Food webs have now been addressed in empirical and theoretical research for more than 50 years. Yet, even elementary foundational issues are still hotly debated. One difficulty is that a multitude of processes need to be taken into account to understand the patterns found empirically in the structure of food webs and communities. Food Webs and Biodiversity develops a fresh, comprehensive perspective on food webs. Mechanistic explanations for several known macroecological patterns are derived from a few fundamental concepts, which are quantitatively linked to field–observables. An argument is developed that food webs will often be the key to understanding patterns of biodiversity at community level. Key Features: Predicts generic characteristics of ecological communities in invasion–extirpation equilibrium. Generalizes the theory of competition to food webs with arbitrary topologies. Presents a new, testable quantitative theory for the mechanisms determining species richness in food webs, and other new results. Written by an internationally respected expert in the field. With global warming and other pressures on ecosystems rising, understanding and protecting biodiversity is a cause of international concern. This highly topical book will be of interest to a wide ranging audience, including not only graduate students and practitioners in community and conservation ecology but also the complex–systems research community as well as mathematicians and physicists interested in the theory of networks. “This is a comprehensive work outlining a large array of very novel and potentially game–changing ideas in food web ecology.” Ken Haste Andersen, Technical University of Denmark “I believe that this will be a landmark book in community ecology … it presents a well–established and consistent mathematical theory of food–webs. It is testable in many ways and the author finds remarkable agreements between predictions and reality.” Géza Meszéna, Eötvös University, Budapest INDICE: Acknowledgments xvii List of Symbols xix Part I Preliminaries 1 Introduction 3 2 Models and Theories 7 2.1 The usefulness of models 7 2.2 What models should model 8 2.3 The possibility of ecological theory 10 2.4 Theory–driven ecological research 11 3 Some Basic Concepts 13 3.1 Basic concepts of food–web studies 13 3.2 Physical quantities and dimensions 15 Part II Elements of Food–Web Models 4 Energy and Biomass Budgets 19 4.1 Currencies of accounting 19 4.2 Rates and efficiencies 20 4.3 Energy budgets in food webs 21 5 Allometric Scaling Relationships Between Body Size and Physiological Rates 25 5.1 Scales and scaling 25 5.2 Allometric scaling 26 6 Population Dynamics 29 6.1 Basic considerations 29 6.1.1 Exponential population growth 29 6.1.2 Five complications 30 6.1.3 Environmental variability 31 6.2 Structured populations and density–dependence 32 6.2.1 The dilemma between species and stages 32 6.2.2 Explicitly stage–structured population dynamics 32 6.2.3 Communities of structured populations 35 6.3 The Quasi–Neutral Approximation 35 6.3.1 The emergence of food webs 35 6.3.2 Rana catesbeiana and its resources 35 6.3.3 Numerical test of the approximation 38 6.4 Reproductive value 40 6.4.1 The concept of reproductive value 40 6.4.2 The role of reproductive value in the QNA 40 6.4.3 Body mass as a proxy for reproductive value 40 7 From Trophic Interactions to Trophic Link Strengths 45 7.1 Functional and numerical responses 45 7.2 Three models for functional responses 46 7.2.1 Linear response 46 7.2.2 Type II response 46 7.2.3 Type II response with prey switching 47 7.2.4 Strengths and weaknesses of these models 48 7.3 Food webs as networks of trophic link strengths 48 7.3.1 The ontology of trophic link strengths 48 7.3.2 Variability of trophic link strengths 49 8 Tropic Niche Space and Trophic Traits 51 8.1 Topology and dimensionality of trophic niche space 52 8.1.1 Formal setting 52 8.1.2 Definition of trophic niche–space dimensionality 53 8.2 Examples and ecological interpretations 55 8.2.1 A minimal example 55 8.2.2 Is the definition of dimensionality reasonable? 55 8.2.3 Dependencies between vulnerability and foraging traits of a species 56 8.2.4 The range of phenotypes considered affects niche–space dimensionality 56 8.3 Determination of trophic niche–space dimensionality 58 8.3.1 Typical empirical data 58 8.3.2 Direct estimation of dimensionality 59 8.3.3 Iterative estimation of dimensionality 59 8.4 Identification of trophic traits 60 8.4.1 Formal setting 60 8.4.2 Dimensional reduction 62 8.5 The geometry of trophic niche space 65 8.5.1 Abstract trophic traits 65 8.5.2 Indeterminacy in abstract trophic traits 65 8.5.3 The D–dimensional niche space as a pseudo–Euclidean space 66 8.5.4 Linear transformations of abstract trophic traits 67 8.5.5 Non–linear transformations of abstract trophic traits 68 8.5.6 Standardization and interpretation of abstract trophic traits 69 8.5.7 A hypothesis and a convention 72 8.5.8 Getting oriented in trophic niche space 73 8.6 Conclusions 75 9 Community Turnover and Evolution 77 9.1 The spatial scale of interest 77 9.2 How communities evolve 78 9.3 The mutation–for–dispersion trick 79 9.4 Mutation–for–dispersion in a neutral food–web model 80 10 The Population–Dynamical Matching Model 81 Part III Mechanisms and Processes 11 Basic Characterizations of Link–Strength Distributions 87 11.1 Modelling the