feeding is part of a larger picture that includes numerical abundance (Cohen, Jonsson & Carpenter, 2003).

Theory Maximal and minimal body masses Consider a food chain based on an animal (prey or host) of mass M0. Let M1 ¼ f (M0) be the typical (e.g. geometric mean) mass of a consumer (predator or parasite) of that prey, ignoring variation in the mass of consumers that eat prey of a given mass. Let M2 ¼ f (M1) ¼ f ( f (M0)) ¼ f 2(M0) be the typical mass of a consumer that eats the consumer of typical mass M1. The notation M2 ¼ f 2(M0) indicates that M2 results from applying two iterations of f to M0; f 2(M0) does not denote the square of f (M0), which would be written [ f (M0)]2. Similarly, f nþ 1(M0) ¼ f ( f n(M0)) is the typical mass of a consumer n þ 1 trophic links above the basal animal of mass M0. When the typical mass Y of predators on animal prey of mass X is a power function Y ¼ f ðXÞ ¼ AXB ; A > 0;

(16:1) b

then by induction (letting ^ denote exponentiation so that a^b means a ) ! n1 X n n n Bn ^ m f ðM0 Þ ¼ M0  ½A B  ¼ M0B  Að1B Þ=ð1BÞ : (16:2) m¼0

The equality on the left of Eq. (16.2) is valid for any B. The equality on the right of n1 P m B ¼ ð1  Bn Þ=ð1  BÞ. Were the Eq. (16.2) is valid when B 6¼ 1, since then m¼0

consumer’s mass directly proportional to the resource’s mass according to Y ¼ AX, i.e. were B ¼ 1, then the mass of the consumer species would change by a factor of A with each additional link in the food chain and then f n(M0) ¼ AnM0. Were B ¼ 0, the mass of consumers would be constant and equal to A, regardless of their position in a food chain. Assume henceforth that 0 < B < 1, in addition to the previous assumption that A > 0. Then according to Eq. (16.1), consumer and resource would have equal body mass X ¼ f(X) when X ¼ A1/(1  B), and this mass is strictly positive. This positivity guarantees that the intersection of the power law Eq. (16.1) with the diagonal line where Y ¼ X lies in the positive quadrant. In this model, a chain is a predator chain or a parasite chain according to whether M0 < A1/(1  B) or M0 > A1/(1  B). With increasing trophic level, the masses of successive consumers approach the finite limit A1/(1  B) > 0 (Fig. 16.1a) because the assumption 0 < B < 1 implies Bn # 0 as n"1 and hence lim f n ðM0 Þ ¼ A1=ð1BÞ : n"1

(16:3)

BODY SIZES IN FOOD CHAINS

The limit Eq. (16.3) is a maximum if each consumer has a bigger mass than its resource, as assumed in a predator chain. The limit Eq. (16.3) is a minimum if each consumer has a smaller mass than its resource, as assumed in a parasite chain. The predicted maximal mass of a top predator is independent both of the number of links leading up to that predator and of the mass M0 of the basal animal prey in the food chain. The predicted minimal mass of a parasite is independent both of the trophic level of that parasite and of the mass M0 of the basal animal host in the food chain. The limit A1/(1  B) is very sensitive to the values estimated for A and B. As B"1, 1/(1  B) A "1. The values of A and B of course are not known exactly. They are usually estimated by a least-squares fit of the coefficients of the linear relation y ¼ a þ bx where y ¼ log10 Y and x ¼ log10 X. The parameters are connected by A ¼ 10a but B ¼ b. For a given value of A, the closer B is to 1, the slower the approach to the limiting size as one proceeds along a food chain from successive resource to successive consumer (Mark Huxham, personal communication, 9 September 1995). So the limit A1/(1  B) may not be closely approached in reality when there are other limitations on food chain length. According to this model of species-average body mass in food chains, in very long chains, the predators are mostly big, close in mass to the limiting maximum, and the parasites are mostly small, close in mass to the limiting minimum (Fig. 16.1a). The removal from a predator chain of top predators shifts the size distribution of species-average body masses from one concentrated near the upper maximum to a more widely spaced distribution across the lower portions of the possible range of average body masses. This prediction could be compared with quantitative data on the body size distributions of North American vertebrate species before and after the major extinction of the megafauna and with quantitative data on the body size distributions of marine fauna before and after widespread industrial fishing. This allometric model of species-average body masses has an implication for predator–parasite cycles. Assume that Mt þ 1 ¼ AMtB along a predator chain of n links, t ¼ 0, . . ., n  1, that the top predator is the starting point for a parasite chain of n links, i.e. V0 ¼ Mn > a1/(1  b) and Vtþ 1 ¼ aVtb, t ¼ 0, . . ., n  1, with a > 0, 0 < b < 1 along the parasite chain. Then it turns out that M0 can be less than, equal to, or greater than Vn. More generally, dropping the assumption that the predator chain and the parasite chain are of equal lengths, it is still possible for M0 to be less than, equal to, or greater than Vn, as long as each chain is sufficiently long. The case where Vn ¼ M0, i.e. where the basal prey of the predator chain weighs the same as the top parasite of the parasite chain, is illustrated numerically in Fig. 16.1b. In this case, if the basal prey and the top parasite were the same

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(a) 100 predator food chain 10 consumer weight

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0.1 parasite food chain 0.01

0.001 0.001

0.01

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100

Figure 16.1 (a) Theoretical progression of body masses along a predator chain and a parasite chain. Arrows go from resource to consumer. Body masses are on logarithmic scales. The power-law relation Eq. (16.1) appears as a straight dashed line with slope B; here, B ¼ 1/2 for both predator chain (A ¼ 10) and parasite chain (A ¼ 0.1). On the solid diagonal line, consumer mass equals resource mass. Predator chains appear above the diagonal; parasite chains appear below the diagonal. In the predator chain, an arbitrary small basal prey mass is chosen (in this example, M0 ¼ 0.001) and the corresponding predator mass M1 is found by moving upward to the upper dash line. This predator is the prey of the predator at the next trophic level of the chain. The mass M1 is located on the abscissa by moving horizontally right to the diagonal line. Then vertical upward motion to the upper dashed straight line gives the mass M2 of the predator two links above the basal prey. Alternating horizontal right and vertical upward motions intersect the power function (upper dashed straight line) at the masses of successively higher predators in the predator chain. All such trajectories converge where the upper dashed line and the diagonal line intersect. In the parasite chain, an arbitrary large basal host mass is chosen (in this example, M0 ¼ 100) and the corresponding parasite mass M1 is found by moving down to the diagonal line. This parasite is the host of the parasite at the next trophic level of the chain. The mass M1 is located on the abscissa by moving horizontally left to the diagonal line. Then moving down to the lower dashed straight line gives the mass M2 of the parasite two links above the basal host. All such trajectories converge where the lower dashed line and the diagonal line intersect. (b) Theoretical masses of species in a predator chain (open bars) and in a parasite chain (filled bars) where the top predator is the basal host, and the top parasite has the same mass as the basal prey. In the predator chain, Mnþ1 ¼ 10 Mn0.5 and the upper limit of mass is 100. In the parasite chain, Vnþ1 ¼ Vn0.5 and the lower limit of mass is 1. M0 ¼ V10 ¼ 1.004503 and M10 ¼ V0 ¼ 99.55172.

BODY SIZES IN FOOD CHAINS

(b)

100 90 80

predator chain

body weight

70 60 50 40 30 20 parasite chain

10 0 0

1

2 3 4 5 6 7 8 9 trophic level in predator chain

10

Figure 16.1 (cont.)

species, the predator chain and the parasite chain would be linked in a predator– prey cycle. On the linear scale of mass used in Fig. 16.1b, after the first few trophic levels in both the predator chain and the parasite chain, the consumers are near in mass to the limiting mass.

Predicted value of the exponent The exponent B may be computed exactly for simple models of the distribution of the pairs (x, y), where x ¼ log10 X and y ¼ log10 Y are log prey (or host) mass and log predator (or parasite) mass, respectively. Suppose xmin is the log10 minimal observed species average mass and xmax is the log10 maximal species average mass. The previous theory predicts that xmax ¼ log10(A1/(1  B)) but the following calculations hold whether or not that prediction is true. The slope of any linear relation between y and x will be unaffected if both x and y are replaced by the identical linear transformation of x and y, so no generality is lost by assuming that xmin ¼ 0 and xmax ¼ 1. Then each trophic link from resource to consumer may be represented by a dot in a square in the (x, y) plane with lower left corner at the origin (0, 0) and upper right corner at (1, 1). The diagonal of the square is the locus of points where consumer body mass equals resource body mass. Suppose that trophic links are uniformly and independently distributed over this square, and that all links above the diagonal are in predator chains and all links below the diagonal are in parasite chains. Then, in a predator chain, for a given x (between 0 and 1), the expected y is halfway between the diagonal and the upper horizontal edge of the square, that is, E(y|x) ¼ x þ (1/2)(1  x) ¼ 1/2 þ x/2. Thus the slope of average y as a linear function

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of x is predicted to be B ¼ 1/2. Similarly, in a parasite chain, for a given x (between 0 and 1), the expected y is halfway between the diagonal and the lower horizontal edge of the square, that is, E(y|x) ¼ x/2. The slope of average y as a linear function of x is again predicted to be B ¼ 1/2. In the part of this model that pertains to a predator chain, the assumption that each trophic link is uniformly and independently distributed in the triangle above the diagonal follows from the cascade model (Cohen, Briand & Newman, 1990) in the continuous limit (possibly with additional assumptions) of many species of predators and prey. The cascade model assumes that all species are ordered by something interpreted here as body mass, and that each consumer species consumes with equal probability and independently every species smaller than it. (The cascade model does not attempt to describe parasite chains because it was intended to account for food-web data that ignored parasites.) The continuous limit of the joint distribution of prey-to-predator links posited in the cascade model is (possibly with additional assumptions) a twodimensional distribution of trophic links that is uniform in the upper triangle above the diagonal from (0, 0) to (1, 1) in the unit square in the plane where x ¼ log10 X and y ¼ log10 Y, as supposed in the previous paragraph. For parasite chains, to derive a distribution of trophic links in the (x, y) plane that is uniform over the triangle below the diagonal, as supposed above, all that is required is to reverse the ordering by body size in the argument just given for predator chains. When the pairs (x, y) are not distributed uniformly but lie in a band parallel to the diagonal, the predicted slope B will move from 1/2 toward 1. Such a band parallel to the diagonal would arise if there were a nearly constant ratio of average body mass between consumer (predator or parasite) and resource. When the pairs (x, y) lie in a band parallel to the x axis (because most predator species are roughly the same size, or most parasite species are roughly the same size), the predicted slope B will move from 1/2 toward 0.

Ratios and differences of consumer mass and resource mass Let R ¼ Y/X ¼ AXB 1 be the ratio of consumer mass to resource mass in a single trophic link. Then R is a decreasing power-law function of X. The exponent B  1 is negative because B < 1. A regression of log R on log X is predicted to have a slope exactly one less than the slope of a regression of log Y on log X, for the same set of data. The ratio R decreases (towards a limit of 1) with increasing trophic level of the prey in predator chains. In parasite chains, because body masses decrease with increasing trophic level, the ratio R increases towards a limit of 1 with increasing trophic level of the host. The difference in masses behaves in a more complex way than the ratio of masses, as the following analysis shows. Let D ¼ Y  X ¼ (R  1)X be the difference between the consumer mass Y and the resource mass X in a single

BODY SIZES IN FOOD CHAINS

trophic link. (In predator chains, D > 0. In parasite chains, D < 0.) Because dD/dX ¼ RB  1, the difference D increases with increasing resource mass X if and only if R > 1/B. The smaller B is, the bigger R must be for D to increase with X. As B < 1, a necessary condition for D to increase with X is that R > 1, and this happens only in predator chains. Thus, in predator chains, the difference D in mass between consumer and resource may increase with increasing trophic position (if initially R > 1/B); but once R  1/B, the difference D will thereafter decrease (towards a limit of 0) with increasing trophic position. By contrast, in parasite chains, where R < 1 and B < 1, it follows that RB  1 < 0 always; hence with increasing trophic level (and therefore decreasing body mass), D is always increasing (from negative values towards a limit of 0), that is, host mass minus parasite mass is always positive and decreases towards a limit of 0.

