Dynamic Energy Budgets in Biological Systems Theory and Applications in Ecotoxicology S.A.L.M. Kooijman Dynamic Energy Budget Theory is about simple, mechanistic, rules for the uptake and use of energy by heterotrophs and its implications for physiological organization and population dynamics. Its predictions are tested against a wide variety of experimental results. Among others, the theory explains the observed body size scaling relationships of physiological traits, such as why respiration rates increase approximately with body weight to the power 0.75. It discusses the coupling between aging and energetics and proposes new quantitative relationships between food intake and life span. The theory is applied to ecotoxicology, leading to a new and simple methodology for characterizing the toxicity of compounds. It provides a basis for the extrapolation of laboratory results to consequences in the field. Each topic is given a general introduction, followed by formulation of the theory in elementary mathematical terms. Methodological aspects of mathematical modelling are discussed in detail. The book is of interest to scientists and mathematicians with a broad interest in fundamental and applied problems in biology. summary of contents 1 ENERGETICS AND MODELS The position of energetics in the biological sciences; historical setting; the methology of modelling and the philosophical status of biological theories 2 INDIVIDUALS A systems theory view of individuals; the significance of isomorphism and homeostasis in the light of surface area vs volume relationships; critical evaluation of measures for size, storage and energy; effects of temperature 3 ENERGY ACQUISITION AND USE A step by step discussion of mechanisms of energy uptake and use by individuals with relevance to the deb model 4 ANALYSIS OF THE DEB MODEL Summary of the model; Evaluation of its consequences for the behaviour of individuals under a variety of circumstances 5 LIVING TOGETHER Evaluation of the consequences of the deb model for populations and commu- nities; a discussion of additional processes operating at the population level 6 COMPARISON OF SPECIES Body size scaling relationships; strategies of parameter selection; evolutionary implications 7 SUBORGANISMAL ORGANIZATION Relationships between the deb model and models for di- gestion, allometric growth of parts, protein synthesis and rna turnover 8 ECOTOXICITY Uptake kinetics and the relationship with effects; the relationship between effects on individuals and on populations Cambridge university press Dynamic Energy Budgets in Biological Systems Theory and Applications in Ecotoxicology S.A.L.M. Kooijman Professor of Theoretical Biology, Vrije Universiteit, de Boelelaan 1087, 1081 HV Amsterdam Cambridge university press Cambridge New York Port Chester Melbourne Sydney Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY 10011-4211, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia c Cambridge University Press 1993 First published 1993 Printed in Great Britain at the University Press, Cambridge British Library Cataloguing in publication data Kooijman, S.A.L.M. Dynamic Energy Budgets in Biological Systems Theory and Applications in Ecotoxicology 1. Energetics—Modelling I. Title ***’.*** QL**** Library of Congress cataloguing in publication data Kooijman, S.A.L.M.(Bas), 1950- Dynamic Energy Budgets Includes bibliographical references and index. 1. Energetics—Modelling QL**** 1993 ***’.*** ****** ISBN 0 521 45223 6 hardback ISBN 0 *** ***** * paperback Cover figure: Sitting on the stone of wisdom, the mediaeval drag- ons symbolize the message that, when reaching out for both the micro- and the macro-world, the wise focus is on individuals. vi Contents Preface xi Acknowledgements .................................. xiv Book organization .................................. xv 1 Energetics and models 1 1.1 Energy and mass fluxes ............................. 1 1.1.1 Hope for generality ........................... 1 1.1.2 Historical setting ............................ 3 1.1.3 Energetics ................................ 4 1.1.4 Population energetics .......................... 6 1.2 The art of modelling .............................. 7 1.2.1 Strategies ................................ 7 1.2.2 Systems ................................. 10 1.2.3 Physical dimensions ........................... 11 1.2.4 Statistics ................................. 14 2 Individuals 17 2.1 Input/output relationships ........................... 17 2.2 State variables .................................. 18 2.3 Size and shape ................................. 21 2.3.1 Length/surface area/volume relationships ............... 21 2.3.2 Isomorphism ............................... 