Data The data presented here deal only with food webs (cross-linked food chains), rather than with isolated food chains. The theory is relevant to these food webs in so far as food chains are a first approximation to more complex food webs. First, two examples of data on the masses of animal predators and their animal prey in a particular community will be analyzed. Then some data will be examined from literature surveys of pooled communities of specified habitat types (terrestrial and coastal). A recent database of the masses of consumers and resources (Brose et al., 2005) has been analyzed by Brose et al. (2006).

Studies of a well-defined community Menge et al. (1986) described the food web and the masses of the animals of a tropical Panamanian rocky intertidal community. From 31 data points (Fig. 16.2a), hand-read in part from their published graphs, linear regression of log10 masses yielded a ¼ 2.2334 (with 95% confidence interval (1.80, 2.67)), and b ¼ 0.4819 (with 95% confidence interval (0.19, 1.15)). The geometric mean mass Y (kg) of animal predators on animal prey of mass X would be estimated from these data as Y ¼ 0.1712X0.4819 and the upper limit in mass A1/(1  B) for the largest predator would be nearly 20.4 kg. The largest observed predator in the data weighed just under 2 kg. The 95% confidence interval for B includes both 0 and 1. If the data satisfy the assumptions of the underlying regression model well enough to justify the conclusion that the asserted confidence interval really has probability 95%, then these data do not specify an allometric relation with sufficient precision to have the predictive upper limit falsified by any finite maximal predator mass. A simple sensitivity calculation, referred to below as ‘the 10% sensitivity range,’ confirms a wide range of uncertainty in the upper limit. If the regression intercept log A and the regression slope B are both replaced by 90% of their estimated values, the maximal predator mass A1/(1  B) is 3.5 kg. If the regression

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(a) 3.5 3 log10 weight (g) of predator

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2.5 2 1.5 1 0.5 0 –0.5 –1 –1

–0.5

0

0.5

1

1.5

2

log10 weight (g) of prey

Figure 16.2 (a) Predator masses and prey masses in trophic links of a tropical rocky intertidal food web described by Menge et al. (1986). The solid diagonal line indicates where predator and prey masses are equal; all but one of the trophic links fall above this line. The upper dashed line is the regression line: log10(predator mass, g) ¼ 2.2334 þ 0.4819 log10(prey mass, g). The regression line is obtained by ordinary least squares using the log-transformed masses; the standard error of the slope coefficient is 0.3268. The data are read from Menge et al. (1986); the analysis and figure are original. (b, c) Prey and predator body mass (kg) in Tuesday Lake in (b) 1984 and (c) 1986, one marker for every trophic link in the unlumped food web. Cannibalistic links are excluded. Dotted line indicates equal prey and predator body mass. The links are coded according to the prey: circles ¼ phytoplankton, squares ¼ zooplankton, stars ¼ fish. For 1984, the regression coefficients were a ¼ 1.5598, b ¼ 0.8445, with correlation r ¼ 0.7859 and 263 trophic links (Jonsson et al., 2005, p. 34). For 1986, the regression coefficients were a ¼ 1.4108 and b ¼ 0.5928, with correlation r ¼ 0.6094 and 233 trophic links. (d) Regression lines from (b, solid diamonds) and (c, open squares) plotted over the approximate range from the mass of the smallest observed organism to the mass where predator and prey are equal. Figure 16.2b is reprinted from Cohen et al. (2003) with permission from the National Academy of Sciences. Figure 16.2c is reprinted from Jonsson et al. (2005), copyright 2005 by T. Jonsson, J. E. Cohen, S. R. Carpenter. Figure 16.2d is original.

intercept log A and the regression slope B are both replaced by 110% of their estimated values, the maximal predator mass is 169.2 kg. Combining 90% of log A with 110% of B and vice versa yields a narrower range of uncertainty from 19.0–21.8 kg. When a plausible range of the predicted maximal size is as large as the 10% sensitivity range, from 3.5–169.2 kg, only order-of-magnitude agreement between predictions and observations should be expected, at best. If seals or sea lions are occasionally part of the rocky intertidal community, the average body mass of those consumers could be compared with the limit

BODY SIZES IN FOOD CHAINS

(b)

10−2

predator body mass (kg)

10−4 10−6 10−8 10−10 10−12 10−14 −14 10

10−12

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10−4

10−2

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10−2 10−4 10−6 10−8 10−10 10−12 10−14 −14 10

10−12

10−10 10−8 10−6 10−4 prey body mass (kg)

10−2

100

Figure 16.2 (cont.)

predicted here. For example, adult Gala´pagos fur seal females Arctocephalus galapagoensis average about 28 kg in body mass (Horning & Trillmich, 1997). Gala´pagos fur seal bulls average about 70 kg in body mass (http://www.tamug. tamu.edu/labb/Galapagos/GFSwork/GFS_work.htm, accessed 27 August 2005). Cohen et al. (2003), Reuman and Cohen (2004), Jonsson, Cohen and Carpenter (2005), Reuman and Cohen (2005), and Cohen and Carpenter (2005) analyzed the community food web, the numerical abundance and the average body size of species in the pelagic community of a small lake, Tuesday Lake, in Michigan. The raw data on the food web, average body mass and numerical abundance by

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(d) 15 10 predator body mass (log10 kg)

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5 0 –5 –10 –15 –10 –14

–9

–4 1 prey body mass (log10 kg)

6

11

Figure 16.2 (cont.)

species are given by Jonsson et al. (2005). Tuesday Lake was intensively sampled during the summers of 1984 and 1986. During the summer of 1985, the three resident species of fishes were largely removed and replaced by a fourth fish species, which consumed the remaining individuals of the original three fish species. In addition to the complete turnover of the fish species present in Tuesday Lake between 1984 and 1986, the other species in the lake also changed dramatically between 1984 and 1986 (Jonsson et al., 2005, p. 23). Almost all predators had larger average body mass than their prey in 1984 (Fig. 16.2b) and 1986 (Fig. 16.2c). The calculated upper limit in 1984 exceeds 10.7  109 kg, far in excess of the largest average species mass observed in 1984, namely, 1.29  103 kg, or 1.29 g. The upper limit in 1986, 0.34  103 kg, or 0.34 g, was exceeded by the average body mass, 1.95  101 kg, of the largest species, the introduced fish Micropterus salmoides. The average body mass of this fish also exceeded the upper limit of the 10% sensitivity range. The allometric model of the relationship between predator and prey mass was probably less adequate in 1986 than in 1984: the correlation (on log-log scales) between predator and prey masses dropped notably from 1984 to 1986. Following the complete manipulation of the fish fauna in 1985, the pelagic community may have been observed in 1986 during a transient response to the manipulation. The regression lines before and after the manipulation appear in Fig. 16.2d. While the predator–prey pairs of Cohen et al. (1993) could reasonably be seen as uniformly distributed in the upper triangle of the square in the (x, y) plane, these trophic links were pooled from a variety of different communities. The

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predator–prey pairs from Tuesday Lake (Figs. 16.2b, c) and some other individual communities indicate that the pairs (x, y) may sometimes lie in a band parallel to the diagonal (Reuman & Cohen, 2004, p. 857). The non-parasite data from Ythan estuary (Leaper & Huxham, 2002, p. 447) seem to be intermediate between lying in an upper triangle and lying in a band parallel to the diagonal; they are distributed in a wedge shape.

Studies that pool multiple communities Numerous studies have collected masses of organisms in defined taxonomic groups from scattered published sources and identified trophic links based on reports of feeding habits, without reference to whether the organisms would be likely to occur within a single habitat at any single time (e.g. Schoener, 1968; Peters, 1983; Ve´zina, 1985; Hansen, Bjı´rnsen & Hansen, 1994). Other studies have combined community studies and literature surveys (e.g. Warren & Lawton, 1987; Cohen et al., 1993; Jonsson & Ebenman, 1998a; Brose et al., 2006). Cohen et al. (1993) presented two independently collected sets of data on the sizes of animal predators and prey in multiple community food webs. Data set A gave average adult masses of predators and prey in 354 trophic links from 18 community food webs. Data set B gave lengths of prey and predators in 478 trophic links from 30 webs of a compendium of sink, source and community webs. In roughly 90% of the trophic links reported in food webs from terrestrial, coastal, freshwater and marine habitats, the body mass of an animal predator exceeded that of its animal prey. Figure 16.3a compares the estimated regression lines of 109 trophic links from coastal webs in data set A, ten trophic links from coastal webs in data set B, and 31 trophic links from Menge et al. (1986). All three regression slopes are less than 1/2. The predicted largest predator from coastal data sets A and B would weigh, respectively, 0.4 kg (10% sensitivity range 0.2–0.8 kg) and 54.0 kg (10% sensitivity range 11.6–293 kg). Figure 16.3b compares the estimated regression lines of 48 trophic links from terrestrial webs in data set A, 162 trophic links from terrestrial webs in data set B, and a line hand-fitted to graphed terrestrial data from Ve´zina (1985). All three regression slopes are greater than 1/2. The predicted largest predator from terrestrial data set A would weigh 23.8 kg (10% sensitivity range 3.6–247 kg). Because the slope for data set B is so close to 1, the predicted maximal predator mass is meaningless. For the estimates from Ve´zina’s data, the largest predator would weigh 168 kg (10% sensitivity range 13.5–4660 kg). For comparison, the heaviest terrestrial vertebrate predator in Ve´zina’s data is the East African lion (Panthera leo), which weighs 160 kg. The eight empirical regression lines of log predator weight as a function of log prey weight plotted in Figs. 16.2 and 16.3 have slopes ranging from 0.1463 to 0.9443, with median value 0.5489, not far from the predicted value of 1/2.

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(a) 6

log10 weight (g) of predator

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4

coastal B

2 Menge 1986

coastal A

0 –2 –4 –6 –6

–4

–2 0 2 log10 weight (g) of prey

4

6

Figure 16.3 (a) Regression lines of predator masses and prey masses in trophic links in three sets of coastal food webs. The regression line for Menge et al. (1986) is taken from Fig. 16.2a. The regression lines for coastal A and coastal B are computed from the statistics of Cohen et al. (1993, p. 71, Table 2). Lengths reported in data set B were converted to masses, assuming spherical geometry, by log10(mass) ¼ log10(p/6) þ 3 log10(length). Although the regression lines for coastal A and coastal B extend to the right of the diagonal line where predator and prey masses are equal, roughly 90% of the data points fell above and to the left of the diagonal. The coastal A regression line is: log10(predator mass, g) ¼ 2.2114 þ 0.1463 log10(prey mass, g). The coastal B regression line is: log10(predator mass, g) ¼ 3.1985 þ 0.3241 log10(prey mass, g). (b) Regression lines of predator masses and prey masses in trophic links in three sets of terrestrial food webs. Procedures of Fig. 16.3a apply here. The terrestrial A regression line is: log10(predator mass, g) ¼ 2.1105 þ 0.5177 log10(prey mass, g). The terrestrial B regression line is: log10(predator mass, g) ¼ 1.9924 þ 0.9443 log10(prey mass, g). Ve´zina (1985) gave numerically only a range of masses for predators and no masses for their prey. Here a single straight line was fitted by hand to Ve´zina’s graph of the data for insectivores, piscivores and carnivores, and the hand-fitted straight line for the data of Ve´zina (1985) is: log10(predator mass, g) ¼ 2.19 þ 0.58 log10(prey mass, g).

Jonsson and Ebenman (1998a) computed the ratio of predator mass to prey mass for all trophic links for which both masses were known using 768 consumer species (697 trophic species) in 52 community food webs. Their finding that, for most food webs, the higher the trophic level of the predator, the smaller the predator–prey mass ratio, agrees with the theory developed here for isolated food chains if higher trophic level correlates closely with higher body mass. It will be desirable to re-examine this asserted pattern using the data of Brose et al. (2005). Data on parasite and parasitoid food webs and body sizes appear to be scarce. Memmott et al. (2000) reported a source food web of a broom community that

BODY SIZES IN FOOD CHAINS

(b) 8 terrestrial B log10 weight (g) of predator

6 4

Vezina 1985

2 0 terrestrial A

–2 –4 –6 –6

–4

–2 0 2 log10 weight (g) of prey

4

6

Figure 16.3 (cont.)

contained one plant species, 19 herbivores, 66 parasitoids, 60 predators, five omnivores and three pathogens. They plotted log consumer-species length as a function of log resource-species length with separate symbols for parasitoids, pathogens and predators (their Fig. 7) but they did not report estimates of allometric relations nor list the length data, though they did provide the foodweb data. According to Leaper and Huxham (2002), the web reported by Memmott et al. (2000) was the first and until 2002 the only published food web to present body masses for both parasites (in fact, they were parasitoids) and other consumers. Leaper and Huxham (2002) calculated but did not publish body masses of 160 of the 171 taxa in the food web of the Ythan estuary: 113 average adult body weights and mean weights for the given life-history stage of the remaining 47 taxa. They reported Pearson’s r2 for log10 consumer and log10 resource body masses for six versions of the web: including non-parasites only, parasites only, and all taxa; and for each group of taxa, with and without distinguishing life stages according to their trophic relations. No regression coefficients of log10 consumer body mass on log10 resource body mass were given. The correlations were positive in all cases and were statistically significantly different from zero at the 0.001 level except for parasites only, disregarding differences among life stages.

Discussion Hutchinson (1959, p. 147) examined ‘the order of magnitude of the diversity that a single food chain can introduce into a community’. It is worthwhile to revisit his influential calculations in the light of data and theory available since he wrote. Hutchinson assumed that ‘in general 20 per cent of the energy passing

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through one [species] can enter the next [species] in the chain’ and that ‘each predator has twice the mass (or 1.26 the linear dimensions) of its prey, which is a very low estimate of the size difference between links . . .’ This assumption may be represented in the model Eq. (16.1) by putting A ¼ 2 and B ¼ 1. This model led Hutchinson (1959, p. 147) to envisage the ‘ultimate predator’ at trophic level 49, with an individual body size ‘vastly greater than the volume of the world ocean’. Hutchinson then implicitly assumed that the numerical abundance N, or population size, of each animal species in a predator food chain equals the total energy available divided by the typical body size M, which is tantamount to assuming that the energy consumption of each animal species is directly proportional to its typical body size M. With each increase in the trophic level of species in a predator chain, according to Hutchinson’s assumptions, 20% as much energy has to be divided among the organisms each twice as big. The population size therefore is reduced by a factor of 0.2/2 ¼ 0.1, i.e. decreases by 90%. Consequently, Hutchinson concluded, the population size or numerical abundance N4 of the fifth animal species will be 10 4 times the population size N0 of the first. In this hypothetical world, food chains cannot be very long. Hutchinson’s assumptions imply an allometric relation between numerical abundance (or population size) and average body mass. Along a trophic link from any species 1 to any species 2, Hutchinson assumes that M2 ¼ 2M1 (mass doubles) while N2 ¼ (1/10)N1 (numerical abundance falls by 90%). The slope of the allometric relation between numerical abundance and body mass is then: D log10 ðNÞ=D log10 ðMÞ ¼ ½log10 ðN2 Þ  log10 ðN1 Þ=½log10 ðM2 Þ  log10 ðM1 Þ ¼  log10 ð10Þ= log10 ð2Þ ¼ 3:32:

(16:4)

Each step in Hutchinson’s argument has been re-examined. Pauly and Christensen (1995) estimated a mean trophic transfer efficiency of 10% (half Hutchinson’s estimate of 20%). Rather than doubling with each trophic link, animal body size in a predator chain is more likely to be described by Eq. (16.2) with A > 0, 0 < B < 1, neglecting the substantial variability in the size of predators on prey of a given size. Animal metabolic energy requirements increase approximately in proportion to M3/4 rather than to M (Kleiber, 1961). In Tuesday Lake, Michigan, the regression of log10(N) on log10(M) had slope 08413 (with 99% confidence interval 098, 071) in 1984 and slope 07461 (with 99% confidence interval 091, 059) in 1986 (Reuman & Cohen, 2004). These slopes are far from the slope of 332 that follows from Hutchinson’s assumptions. Cohen and Carpenter (2005) showed that the statistical assumptions underlying linear regression were justified for Tuesday Lake data in regressions of log10(N) on log10(M) but not vice versa. If animal population size were constrained by available energy alone, as Hutchinson supposed, and if the food chain were isolated from all other food chains to or from which energy might be diverted, then, in principle, a better

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formula than Hutchinson’s for the ratio of the population size or numerical abundance Nn at trophic level n to the numerical abundance N0 of the basal animal in a predator chain would appear (for the moment) to be: Nn =N0 ¼ ðM0 =Mn Þ3=4 ð0:1Þn

(16:5)

and the slope of the relation between numerical abundance and body mass is predicted by these assumptions to be: D log10 ðNÞ=D log10 ðMÞ ¼ ½log10 ðNnþ1 Þ  log10 ðNn Þ=½log10 ðMnþ1 Þ  log10 ðMn Þ ¼ 3=4 þ 1= log10 ðMnþ1 =Mn Þ:

(16:6)

For large n, M0/Mn approaches a constant (less than 1) and the ratio Eq. (16.5) declines by a factor of 0.1 with each increase in trophic level. Apparently by coincidence, this is exactly the behaviour Hutchinson calculated. That is the good news. The rest of the news is bad, and gets worse. For small n, Eq. (16.5) predicts a slower-than-exponential decline, unlike Hutchinson’s calculation. For large n, Mnþ 1/Mn ! 1 so log10(Mnþ 1/Mn) ! 0 and the right side of Eq. (16.6) diverges to infinity, clearly an unrealistic prediction. Evidently the assumptions stated just before Eq. (16.5) do not hold in the real world. One weak assumption is that the predator chain is energetically isolated from all other food chains. In addition, the population sizes of species, especially species with small body sizes, are often not limited by energy (Blackburn, Lawton & Pimm, 1993; Blackburn & Lawton, 1994). While large-bodied animal species are usually rare, small-bodied animal species commonly have a wide range of population sizes, from abundant to rare. Overall, Hutchinson’s argument that a predator chain (and by his off-hand extension, a parasite chain) ‘clearly . . . of itself cannot give any great diversity’ founders in the face of more recent facts and models. For three collections of data from coastal communities, 0 < b < 1/2, while for three collections of data from terrestrial communities, 1/2 < b < 1. Is this difference true in general? If confirmed by data of better quality from more communities, then a kilogram of resource supports a predator of larger body mass in a terrestrial community than in a coastal community. Why is this? The starting hypothesis here is that the mass of the consumer (predator or parasite) is related to the mass of the animal resource (prey or host) by a power law with exponent less than 1. This hypothesis is at best an approximation to reality, on both empirical and theoretical grounds (Cohen et al., 1993). Empirically, large predators sometimes eat prey of a wide range of masses while small predators eat prey with a narrower range of masses (as in Figs. 1 and 2 of Cohen et al., 1993). However, in Tuesday Lake, observed trophic links appear to fall in a band above and parallel to the diagonal line where predator mass equals prey mass, rather than in a triangular region in the (x, y) plane (Reuman & Cohen, 2004). Approximating both such relations by a power-law

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function ignores the apparent differences between them in how the variance in predator mass changes with the mass of the prey. The only direct evidence on how well a power-law relation describes body masses in parasite chains is Fig. 1 of Leaper and Huxham (2002, p. 447). Their scatter plots for parasites only in the Ythan estuary provide weak support for the usefulness of a power-law approximation. For log parasite size and log host size of parasites only, without trophospecies r2 ¼ 0.015 was not significant, and with trophospecies r2 ¼ 0.125 was statistically significant but still small. An approximate power law with exponent less than 1 has been derived theoretically from models of food-web structure, species abundance distributions, and the distribution of biomass across species mass categories (Cohen, 1991, pp. 5–8). Cohen et al. (1993) suggested that the logarithm of animal species masses may be approximately normally distributed, and that E(y|x) is the mean of a normal distribution censored below x (i.e. retaining only that portion of the normal distribution to the right of x). Unpublished numerical calculations show that, under this model, E(y|x) is a convex nonlinear function (always with slope less than 1) of x, rather than a strictly linear function as expected by the powerlaw relation Eq. (16.1). With the observed distribution of body mass reported by Cohen et al. (1993, p. 73, their Table 4), the power law approximates reasonably the convex nonlinear function in the range of animal body masses from 106 g to 10þ6 g. Terrestrial vertebrate predators far larger than contemporary top carnivores lived in the past (Burness, Diamond & Flannery, 2001). It would be interesting to determine whether predator and prey masses during the Cretaceous and late Pleistocene are consistent with a power law Eq. (16.1); if so, whether the coefficients A and B had different values from those estimated here; and if so, whether the maximum predator mass at that time could be predicted from the predator–prey body mass relations then in effect. Jonsson and Ebenman (1998b) suggested that the decrease they observed (Jonsson & Ebenman, 1998a) in the ratio of predator mass to prey mass with increasing trophic level in predator chains has significant consequences for stability in dynamic models of food chains. This suggestion could be extended to parasite chains, and merits further analysis and testing. The derivation of maximal body mass from the phenomenology of body sizes in trophic links is only one among many possible approaches. Other constraints on maximal body mass include mechanical or design constraints, energetics of food supply and metabolism, land area (for terrestrial consumers), natural selection of life histories and the processes of development (e.g. Bonner, 1988; Yoshimura & Shields, 1995; Burness, Diamond & Flannery, 2001; Gomer, 2001). It remains to be demonstrated whether, and if so how, these approaches are compatible. To summarize, food chains in which animal predators are bigger than their animal prey are called predator chains. Food chains in which the consumers are

BODY SIZES IN FOOD CHAINS

smaller than their animal prey are called parasite chains. If the mass of the consumer (predator or parasite) is related to the mass of the animal resource (prey or host) by a power law with exponent less than 1, then, in predator chains, there is an upper limit to the mass of the largest predator and prey, and in parasite chains, there is a lower limit to the mass of the smallest host and parasite. These limits are independent of the number of trophic links in the chain and independent of the mass of the basal animal species. In a predator chain that obeys this allometric relation of predator and prey masses, the ratio of predator mass to prey mass decreases as the trophic level and mass of the prey increase. In a parasite chain that obeys this allometric relation of predator and prey masses, the ratio of parasite mass to host mass increases as the trophic level of the host increases and the mass of the host decreases. In the data on predator chains here, predator masses generally exceed prey masses. The regression of the logarithm of predator mass on the logarithm of prey mass has slope b less than 1 in all cases. While it is possible to calculate maximal predator sizes from these regressions, estimates of maximal predator size are highly sensitive to uncertainty in the parameters of the regression lines. For three collections of data from coastal communities, 0 < b < 1/2, while for three collections of data from terrestrial communities, 1/2 < b < 1. A model of the joint distribution of consumer and resource body masses predicts a slope of 1/2 for both predator and parasite chains, and specifies conditions under which the slope should deviate up or down from 1/2. The theory developed here pertains to isolated chains, but all the data are drawn from webs with interconnecting chains. An ideal test of the theory would describe the full frequency distribution of body sizes of each species in a more or less isolated chain, if such can be found in nature. It would also be useful to extend the theory from isolated chains to more complex food webs and to analyze the consequences in the variability of body sizes of both resources and consumers.