22 2.3.3 Changing shapes ............................ 27 2.3.4 Weight/volume relationships ...................... 33 2.3.5 C-mole/volume relationships ...................... 37 2.4 Homeostasis ................................... 38 2.4.1 Storage materials ............................ 39 2.4.2 Storage deposits ............................. 41 2.5 Energy ...................................... 41 2.6 Temperature ................................... 44 2.7 Life-stages .................................... 49 vii viii CONTENTS 3 Energy acquisition and use 53 3.1 Feeding ..................................... 54 3.1.1 Feeding methods ............................ 55 3.1.2 Selection ................................. 60 3.1.3 Feeding and movement costs ...................... 62 3.1.4 Functional response ........................... 63 3.1.5 Food deposits and claims ........................ 67 3.2 Digestion .................................... 68 3.2.1 Smoothing and satiation ........................ 68 3.2.2 Gut residence time ........................... 70 3.3 Assimilation ................................... 72 3.4 Storage dynamics ................................ 72 3.5 The κ-rule for allocation ............................ 74 3.6 Maintenance ................................... 76 3.7 Homeothermy .................................. 78 3.8 Growth ..................................... 80 3.8.1 Embryonic growth ........................... 83 3.8.2 Growth for non-isomorphs ....................... 93 3.9 Development .................................. 97 3.10 Propagation ................................... 100 3.10.1 Reproduction .............................. 100 3.10.2 Division ................................. 103 3.11 Respiration ................................... 103 3.12 Aging ...................................... 105 3.13 Genetics and parameter variation ....................... 112 4 Analysis of the DEB model 115 4.1 Summary of the deb model .......................... 115 4.1.1 Equivalent assumptions ......................... 119 4.1.2 State space ............................... 120 4.1.3 Scatter structure of weight data .................... 121 4.1.4 Yield ................................... 123 4.2 Changing and poor feeding conditions ..................... 126 4.2.1 Step up/down .............................. 126 4.2.2 Mild starvation ............................. 126 4.2.3 Prolonged starvation .......................... 128 4.2.4 Dormancy ................................ 131 4.2.5 Determination of sex .......................... 132 4.2.6 Geographical size variations ...................... 132 4.3 Reconstruction problems ............................ 134 4.3.1 Temperature reconstruction ...................... 135 4.3.2 Food intake reconstruction ....................... 137 4.4 Special case studies ............................... 141 4.4.1 Diffusion limitation ........................... 141 CONTENTS ix 4.4.2 Growth of 0D- and 2D-isomorphs ................... 144 4.4.3 Reproduction measurement from length data ............. 147 4.4.4 Suicide reproduction .......................... 149 4.4.5 Changing parameter values ...................... 150 4.4.6 Pupa and imago ............................. 151 4.4.7 Food induced aging acceleration .................... 154 4.4.8 Segmented individuals ......................... 155 5 Living together 159 5.1 Non-structured populations .......................... 160 5.1.1 Lotka–Volterra ............................. 161 5.1.2 Monod, Marr–Pirt and Droop ..................... 162 5.1.3 Death .................................. 165 5.1.4 deb filaments .............................. 166 5.1.5 Realism ................................. 168 5.2 Structured populations ............................. 168 5.2.1 Stable age distributions ......................... 169 5.2.2 Reproducing neonates ......................... 171 5.2.3 Discrete individuals ........................... 171 5.2.4 Differing daughters ........................... 173 5.2.5 Maintenance ............................... 174 5.3 deb-structured populations .......................... 174 5.3.1 Population growth rates ........................ 174 5.3.2 Stable age and size distributions .................... 177 5.3.3 Mean size of individuals ........................ 181 5.4 Yield at the population level .......................... 181 5.4.1 Product and weight yield for deb filaments .............. 189 5.4.2 Mass-energy coupling .......................... 192 5.4.3 Dissipating heat ............................. 201 5.5 Computer simulations ............................. 206 5.5.1 Synchronization ............................. 208 5.5.2 Variation between individuals ..................... 210 5.6 Chains .....................................