Acknowledgements I am grateful for helpful, critical comments on previous drafts from John Tyler Bonner, Benni Hansen, Mark Huxham, Tomas Jonsson, Mark Laska, Robert H. Peters, Dave Raffaelli, Thomas W. Schoener, Alain Ve´zina and two reviewers; the support of US National Science Foundation grants BSR92-07293, DEB 9981552 and DMS-0443803; the assistance of Priscilla K. Rogerson; and the hospitality of Mr and Mrs William T. Golden during this work.

References Blackburn, T. M. & Lawton, J. H. (1994). Population abundance and body size in animal assemblages. Philosophical Transactions of the Royal Society of London Series B, 343, 33–39.

Blackburn, T. M., Lawton, J. H. & Pimm, S. L. (1993). Non-metabolic explanations for the relationship between body size and animal abundance. Journal of Animal Ecology, 62, 694–702.

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Bonner, J. T. (1988). The Evolution of Complexity. Princeton, NJ: Princeton University Press. Brose, U., Cushing, L., Berlow, E. L. et al. (2005). Body sizes of consumers and their resources. Ecology, 86, 2545. Brose, U., Jonsson, T., Berlow, E. L. et al. (2006). Consumer-resource body-size relationships in natural food webs. Ecology, 87, 2411–2417. Burness, G. P., Diamond, J. & Flannery, T. (2001). Dinosaurs, dragons, and dwarfs: the evolution of maximal body size. Proceedings of the National Academy of Sciences, 98, 14518–14523. Cohen, J. E. (1991). Food webs as a focus for unifying ecological theory. Ecology International (International Association for Ecology Bulletin), 19, 1–13. Cohen, J. E. & Carpenter, S. R. (2005). Species’ average body mass and numerical abundance in a community food web: statistical questions in estimating the relationship. In Dynamic Food Webs: Multispecies Assemblages, Ecosystem Development and Environmental Change – A Volume of Theoretical Ecology, ed. P. C. de Ruiter, V. Wolters & J. C. Moore. Amsterdam: Elsevier, pp. 137–156. Cohen, J. E., Briand, F. & Newman, C. M. (1990). Community Food Webs: Data and Theory. Biomathematics Vol. 20. Heidelberg, Berlin, New York: Springer-Verlag. Cohen, J. E., Pimm, S. L., Yodzis, P. & Saldan˜a, J. (1993). Body sizes of animal predators and animal prey in food webs. Journal of Animal Ecology, 62, 67–78. Cohen, J. E., Jonsson, T. & Carpenter, S. R. (2003). Ecological community description using the food web, species abundance, and body size. Proceedings of the National Academy of Sciences, 100, 1781–1786. Cohen, J. E., Jonsson, T., Mu¨ller, C. B., Godfray, H. C. J. & Savage, V. M. (2005). Body sizes of hosts and parasitoids in individual feeding relationships. Proceedings of the National Academy of Sciences, 102, 684–689.

Elton, C. (1927). Animal Ecology. (New impression with additional notes 1935.) New York: Macmillan. Gomer, R. H. (2001). Not being the wrong size. Nature Reviews Molecular Cell Biology, 2, 48–54. Hansen, B., Bjı´rnsen, P. K. & Hansen, P. J. (1994). The size ratio between planktonic predators and their prey. Limnology and Oceanography, 39, 395–403. Horning, M. & Trillmich F. (1997). Development of hemoglobin, hematocrit and erythrocyte values in Gala´pagos fur seals. Marine Mammal Science, 13, 100–113. Hutchinson, G. E. (1959). Homage to Santa Rosalia or why are there so many kinds of animals? American Naturalist, 93, 145–159. Jonsson, T. & Ebenman, B. (1998a). Trophic links and the relationship between predator and prey body sizes in food webs. Chapter 2 in T. Jonsson, Food Webs and the Distribution of Body Sizes. Linko¨ping Studies in Science and Technology, Dissertation 535, Linko¨ping, Sweden, pp. 63–81. Jonsson, T. & Ebenman, B. (1998b). Effects of predator-prey body size ratios on the stability of food chains. Journal of Theoretical Biology, 193, 407–417. Jonsson, T., Cohen, J. E. & Carpenter, S. R. (2005). Food webs, body size and species abundance in ecological community description. In Food Webs: From Connectivity to Energetics, Advances in Ecological Research Vol. 36, ed. H. Caswell. San Diego: Elsevier, pp. 1–84. Kleiber, M. (1961). The Fire of Life: An Introduction to Animal Energetics. New York: John Wiley. Leaper, R. & Huxham, M. (2002). Size constraints in a real food web: predator, parasite and prey body-size relationships. Oikos, 99, 443–456. Memmott, J., Martinez, N. D. & Cohen, J. E. (2000). Predators, parasitoids and pathogens: species richness, trophic generality and body sizes in a natural food web. Journal of Animal Ecology, 69, 1–15.

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Menge, B. A., Lubchenco, J., Gaines, S. D. & Ashkenas, L. R. (1986). A test of the Menge-Sutherland model of community organization in a tropical rocky intertidal food web. Oecologia (Berlin), 71, 75–89. Pauly, D. & Christensen, V. (1995). Primary production required to sustain global fisheries. Nature, 374, 255–257. Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge: Cambridge University Press. Reuman, D. C. & Cohen, J. E. (2004). Trophic links’ length and slope in the Tuesday Lake food web with species’ body mass and numerical abundance. Journal of Animal Ecology, 73, 852–866. Reuman, D. C. & Cohen, J. E. (2005). Estimating relative energy fluxes using the food web, species abundance, and body size. In Food Webs: From Connectivity to Energetics, Advances in Ecological Research Vol. 36, ed. H. Caswell. San Diego: Elsevier, pp. 137–182. Rott, A. S. & Godfray, H. C. J. (2000). The structure of a leafminer-parasitoid community. Journal of Animal Ecology, 69, 274–289. Schoener, T. W. (1968). Size of feeding territories among birds. Ecology, 49, 123–141.

Sheldon, R. W., Prakash, A. & Sutcliffe, W. H., Jr. (1972). The size distribution of particles in the ocean. Limnology and Oceanography, 17, 327–340. Ve´zina, A. F. (1985). Empirical relationships between predator and prey size among terrestrial vertebrate predators. Oecologia (Berlin), 67, 555–565. Wallace, A. R. (1858). On the tendency of varieties to depart indefinitely from the original type. In C. R. Darwin & A. R. Wallace, On the tendency of species to form varieties; and on the perpetuation of varieties and species by natural means of selection. Journal of the Proceedings of the Linnean Society, Zoology, 20 Aug. 1858, 3, 45–62. Online: http://pages.britishlibrary.net/charles. darwin3/jpls.html#natsel Warren, P. H. & Lawton, J. H. (1987). Invertebrate predator-prey body size relationships: an explanation for upper triangular food webs and patterns in food web structure? Oecologia (Berlin), 74, 231–235. Yoshimura, J. & Shields, W. M. (1995). Probabilistic optimization of body size: a discrepancy between genetic and phenotypic optima. Evolution, 49, 375–378.

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CHAPTER SEVENTEEN

Body size in aquatic ecology: important, but not the whole story ALAN G . HILDREW School of Biological and Chemical Sciences, Queen Mary, University of London

DAVI D G . RAFFAELLI Environment Department, University of York

RONNI EDMONDS - BROWN Division of Geography and Environmental Sciences, University of Hertfordshire

Introduction Ecologists have long been aware of regularities and patterns in the body size of organisms in populations and communities, observations that go back at least to Alfred Wallace and continue through the works of Elton, Thienemann, Hutchinson, MacArthur and many others. The classical contribution of R. H. Peters (1983) codified such patterns through the concept of body-size allometry, of metabolic rate and other features, and led on to many of the phenomena now included under macroecology (Blackburn & Gaston, 2003). Brown and colleagues (Brown et al., 2004; Brown, Allen & Gillooly, this volume), in particular, added new advances in scaling theory and, incorporating the exponential effect of temperature on metabolic rate, sought to explain a wide variety of patterns and processes in ecology at levels of organization from individuals to ecosystems. The focus on aquatic systems at the Hatfield symposium, and in this resultant volume, is justified because body-size patterns may be more important, or at least more obvious, in aquatic ecosystems. Woodward and Warren (this volume) offer three possible reasons. First, the most important primary producers in water are small and, along with small heterotrophic micro-organisms and small detritus particles, are gathered from suspension by larger consumers. Second, they point out that conventional predators, larger in turn than their prey, seem particularly prominent in aquatic systems where there may be fewer parasite food chains (see Cohen, this volume). A third, methodological reason for a particular emphasis on body size by aquatic ecologists, may be the relative ease of automated counting of particles and organisms in suspension across a wide range of scales. Perhaps with particular reference to methodology, it is noteworthy that terrestrial and aquatic ecologists have also generally taken different perspectives on body size. Thus, in describing assemblages, aquatic Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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ecologists often present their data as a continuous size spectrum of individuals, irrespective of taxonomic affinities, whereas terrestrial ecologists generally view the species as the individual datum, and usually as a fixed entity – mean adult body mass. The ways these two research communities present and subsequently interpret their data affect their understanding of how aquatic and terrestrial systems work (Raffaelli, Solan & Webb, 2005). To these speculations we might add that aquatic systems show one feature for which there is no obvious parallel in the terrestrial world: a viscous medium that greatly shapes how organisms function and behave. This unique attribute of aquatic systems has understandably been a major focus for aquatic ecology and has accordingly produced a perspective that is quite different from that of terrestrial ecologists. As the chapters in this book testify, body size has clearly remained a major research focus for the ecological community, from ecophysiology to the ecosystem. In part this is because body size sets real mechanical limits on what organisms can do (e.g. limits to the dimensions of prey that can be physically ingested), and in part because body size is a super-parameter, which does well at capturing a range of associated physiological and ecological traits, but is much more easily measured (or found in books) than those traits themselves. A few of the authors herein have set out explicitly to test such data against the predictions of the metabolic theory of ecology (Brown et al., 2004), with varying degrees of success, while others chose ostensibly different theoretical backgrounds against which to consider patterns and dynamics related to body size.

Body size and metabolic theory We consider first the few chapters that explicitly mention explorations of metabolic theory, or at least consider metabolic theory against patterns in the different fields of literature. With respect to life history, Atkinson and Hirst (this volume) consider whether selection can alter the scaling exponent (b) relating metabolic rate to body size, the core of metabolic theory. They ask to what extent is b fixed at 3/4? They cite Glazier’s (2005) survey of 642 metabolic rates during ontogeny, around half of which deviated from 3/4 and, interestingly, with higher values (mean 0.95) in pelagic compared to benthic (mean 0.74) species, perhaps due to the increased costs of buoyancy or avoiding predation in pelagic species. Huryn and Benke (this volume) consider biomass turnover and body size in stream benthic invertebrates, analyzing the relationships between body size (M) and population density, biomass (B), production (P) and P/B. They found an encouraging degree of fit with theory for three temperate streams, with the relationship between P/B and body size (as mass) having a scaling exponent varying between 0.24 and 0.27, bracketing the predicted value of 0.25. Huryn and Benke (this volume) consider this precise fit ‘extraordinary when considering the large ecological differences between the streams’, forested or grassland, with or without fish, etc. The ‘snag’ community

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(organisms sedentary on woody debris in the channel) of the warm water Ogeechee River (Georgia, USA) was inconsistent with the theory (scaling exponent of M and P/B, 0.50), though this discrepancy could be accounted for in various ways. Thus, for Huryn and Benke’s data on stream benthos, metabolic theory does fairly well. Several other authors found encouraging, though patchy, fits of pattern with metabolic theory in different contexts (Petchey, Long & Morin, this volume; Humphries, this volume; Hall et al., this volume; Jennings & Reynolds, this volume), leaving us with the intellectually awkward task of judging whether the theory survives because we can explain the discrepancies, or if the theory falls in general. The problems of testing theory in this way are several and were vigorously debated at the meeting, and there seem to be three major issues involved. First, testing has essentially been a post-hoc exercise in which data gathered for completely different purposes are used to challenge the theory, always a tricky process. Second, different measures of body size were used in the present collection of chapters: mass or weight (dry, ash-free, wet, whole-body or elemental), volume or equivalent spherical diameter, individual, average or adult body size. Different measures will be appropriate for different research questions and in many cases a clear rationale for selecting a particular measure of body size is presented. For other studies, however, including many macroecological investigations, the data used are simply those at hand, often adult body sizes, which can be extracted from field guides or species survey lists. If patterns that emerge from the analyses of such data are interpreted in the context of theory that assumes other expressions of body size, such as individual biomass, then the value of the research is compromised. One solution to this potential problem is to make available a much greater variety of body-size measurements for a broad range of systems within a public domain database, so that analyses can be tailored more closely to theory. Third, body-size data and relationships are presented in a variety of forms within the present volume. Several chapters reported bi- or tri-variate relationships, with body size as the explanatory variable, often seeking to allow comparisons with theory (mainly as judged by slopes of regression lines). However, testing for deviation from theoretical relationships opens up a can of worms. For instance, the choice of regression models (least squares, geometric mean, bisector regressions and others) is important because each estimates a different value for the slope. Similarly, it is not good enough to assume that, because a slope through the observed data is not significantly different from the theoretical prediction, the data are consistent with theory. An alternative explanation is that there is not enough power (essentially the number of data points) in the analysis to falsify the model, and formal power analyses should be carried out to check this, although this is rarely done. More suitable statistical procedures to demonstrate negligible trends in data are now available (Dixon & Pechmann,

BODY SIZE: IMPORTANT, BUT NOT THE WHOLE STORY

2005), and these authors also provide a good discussion of the difference between a failure to reject a null hypothesis and verifying that null hypothesis. In addition, for claimed invariant relationships, where a slope of zero is predicted by theory, it is incredibly difficult to distinguish such invariance in a data set from a non- (and therefore meaningless) relationship. Finally, different representations of the data could well generate quite different perspectives on the significance of body size in ecology. Within taxonomic collections (e.g. a family of water beetles or harpacticoid copepods), bivariate plots of body size against abundance provide reasonable representations of relationships. As the taxonomic grouping becomes coarser (e.g. freshwater benthos or marine benthic invertebrates), regression techniques begin to fail to provide an adequate model of the data. At the whole system level, a constraint space (e.g. Brown, 1995) or biomass spectrum (e.g. Stead et al., 2005) might be more appropriate, although formally quantifying such pattern and exploring deviations from theoretical prediction is fraught with difficulty (Leaper & Raffaelli, 1999).

Other empirical, theoretical and conceptual backgrounds Most chapters in this book do refer to metabolic theory, but perhaps wisely do not attempt explicit tests, instead setting their findings in the context of a variety of other areas of theory and concept. For instance, Humphries (this volume) considers suspension feeding, a mode of feeding virtually restricted to aquatic systems, in relation to body size and the physics of water and flow. Body size is crucial for aquatic organisms because it determines flow regime and thus, for suspension feeders, food supply. We are particularly struck by Humphries’ remark that body size is particularly ‘nebulous and difficult to specify’ for suspension feeding organisms, because they stretch to the very limits the relationship between the various measures of size that ecologists can use. Consider for instance gelatinous pelagic filter feeders, of large physical dimensions but very low body mass; benthic filter feeders with large and heavy, but metabolically inactive, shells; and organisms that build extensive nets and mucus sheets to capture food at a rate beyond that expected from their body size alone. Perhaps for this reason there is still no clear relationship between body size and food-particle size for suspension feeders, in contrast to the situation for conventional predators. Townsend and Thompson, Atkinson and Hirst, and Huryn and Benke (all this volume) all deal with body size as a species trait in relation, respectively, to the habitat templet hypothesis, life-history theory and metabolic theory. Townsend and Thompson (this volume) consider body size against the habitat templet hypothesis of Southwood (1977), and allied predictions specifically developed for streams by Townsend and Hildrew (1994), and referring to traits in relation to disturbance, productivity, land use, predation and others. They conclude that

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clear patterns of macroinvertebrate body size are ‘sometimes apparent but rarely account for a large proportion of variation along the (environmental) dimension of interest’. They attribute this result to the complexity of multiple stressors in natural systems and to the inclusion of mixtures of organisms with different ‘solutions’ (including body size) to particular environmental conditions. We also wonder whether in such systems, population and community dynamics will often be transient and thus the ‘snapshot’ patterns often weak. Disturbance is one obvious cause of fluctuations, though others are feasible, and we return to this notion below. Jennings and Reynolds (this volume) relate body size to the pressures of commercial fishing and to fisheries management (see also Atkinson & Hirst, this volume). The effects of fishing on the population size structure of exploited species have been stark and, apart from the well-known phenomenon of ‘fishing down the food chain’ in overexploited systems, Jennings and Reynolds (this volume) have managed to use theory and data to predict that the abundance of large fish (16–66 kg body weight) in the North Sea may now be a remarkable 99.2% lower than before exploitation. Jennings and Reynolds’ paper is wide ranging, and also deals with community-level phenomena such as trophic structure and biomass size spectra, and they point out the practical applications of food-web theory in the adoption of ecosystem and community-level management of fisheries and the oceans. In terms of trophic structure, they highlight the absence of clear trophic steps (trophic levels) in most aquatic (as opposed to terrestrial) ecosystems, and the prevalence of life-cycle omnivory and size-based predation, all arguments for a size-based analysis of the ecosystem impacts of exploitation. Two other chapters focus on body size in relation to species interactions, food-webs and food web theory. Woodward and Warren (this volume) provide much evidence for the importance of body size in determining feeding links, food-web structure and life-cycle omnivory. Communities of freshwater benthic invertebrates evidently provide some of the clearest evidence of all of the primacy of body size in natural food webs, thus chiming with Jennings and Reynolds’ (this volume) conclusions. They analyze explicitly the limits, both upper and lower, to the size disparity observed between predator and prey – i.e. both upper and lower size refugia exist – and show the effect of basing estimates of size disparity on individuals and on species averages. If species averages are taken (i.e. the average size of the predator and the average size of the prey) it turns out that the predator is about ten times greater than the prey, whereas if individual links are considered (i.e. the size of the particular predator and its actual prey) the mean size disparity is about 100. Jones and Jeppesen (this volume) consider further the role of body size in relation to trophic structure, and in their case to the occurrence of alternative regimes and in particular of trophic cascades, many examples of which seem to be ‘wet’ (Strong, 1992). In the

BODY SIZE: IMPORTANT, BUT NOT THE WHOLE STORY

sense that trophic cascades are characterized by clear trophic levels, there seems a disparity between the view that cascades are prevalent and the rejection by Jennings and Reynolds (this volume) of integer trophic levels for most aquatic ecosystems, as well as Woodward and Warren’s (this volume) findings for simple freshwater benthic communities. Jones and Jeppesen (this volume) argue that cascades are common where there is a large size disparity between predator and prey, such that ‘prey’ are so small that they are fed on unselectively by the consumers, and where small productive producers turn over very rapidly and can sustain a large biomass of long-lived predators. These features may be more decisive than body size per se in determining the occurrence of cascades. Several chapters took a biogeographical or macroecological approach. These include Finlay and Esteban; Rundle, Bilton and Foggo; Warwick; and Schmid and Schmid-Araya (all this volume). Finlay and Esteban (this volume) consider the biogeography of organisms in relation to their notion of a ‘biogeographical divide’, a body size below which species, by consequence of their enormous population abundances (thus linking this concept to macroecological theory), are cosmopolitan, but above which they are not. This body-size transition seems to be in the range 1–10 mm. For macro-organisms, Rundle et al. provide evidence of a positive relationship between range size and body size in actively dispersing dragonflies. For passively dispersing freshwater organisms, they find that those within the body-size transition of Finlay and Esteban, such as small crustaceans, do indeed have a biogeography and are not cosmopolitan. For passively dispersing marine and freshwater organisms, range size increases with body size, perhaps related to the covariance between body size and propagule output, and hence dispersal probability. It might be that microbial species below about 1 mm tend to be cosmopolitan, but that above this body size, geographical range again increases, as the ability to disperse actively goes up with body size in active dispersers, and the likelihood of dispersal goes up with propagule output (and therefore with body size) in passive dispersers. It seems clear that data on range size for aquatic organisms lag well behind those for terrestrial organisms, which may explain the general paucity of (biogeographical) macroecological relationships for aquatic organisms. Warwick (this volume) deals with a macroecological pattern for which there is a long history of research in aquatic ecosystems, the species–body size spectrum. He reports a regularly bimodal spectrum for the marine benthos, apparently contrasting with a unimodal one for freshwater. In the marine benthos the small mode consists of meiofauna and the large mode the macrofauna, with few intermediate species. Warwick attributes this pattern not to local ecological interactions or habitat architecture, as originally advocated by Schwinghamer (1981), but to the evolutionary history of the marine benthos. The trough of species in the spectrum equates to the size of the planktonic, larval forms of the larger macroinvertebrate benthos. These cannot be benthic because the smaller

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meiofaunal species would predate on or compete with them (many meiofaunal predators take relatively large prey, often larger than themselves). According to Warwick, this general regional pattern of species–body size then produces the local patterns observed. In contrast, Schmid and Schmid-Araya (this volume) analyze such community patterns in relation to fractal geometry, potentially the most fundamental of all the approaches in this volume since fractals may underly the scaling of metabolic rate with body size itself. Schmid and SchmidAraya did not find a self-similar pattern of body size across all scales, however, referring to the changes in scale as ‘multifractal’. Interestingly, Warwick (this volume) also rejected a single fractal scaling for the marine benthos. Other chapters took experimental or modelling approaches. In their experiments using model ecosystems of protists, Petchey, Long and Morin (this volume) demonstrated the effects of body size at three levels of organization: the population, community and ecosystem. The results were encouraging, but there were discrepancies with allometric theory and we can conclude that the effects of body size on ecological processes are modified by trophic complexity (connectedness) and species richness. Persson and De Roos (this volume) also looked at model systems, but focused on individual variation using physiologically structured population models. They stress the within-species variation, much of it ontogenetic, in food intake, growth and body size that is so characteristic of most metazoans. This variation generates intrinsic dynamics and divergent body-size distributions, not wholly predictable by metabolic theory for instance. Systems with strong cohorts that are constantly changing are non-equilibrial systems that can approach alternate states. In short, they emphasize population and community dynamics rather than the structure and pattern that was addressed by many of the other authors. These models are remarkably powerful, and explain effects apparent in many fish populations, but we can only join Persson and De Roos (this volume) in concluding that ‘a major challenge . . . is to develop approaches that allow the analysis of more complex configurations in terms of the numbers of species present’. When even simple real food webs may contain tens or hundreds of species, this is a challenge indeed. Several authors referred to the ecosystem consequences of body size, including CO2 production (Petchey et al., this volume) and nutrient cycling, though this aspect was most explicitly addressed by Hall et al. (this volume). The latter address the extent to which animals affect nutrient cycling directly, through ingestion, egestion, production and excretion, and how body size controls such effects. Partially as expected, nutrient excretion rates scaled allometrically, with an exponent less than 1. Ammonium excretion of stream invertebrates from 18 taxonomic orders scaled at 0.85 with body mass, though there is an interesting degree of variation, apparently related to taxonomy and thus also potentially to the measure of body size used for different taxa. For instance, why are there differences in the scaling of the excretion of P, but not N, between two species of

BODY SIZE: IMPORTANT, BUT NOT THE WHOLE STORY

zebra mussel (Dreissena), and why does excretion of N and P in Dreissena scale so disproportionately with body size (b ¼ 1.38)? There are some fascinating insights in this chapter into how body size could feed back onto ecosystem processes. For instance, they note that the removal of large, migratory salmon has reduced nutrient subsidies to many rivers and their catchments, and that the harvesting of large fish will similarly feed back onto nutrient regeneration rates. Joel Cohen (this volume) closed our symposium with a consideration of the consequences, in both predator and parasite food chains, of the average body mass of a consumer being related to the average mass of the species consumed by a power law with an exponent less than 1. We were struck by Cohen’s finding that ‘one kilogram of resource supports a predator of larger body mass in a terrestrial community than in a (marine) coastal community’, though it is not at all obvious why this should be so. This and other intriguing outcomes of his analyses only serve to highlight the need for more data on body size in natural systems.

Concluding remarks We finish with some speculations. Body-size allometry, and its extension to the metabolic theory of ecology, does pretty well at predicting some, but not all, of the patterns and processes dealt with in this book, and hence provides our chapter title. Whilst appealing to issues of scale may these days seem like the resort of the scoundrel, it is obvious that patterns appear and disappear as spatial and temporal resolution changes and analyses include more and more heterogeneous groups of species at different trophic levels. Further, the appropriate measure of body size is difficult to specify a priori, and we are struck by nature’s ingenuity in creating ways of cheating the scaling and limitations of body size, allowing organisms to ‘punch above their weight’ in obtaining food, and in the process making the ecologist’s task more difficult. Examples include filterers that build large external feeding structures and Cohen’s (this volume) cases of social hunting that enables predators to feed on prey much larger than themselves. Perhaps even the very large marine filter feeders are only possible because they can exploit whole aggregations of prey, effectively a ‘superindividual’, with a combined body size much larger than the single krill ‘particle’. The greatest challenge to a size-based approach to food webs lies with the enormous terrestrial primary producers, trees, the largest of all organisms but which lie at the base of land-based food webs, though their biomass is mainly metabolically inactive (Cousins et al., 2005). Transient dynamics and temporal fluctuation are referred to in several papers, and clearly point to the notion that patterns based on energetic rules and allometry may be obscured at the scale at which it is possible to observe them. It seems likely that the processes underlying metabolic theory provide an envelope or a constraint outside which natural systems may not sustainably lie,

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but that heterogeneity, fluctuations and non-equilibrial processes mean that systems obey such rules only in an approximate way. Energy subsidies among neighbouring systems can be considered in a similar way to transient dynamics. Thus, subsidies to top predators can produce ‘apparent’ cascades in shallow lakes (Jones & Jeppesen, this volume) and might have produced the discrepancies with metabolic theory in the highly productive snag communities of filter feeding organisms in the Ogeechee River observed by Huryn and Benke (this volume). In short, our title captures the discussions and conclusions at the symposium about the role of body size – it is important, but not the whole story.

References Blackburn, T. M. & Gaston, K. J. (2003). Macroecology: Concepts and Consequences. Oxford: Blackwell Science. Brown, J. H. (1995). Macroecology. Chicago:University of Chicago Press. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage. V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789. Cousins, S. H., Bracewell, K. V. & Attree, K. (2005). Measuring the ability of food to fuel work in ecosystems. In Dynamic Food Webs, ed. Ruiter et al. London: Academic Press, pp. 248–257. Dixon, P. M. & Pechmann, J. H. K. (2005). A statistical test to show neglible trend. Ecology, 86, 1751–1756. Leaper, R. & Raffaelli, D. G. (1999). Defining the body size-abundance constraint space: data from a real web. Ecology Letters, 2, 191–199. Peters, R. H. (1983). The Ecological Implications of Body Size. New York: Cambridge University Press.

Raffaelli, D., Solan, M. & Webb, T. J. (2005). Do marine and terrestrial ecologists do it differently? Marine Ecology Progress Series, 304, 271–307. Schwinghamer, P. (1981). Characteristic size distributions of integral benthic communities. Canadian Journal of Fisheries and Aquatic Sciences, 38, 1255–1263. Stead, T. K., Schmid-Araya, J. M., Schmid, P. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487. Strong, D. R. (1992). Are trophic cascades all wet? – differentiation and donor-control in speciose ecosytems. Ecology, 73, 747–754. Southwood, T. R. E. (1977). The habitat, the templet for ecological strategies. Journal of Animal Ecology, 46, 337–365. Townsend, C. R. & Hildrew, A. G. (1994). Species traits in relation to a habitat templet for river systems. Freshwater Biology, 31, 265–275.

Index

absolute abundance, microbial species 169–171 abundance and metabolic rate 8–9 consumer:producer ratios 11–12 distribution across species 2 Acartia tonsa (copepod) 24–25 acidification effects in freshwaters 112–113 adaptive dynamics evolutionarily unbeatable strategy 36 fitness definition 36 frequency and density dependence 36–37 relationship of traits to fitness 35–36 trade-offs among traits 35–36 adaptive dynamics life history model 35–36 Allee effect 236–237 allometric equations, form of 1–2 allometric scaling strategies 227–228 alternative states and body size distributions 235–239 aquatic ecosystems body size as a structuring force 98–99 individual biomass production rates 5 individual metabolic rate and body size 4–5 temperature corrections 3–4 aquatic invertebrates (dispersal and body size) 188–193, 195, 196, 198, 200, 201 active dispersers in freshwaters 188–189 active dispersers in freshwaters (case studies) 188, 193–196 dispersal in marine systems 191–193 dispersal in marine systems (case studies) 199–203 passive dispersers in freshwaters 188, 190–191 passive dispersers in freshwaters (case studies) 188, 196–199 Arctic char 236, 237 Atlantic silverside (Menidia menidia) 41 Avelia martinicensis 175 B (mass-specific metabolic rate) 2 b (scaling exponent) 1–44, 45 Bacillus cereus 247 Bacillus subtilus 247 bacteria, body size 1 barndoor skate (Dipturus laevis) 267–268

biodiversity characteristics macroscopic organisms 169 microbial species 169 biogeography and size see microbial species biological scaling relations 1–4 biomass and body size (stream communities) 56, 57, 60, 61, 62, 68–71 and diversity 246–247 consumer:producer ratios 11–12 distribution across species 2 estimates 42 biomass invariance mechanisms 146, 148–152 biomass per unit volume, consistency of 245 biomass production rates, individual organisms 5 biomass turnover (P/B) factors affecting 000 range of rates 000 biomass turnover (P/B) and body size (stream communities) 000 application of the MTE 60, 62–68 biomass 56, 57, 60, 61, 62, 68–71 biomass turnover rate (P/B) predictions and results 56, 57, 61, 62, 63, 66, 68–71 differences in temperate and subtropical streams 60, 62–68 discussion 60, 62–68 metabolic theory of ecology 55–56 population density 56, 60, 61–62, 65, 68–71 predictions 56–57, 68–71 production (P) 56, 57, 61, 63, 64, 68–71 results 60–62, 63, 64, 65, 66 secondary production rate 55–56, 68–71 study streams 57–59 tests of predictions 59–60 bluegill sunfish (Lepomis macrochirus) 39, 40 body size adaptive plasticity in Cladocera 37–39 correlation with characteristics of organisms 1–2 early writings and studies ix–x link to patterns in natural systems 98 range of variation among organisms 1 relation to metabolic rate 1–2

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body size (cont.) relationship with temperature 42 variation within species 226 body-size distribution (BSD) in communities 140 effects of shifts in 112–113 multifractal properties 155–156, 157, 158–159 body-size increase, costs and benefits in suspension feeders 19–24 body-size measurement, difficulties in suspension feeders 17 Boltzmann-Arrhenius factor 2 Boltzmann’s constant (k) 2 brown trout 236, 237 BSD see body-size distribution cannibalistic system 233–234, 235 capelin 237 carbon cycle, and metabolism of organisms 9–11 carbon:phosphorus:nitrogen ratio 9–10 carbon:phosphorus ratio influence on growth rate 6 relation to body size 6 carbon turnover and plant size 10–11 Cladocera, adaptive plasticity in body size 37–39 common skate (Dipturus batis) 267–268 community consequences of body size (microbial systems) 249–250, 252–256, 257, 258, 259, 260, 261–262 community size distributions 110–112 and food web construction 110–112 distinct multiple nodes 111–112 factors affecting size structure 112 invertebrate macrofauna 111–112 megafauna 111–112 meiofauna 111–112 vertebrate macrofauna 111–112 Condylostoma reichi 175 consumer:producer ratios abundance 11–12 biomass 11–12 metabolic energy flux 11–12 copepods body size in relation to prey size 24–25 estimation of global patterns of mortality 46–47, 48 Coregonus albula 229 cosmopolitan-biogeography transition size 171–172 general validity 180–181 cosmopolitan distribution theory (microbial species) 168, 172–180 ‘biogeography’ of microbes 180 cosmopolitan genotypes (rDNA) 178–180 diversity of cryptic protists exceeds active species 172–174 endemic species 168, 175–178, 179 habitat influence on species composition 168, 175–176 habitat selects for cryptic or active phase 172–174 local:global species ratios 176, 177 random dispersal of free-living protists 168, 174

similar species inventories irrespective of geographical distance 174 species concepts 178 undersampling problem 176–178, 179 Cyclidium glaucoma 178–179, 181 density and biomass scaling 146–148 density–body-mass scaling 144–145 with sample area 145–146, 147 density dependence (strength of compensation), response to additional mortality 270–273 determinate growth 228 diatom communities, influences on species composition 175–176 Dipturus batis (common skate) 267–268 Dipturus laevis (barndoor skate) 267–268 dispersal challenges for aquatic organisms 187–188 microbial species 169–171 dispersal ability macroecological significance 187 traits which influence 187 dispersal and body size (aquatic invertebrates) 188–193, 195, 196, 198, 200, 201 active dispersers in freshwaters 188–189 active dispersers in freshwaters (case studies) 188, 193–196 dispersal in marine systems 191–193 dispersal in marine systems (case studies) 199–203 passive dispersers in freshwaters 188, 190–191 passive dispersers in freshwaters (case studies) 188, 196–199 distribution, cosmopolitan-biogeography transition size 171–172 disturbance, effects on marine species diversity 216, 218–220, 221 diversity see species diversity Dreissena spp. (mussels) 289 Dyar’s constant 211, 212 E-state (environmental state) 231 ecological stoichiometry and nutrient relations 2 ecosystems application of MTE 9–12 biomass invariance mechanisms 146, 148–152 body-size distribution (BSD) 140 body-size scaling relationships 98 carbon turnover and plant size 10–11 consequences of body size (microbial systems) 250–251, 256–259, 260, 262–263 effects of community size spectrum 43 element turnover rate and metabolic rate 9–10 energy and materials flow in food webs 11–12 flux and storage of elements 9–12 flux and storage of energy 9–12 fractal geometry framework for patterns and relationships 141–143 influence of body size 225–226 influence of body-size attributes 140 particle-size distribution (PSD) in benthic habitats 142 power-law behaviour 140–143

INDEX

role of metabolism in trophic relationships 11–12 scale-invariance and fractal properties of SADs 141–142 scale-invariance and fractal properties of SARs 141–142 scale-invariance properties 140–143 species-abundance distribution (SAD) mechanisms 146, 148–152 storage of elements in living biomass 9–10 stressor-induced size-spectrum changes 112–113 stressor-induced species loss 112–113 egg hatch times and egg protection strategy 48–49 model 47–49 egg-to-adult times, model 47–49 endothermy and individual growth rate 228 energy availability models 273–274 energy equivalence rule 8–9 energy flux, consumer:producer ratios 11–12 energy transfer in predator–prey interactions 274 energy use across species 2 energy use of populations, and body size 8–9 environmental gradients and body size 78 biomonitoring tools 94 body size patterns 90–94 in stream ecosystems 78 environmental gradients and body size (stream studies) 78–85 agricultural and mining pollution 84–85 altitude 82–83 catchment land use 82 chemical contaminants 84–85 descriptive studies of abiotic gradients 79–81 descriptive studies of biotic gradients 81–82 descriptive studies of complex gradients 82–83 disturbance regime 79–80 experimental studies 83–85 floods 81 hydraulic stress 81 New Zealand streams database 85–88, 89, 90, 91, 92 phosphate availability 81–82 predation 82, 83–84 primary productivity 82 substrate particle size 80, 83–84 evolution fisheries-induced 40–41 of body size see life history analysis; life history theory feeding and size factors affecting variation in prey choice 101–105 individual level processes 100–105 ontogenetic dietary shifts in predators 104–105 scaling to species 105–110 size constraints on predation 100–105 fish eggs, ontogenetic development rate and body size 5–6 fish species, mortality selection for smaller size at maturity 40–41, 42

fisheries describing and predicting community responses 274–280 genetic shifts in mature size of fish 40–41 modelling effects on community size structure 274–280 shifts in fish community size spectrum 43 size-based responses to fishing 274–280 fisheries-induced evolution 40–41 fisheries management changes in size-spectra slopes 269 extinction of marine species 267–268 ‘fishing down the food web’ 268 indirect effects of fishing 269 magnitude of fishing effects 267–268 population and community effects of exploitation 266, 267–268 seabed damage by fishing gear 268, 269 significance of body size 266 size-related effects of fishing 268–269 size-related responses to exploitation 268–269 state of the world’s fisheries 267–268 flow regime (Reynolds number, Re), and body size 17–18 food availability, and body size (suspension feeders) 21, 26–28 food-chain body sizes lower limit to mass of host and parasite 307 metaphoetesis 306–307 parasite chains 306–308 parasitoid chains 306, 307 power-law relationships 306, 307 predator chains 306–308 predator–prey size relationships 306–308 social hunters 306–307 upper limit to mass of predators and prey 307 food-chain body sizes data differences between terrestrial and coastal communities 310, 314, 321–322 empirical values of the exponent 310, 314, 321–322 examination of Hutchinson’s (1959) arguments 319–321 limits to mass of host and parasite 310, 314, 321–323 limits to mass of predator and prey 310, 314, 321–323 power-law relationships 310, 314, 321–323 food-chain body sizes theory 308–313 maximal and minimal body masses 308–311 predicted value of the exponent 311–312 ratios and differences of consumer mass and resource mass 312–313 see also food webs data food-dependent development 235–239 food-dependent growth 228 food webs 2 application of MTE conceptual framework 11–12 body size structure 11–12 construction of size-based models 113–114 construction related to community size distributions 110–112 feeding loops 110

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food webs (cont.) ‘life history’ omnivory 110 masking of size-related effects 107, 108, 109–110 rates of energy and material flow 11–12 role of metabolism 11–12 species-averaging effects 105–110 structure by size rather than species 110 synthesis of approaches to 12 food webs data 313–319 studies of a well-defined community 313–317 studies that pool multiple communities 314, 317–319 fractal geometry framework for patterns in ecosystems 141–143 fractal properties of size-structured communities 152–159 Gadus morhua (North Atlantic cod) 237 Gadus morhua (northern cod) 40–41 global patterns of life history, prediction 47–49 global patterns of mortality in copepods, estimation 46–47, 48 growth and development patterns 226–229 allometric scaling strategies 227–228 classification of growth types 228 determinate growth 228 endothermy and individual growth rate 228 food-dependent growth 228 indeterminate/plastic growth 228 link between individual traits and community attributes 229 population-level feedback and dynamics 229 scaling constraints 227–228 see also ontogenetic development growth-rate hypothesis 6 habitat complexity and predator–prey interactions 129–132 and species complexity 129–132 and trophic cascades 129–132 hatching rate and body mass 5–6 Hubbell’s unified theory of biodiversity (UTB) 149–152 Hutchinson’s (1959) arguments, food chain body size and diversity 319–321 Hutchinsonian ratio 211 i-state (individual) distribution models 230–231 indeterminate/plastic growth 228 individual body size and population dynamics 229–240 alternative states and body size distributions 235–239 cannibalistic system 233–234, 235 E-state (environmental state) 231 emergent Allee effect 236–237 extensions to more complex configurations 239–240 food-dependent development 235–239 i-state (individual) distribution models 230–231 modelling framework 230–231

ontogenetic development and community structure 235–239 ontogenetic development dynamics 231–234, 235 p-state (population state) 230–231 physiologically structured population models (PSPMs) 230–231 size-dependent predation 235–239 size-structured consumer-resource system 231–233, 234 structured biomass community model 239–240 tritrophic food chains 235–239 individual organism biomass production 5 influence of body size on performance 225 metabolic rate and body size 4–5 intrinsic rate of increase (rmax), response to additional mortality 270–271 intrinsic rate of increase in a habitat (r) 34–35, 38–39 invariant quantities 44 invertebrate macrofauna 111–112 Leeuwenhoek, Antonie van 167 Lepomis gibbosus (pumpkinseed sunfish) 39, 40 Lepomis macrochirus (bluegill sunfish) 39, 40 life histories and body size 269–271 and population dynamics 269–271 and responses to exploitation 270–271 trade-offs 270–271 see also growth and development patterns life history analysis 33 biomass estimates 42 body size relationship with temperature 42 ecological applications 40–43 ecosystem function and community size spectrum 43 fisheries-induced evolution 40–41 prediction of body size variation within species 40–41, 42 shifts in community size spectrum 43 temperature-size rule (TSR) 42 life history analysis and scaling relationships ecological applications 46–49 estimation of global patterns of mortality 46–47, 48 intra- and interspecific allometries 45–46 invariant quantities 44 key elements 43–44 methodological issues 44–46 prediction of global patterns of life history 47–49 scaling exponents 43–44, 45 selection effects on scaling exponents 45 life history theory adaptive dynamics model 35–37 adaptive plasticity in life histories 37–39 fitness definition 34–35, 36 frequency and density dependence 36–37 interpretation of phenotypic variation 39 intrinsic rate of increase in a habitat (r) 34–35, 38–39 key elements 34–36 lifetime reproductive success (LRS) 34–35, 38–39

INDEX

methodological issues 36–39 optimality (optimization) model 34–35, 36–37 phenotypic plasticity 37–39 prediction of life history plasticity 37–39 reaction norms 37–39 relationship of traits to fitness 35–36 trade-offs among traits 35–36 life history traits, stream habitats 77–78 lifespan and body size 6–7 and temperature 6–7 lifetime reproductive success (LRS) 34–35, 38–39 Lindeman efficiency 11–12 local:global species ratios, size dependence 181–182 Lontra canadensis (river otter) 292–293 Loxodes rex 175 macroecological patterns acidification effects in freshwaters 112–113 aquatic ecosystems 186–187 effects of individual level processes 99–100 effects of shifts in body-size distribution 112–113 effects of species dispersal ability 187 influence of body-size relationships 186 size-spectrum changes in stressed ecosystems 112–113 stressor-induced species loss 112–113 macroscopic organisms, characteristics of biodiversity 169 marine communities describing and predicting responses to mortality 274–280 energy availability models 273–274 energy transfer in predator–prey interactions 274 modelling fishing effects on size structure 274–280 PPMR (ratio of mean predator size to mean prey size) 274 size-based features of aquatic food webs 273 size-based responses to fishing 274–280 size-based structuring 273–274 size-spectra emergence models 273–274 slope of size spectra 273–280 see also fisheries marine systems, similarities to terrestrial systems 210 marine systems species diversity benthic species adult body size distributions 212–216, 217, 218, 219 benthic species all-animal body size distributions 216–217, 219, 220 Dyar’s constant 211, 212 effects of disturbance 216, 218–220, 221 effects of pollution 216, 218–220, 221 evolutionary influences 214–216, 217, 218, 219 Hutchinsonian ratio 211 influence of feeding traits 215–216, 217, 218, 219 influence of habitat architecture 213–214, 215 influence of life history characteristics 214–216, 217, 218, 219 number of co-occurring species in a guild 211–212, 213

pelagic species size distributions 218, 220 relationship with body size 210–211 size difference between competing species 211, 212 species guilds 211–212, 213 mass-specific metabolic rate (B), equation for 2 maximal population growth rate (rmax) 7, 8 megafauna 111–112 meiofauna 111–112 Menidia menidia (Atlantic silverside) 41 metabolic energy flux, consumer:producer ratios 11–12 metabolic rate and body size in aquatic ecosystems 4–5 effect of temperature 2 factors affecting 3 relation to body size 1–2 metabolic theory of ecology (MTE) 98, 226 and body size (summary) 327–329 application to biomass turnover (P/B) and body size 60, 62–68 applications 2–3, 13 conceptual framework 3 development of 1–2 effects of body size 2–3 flow of energy and materials between trophic levels 11–12 food web structure and body size 11–12 in aquatic ecology 2–3 predictions 3 quantitative links from individual to ecosystem levels 10–11 synthesis of approaches to food webs 12 metaphoetesis 306–307 microbial species absolute abundance and dispersal 169–171 cosmopolitan-biogeography transition size 171–172 cosmopolitan distribution hypothesis 167–169 endemism question 169 general validity of geographical distribution data 180–181 geographical restriction hypothesis 167–169 neutral dispersal hypothesis 167–169 neutral theory of community structure 181–182 size dependence of local:global species ratios 181–182 size effects on biodiversity 169 size effects on dispersal and distribution 167–169 size range 170 see also cosmopolitan distribution theory microbial systems (experimental) 246–247 community consequences of body size 249–250, 252–256, 257, 258, 259, 260, 261–262 description of the experiments and data sets 248–249 discussion 259–263 ecosystem consequences of body size 250–251, 256–259, 260, 262–263 methods 247–251

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340

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microbial systems (experimental) (cont.) population consequences of body size 249, 251–252, 253, 254, 255, 259–261 results 251–259, 260 species choice 247–248 mortality rate and body mass 7–8 mortality selection in fish species, evolutionary responses 40–41, 42 MTE see metabolic theory of ecology multifractal behaviour in ecosystems 142–143 empirical applications 142 multifractal properties of PSDs in river ecosystems 156–159 multifractal SARs 159–163 multifractality of BSDs in river ecosystems 155–156, 157, 158–159 mussels (Dreissena spp.), nutrient excretion 289 Mycoplasma, body size 1 Neobursaridium gigas 175, 181 neutral theory of community structure 181–182 New Zealand streams database analysis 85–88, 89, 90, 91, 92 algal productivity effects 88, 90, 92 biomonitoring tools 94 body size patterns 90–94 disturbance effects 88, 90 factors affecting body size 88, 89, 90, 91, 92 fish 85 fish-predation effects 88, 92 land-use effects 88, 91 macroinvertebrates 85–86 methods 85–86 physicochemical conditions 86, 87 Principal Components Analysis 88, 92 results 88, 89, 90, 91, 92 statistical analyses 86 study sites 85 substrate effects 88, 90, 92 normalization constant 1–2 North Atlantic cod (Gadus morhua) 237 northern cod (Gadus morhua) 40–41 nutrient cycling in aquatic systems consequences of variation by size 293–300 direct and indirect regulation 286–287 effects of harvesting-induced changes in size structure 298–300 influence of body size 287 nutrient flux estimation from biomass size distributions 294–296 predator impact on prey size structure 296–297, 298 regulation by aquatic animals 286–287 variation in body-size distributions 293–294 nutrient excretion in aquatic systems chemical form of excreted N and P 287 fed and unfed animals 288–289, 290 influence of body size 287–292 influence of temperature 288–289, 290 rates of N and P excretion 287–290, 291 ratios of N and P excretion 291–292 taxonomic differences 289–290, 291

nutrient relations and ecological stoichiometry 2 nutrient translocation in aquatic systems and body size 292–293 and speed of movement 292–293 behavioural constraints on home range 292–293 Onchorhynchus spp. (Pacific salmon) 292–293 ontogenetic development and community structure 235–239 dynamics 231–234, 235 rate and body size 5–6 see also growth and development ontogenetic dietary shifts in predators 104–105 ontogenetic size refugia for prey species 107, 108, 109–110 ontogenetic variation in body size 226 optimality (optimization) model (of life history) 34–35 fitness definition 34–35 frequency and density dependence 36–37 intrinsic rate of natural increase (r) 34–35, 38–39 lifetime reproductive success (LRS) 34–35, 38–39 relationship of traits to fitness 35 trade-offs among traits 35, 36 P see production p-state (population state) 230–231 Pacific salmon (Onchorhynchus spp.) 292–293 Paraphysomonas 172, 181 parasite and host, lower limit to mass of 307, 310, 314, 321–323 parasite chains 306–308 parasitoid chains 306, 307 particle-size distributions (PSDs) in benthic habitats 142 multifractal properties in river ecosystems 156–159 perch (Perca fluviatilis) 234, 235, 238 phenotypic plasticity in life histories 37–39 phenotypic variation co-gradient 88 counter gradient 39, 40 interpretation 38, 39 phosphorus, as a growth-limiting nutrient 6 physiologically structured population models (PSPMs) 230–231 Plagiopyla frontata 174 Poecilia reticulata (Trinidadian guppy) 41, 42 Polarella glacialis 181 pollution, effects on marine species diversity 216, 218–220, 221 Polycentropus flavomaculata 24 population consequences of body size (microbial systems) 249, 251–252, 253, 254, 255, 259–261 population density and body size (stream communities) 56, 60, 61–62, 65, 68–71 population density at steady state, and metabolic rate 8–9 population dynamics and body size 269–271 and life histories 269–271

INDEX

and species interactions 2 intrinsic rate of increase (rmax) 270–271 responses to additional mortality 270–273 strength of compensation (density dependence) 270–273 population dynamics and individual body size 229–240 alternative states and body size distributions 235–239 cannibalistic system 233–234, 235 E-state (environmental state) 231 emergent Allee effect 236–237 extensions to more complex configurations 239–240 food-dependent development 235–239 i-state (individual) distribution models 230–231 modelling framework 230–231 ontogenetic development and community structure 235–239 ontogenetic development dynamics 231–234, 235 p-state (population state) 230–231 physiologically structured population models (PSPMs) 230–231 size-dependent predation 235–239 size-structured consumer-resource system 231–233, 234 structured biomass community model 239–240 tritrophic food chains 235–239 see also adaptive dynamics life history model population-level feedback and dynamics 229 population maximal growth rate (rmax) 7, 8 population turnover rate, and metabolic rate 7–8 Power Fraction (PF), niche-assembly model 148–152 power-law and scaling relationships in ecosystems 144–145 power-law behaviour in ecosystem features 140–143 power-law relationships food-chain body sizes 306, 307 food-chain body sizes data 310, 314, 321–323 PPMR (ratio of mean predator size to mean prey size) 274 predator chains 306–308 predator–prey interactions and trophic cascades 129–132 energy transfer 274 factors influencing variation in prey choice 101–105 feeding loops 110 individual level processes 100–105 ‘life history’ omnivory 110 networks structured by size 110 ontogenetic dietary shifts in predators 104–105 ontogenetic size refugia for prey species 107, 108, 109–110 particle capture by suspension feeders 24–26 PPMR (ratio of mean predator size to mean prey size) 274 predator impact on prey size structure 296–297, 298 scaling to species 105–110 size-dependent foraging 100–105 size-dependent predation 235–239

size relationships 24–26, 306–308 species-averaging effects in food webs 105–110 upper limits to mass of predator and prey 307, 310, 314, 321–323 production (P) (whole organism metabolic rate) and body size (stream communities) 56, 57, 61, 63, 64, 68–71 equation for 2 individual organisms 5 Proteus vulgaris 247 PSDs see particle-size distributions PSPMs (physiologically structured population models) 230–231 pumpkinseed sunfish (Lepomis gibbosus) 39, 40 quarter-power exponents (b), explanation for 1–2 r (intrinsic rate of increase in a habitat) 34–35, 38–39 rmax (intrinsic rate of increase), response to additional mortality 270–271 rmax (maximal population growth rate) 7, 8 Re see Reynolds number reaction norms 37–39 Redfield ratio 9–10 resource supply and abundance 8–9 Reynolds number (Re) 17–18, 293 collecting elements of suspension feeders 19, 20, 21 river ecosystems data collection 143–144 density and biomass scaling 146–148 density-body mass scaling 144–145 density-body mass scaling with sample area 145–146, 147 fractal properties of size-structured communities 152–159 multifractal behaviour 142–143 mulitfractal properties of BSDs 155–156, 157, 158–159 multifractal properties of PSDs 156–159 multifractal SARs 159–163 power-law and scaling relationships 144–145 scale-related patterns 142–143 river otter (Lontra canadensis) 292–293 RNA, influence on growth rate 6 roach (Rutilus rutilus) 238 SADs see species-abundance distributions sapuara (Semaprochilodus kneri) 293 SARs see species-area relationships scale-invariance of power laws 144–145 scale invariance properties of ecosystems 140–143 fractal properties of size-structured communities 152–159 scaling constraints 227–228 scaling exponent (b) 1–2, 43–44, 45 secondary production rate and biomass turnover rate 55–56, 68–71 self-similarity, fractal properties of size-structured communities 152–159 Sequoia trees, size of 1 Serratia marcescens 247

341

342

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Simulium (blackfly) larvae, feeding strategy 28 size-spectrum changes in stressed ecosystems 112–113 size-structured consumer-resource system 231–233, 234 social hunters 306–307 solid–fluid interfaces, and body size 21, 26–28 species-abundance distributions (SADs) mechanisms 146, 148–152 scale-invariance and fractal properties 141–142 species-area curves 141–142 species-area relationships (SARs) multifractal properties 159–163 scale-invariance and fractal properties 141–142 species-averaging in food webs 105–110 species complexity and habitat complexity 129–132 and trophic cascades 129–132 species diversity, and total biomass 246–247 species diversity (marine systems) benthic species adult body size distributions 212–216, 217, 218, 219 benthic species all-animal body size distributions 216–217, 219, 220 Dyar’s constants 211, 212 effects of disturbance 216, 218–220, 221 effects of pollution 216, 218–220, 221 evolutionary influences 214–216, 217, 218, 219 Hutchinsonian ratio 211 influence of feeding traits 215–216, 217, 218, 219 influence of habitat architecture 213–214, 215 influence of life history characteristics 214–216, 217, 218, 219 number of co-occurring species in a guild 211–212, 213 pelagic species size distributions 218, 220 relationship with body size 210–211 size difference between competing species 211, 212 species guilds 211–212, 213 species interactions and population dynamics 2 stoichiometry, whole body carbon:phosphorus ratio 6 stream habitats and life history traits 77–78 community size structure 78 species traits related to disturbance regimes 78 trophic roles 77 see also biomass turnover; environmental gradients streams database analysis (New Zealand) 85–88, 89, 90, 91, 92 algal productivity effects 88, 90, 92 biomonitoring tools 94 body-size patterns 90–94 disturbance effects 88, 90 factors affecting body size 88, 89, 90, 91, 92 fish 85 fish-predation effects 88, 92 land-use effects 88, 91 macroinvertebrates 85–86 methods 85–86

physicochemical conditions 86, 87 Principal Components Analysis 88, 92 results 88, 89, 90, 91, 92 statistical analyses 86 study sites 85 substrate effects 88, 90, 92 strength of compensation (density dependence), response to additional mortality 270–273 stressor-induced size-spectrum changes 112–113 stressor-induced species loss 112–113 structured biomass community model 239–240 Sugihara Fraction (SF), niche-assembly model 148–152 suspension feeders active 16–17 body size and flow regime (Reynolds number, Re) 17–18 body size and food availability 21, 26–28 body size and solid-fluid interfaces 21, 26–28 body-size measurement difficulties 17 body size relation to food particle size 24–26 collecting elements 16 colonial or clonal animals 22–23 costs and benefits of feeding structure size increase 19–24 dependence on flow characteristics 17–18 deposit-suspension feeders 16–17 development of gelatinous bodies 24 feeding structure 16 hydrodynamic implications of body size 17–18 influence on local sediment deposition 26–27 limits to maximum body size 19–24 modification of body parts into feeding structures 23–24 ontological shifts between flow regimes 19 overcoming velocity gradients 27–28 particle capture as predator–prey relationship 24–26 particle encounter mechanisms 18 passive 16–17 range of feeding adaptations 18 Re of collecting elements 19, 20, 21 role in ecosystem energy transfer 16 roles in the food web 16 transport of particles to feeding structure (particle flux) 16–17 use of external capture apparatus 24 vortex shedding rate and body size 26–27 temperature and lifespan 6–7 effect on metabolic rate 2 temperature correction 3–4 temperature-size rule (TSR) 42 terrestrial ecosystems role of body size 98–99 trophic cascades 134 Tracheloraphis caudata 174 Trichoptera (caseless caddis flies) larvae, use of external feeding structures 24 Trinidadian guppy (Poecilia reticulata) 41, 42 tritrophic food chains 235–239

INDEX

trophic cascades alternative equilibria 132–133 and biomass distribution 122 and habitat complexity 129–132 and predator–prey interactions 129–132 and species complexity 129–132 body-size disparity between predators and prey 119–122 body-size effects 133–134 body size of primary producers 127–128 conditions which lead to 119 definition 118–119 effects of herbivory 127–128 in terrestrial ecosystems 134 predation effects 118 shape of the trophic pyramid 128–131

system productivity and food web structure 122–124, 125–126 turnover rate of primary producers 127–131 trophic roles, in stream ecosystems 77 unified theory of biodiversity (UTB) 149–152 vertebrate macrofauna 111–112 vortex shedding rate, and body size 26–27 whales, body size 1 within-species variation in body size 226 Zero-Sum Multinomial (ZSM) distribution, dispersal-assembly model 148, 149–152 zooplankton eggs, ontogenetic development rate and body size 5–6

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