distribution of logarithmic link strengths 88 11.1.1 General normally distributed trophic traits 88 11.1.2 Isotropically distributed trophic traits 91 11.2 High–dimensional trophic niche spaces 93 11.2.1 Understanding link stengths in high–dimensional trophic niche spaces 93 11.2.2 Log–normal probability distributions 94 11.2.3 The limit of log–normally distributed trophic link strength 95 11.2.4 Correlations between trophic link strengths 96 11.2.5 The distribution of the strengths of observable links 97 11.2.6 The probability of observing links (connectance) 99 11.2.7 Estimation of link–strength spread and Pareto exponent 100 11.2.8 Empirical examples 101 12 Diet Partitioning 103 12.1 The diet partitioning function 103 12.1.1 Relation to the probability distribution of diet proportions 105 12.1.2 Another probabilistic interpretation of the DPF 106 12.1.3 The normalization property of the DPF 106 12.1.4 Empirical determination of the DPF 107 12.2 Modelling the DPF 107 12.2.1 Formal setting 107 12.2.2 Diet ratios 108 12.2.3 The DPF for high–dimensional trophic niche spaces 109 12.2.4 Gini–Simpson dietary diversity 110 12.2.5 Dependence of the DPF on niche–space dimensionality 112 12.3 Comparison with data 113 12.4 Conclusions 114 13 Multivariate Link–Strength Distributions and Phylogenetic Patterns 117 13.1 Modelling phylogenetic structure in trophic traits 118 13.1.1 Phylogenetic correlations among logarithmic link strengths 120 13.1.2 Phylogenetic correlations among link strengths 121 13.1.3 Phylogenetic patterns in binary food webs 122 13.2 The matching model 123 13.2.1 A simple model for phylogenetic structure in food webs 123 13.2.2 Definition of the matching model 124 13.2.3 Sampling steady–state matching model food webs 124 13.2.4 Alternatives to the matching model 126 13.3 Characteristics of phylogenetically structured food webs 126 13.3.1 Graphical representation of food–web topologies 127 13.3.2 Standard parameter values 127 13.3.3 Intervality 128 13.3.4 Intervality and trophic niche–space dimensionality 129 13.3.5 Degree distributions 131 13.3.6 Other phylogenetic patterns 134 13.3.7 Is phylogeny just a nuisance? 135 14 A Framework Theory for Community Assembly 137 14.1 Ecological communities as dynamical systems 137 14.2 Existence, positivity, stability, and permanence 138 14.3 Generic bifurcations in community dynamics and their ecological phenomenology 139 14.3.1 General concepts 139 14.3.2 Saddle–node bifurcations 140 14.3.3 Hopf bifurcations 142 14.3.4 Transcritical bifurcations 142 14.3.5 Bifurcations of complicated attractors 144 14.4 Comparison with observations 144 14.4.1 Extirpations and invasions proceed slowly 145 14.4.2 The logistic equation works quite well 145 14.4.3 IUCN Red–List criteria highlight specific extinction scenarios 147 14.4.4 Conclusion 148 14.5 Invasion fitness and harvesting resistance 148 14.5.1 Invasion fitness 148 14.5.2 Harvesting resistance: definition 149 14.5.3 Harvesting resistance: interpretation 149 14.5.4 Harvesting resistance: computation 151 14.5.5 Interpretation of h → 0 152 14.6 Community assembly and stochastic species packing 152 14.6.1 Community saturation and species packing 152 14.6.2 Invasion probability 154 14.6.3 The steady–state distribution of harvesting resistance 157 14.6.4 The scenario of stochastic species packing 158 14.6.5 A numerical example 160 14.6.6 Biodiversity and ecosystem functioning 162 15 Competition in Food Webs 165 15.1 Basic concepts 166 15.1.1 Modes of competition 166 15.1.2 Interactions in communities 166 15.2 Competition in two–level food webs 167 15.2.1 The Lotka–Volterra two–level food–web model 168 15.2.2 Computation of the equilibrium point 168 15.2.3 Direct competition among producers 169 15.2.4 Resource–mediated competition in two–level food webs 169 15.2.5 Consumer–mediated competition in two–level food webs 170 15.3 Competition in arbitrary food webs 173 15.3.1 The general Lotka–Volterra food–web model 173 15.3.2 The competition matrix for general food webs 174 15.3.3 The L–R–P formalism 176 15.3.4 Ecological interpretations of the matrices L, R, and P 176 15.3.5 Formal computation of the equilibrium point 177 15.3.6 Consumer–mediated competition in general food webs 178 15.3.7 Consumer–mediated competitive exclusion 179 15.3.8 Conclusions 179 16 Mean–Field Theory of Resource–Mediated Competition 181 16.1 Transition to scaled variables 182 16.1.1 The competitive overlap matrix 182 16.1.2 Free abundances 183 16.2 The extended mean–field theory of competitive exclusion 184 16.2.1 Assumptions 184 16.2.2 Separation of means and residuals 186 16.2.3 Mean–field theory for the mean scaled abundance 187 16.2.4 Mean–field theory for the variance of scaled abundance 188 16.2.5 The coefficient of variation of scaled abundance 190 16.2.6 Related theories 191 17 Resource–Mediated Competition and Assembly 193 17.1 Preparation 193 17.1.1 Scaled vs. unscaled variables and parameters 193 17.1.2 Mean–field vs framework theory 195 17.2 Stochastic species packing under asymmetric competition 197 17.2.1 Species richness and distribution of invasion fitness (Part I) 198 17.2.2 Community response to invasion 199 17.2.3 Sensitivity of residents to invaders 200 17.2.4 Species richness and distribution of invasion fitness (Part II) 203 17.2.5 Random walks of abundances driven by invasions 204 17.2.6 Further discussion of the scenario 206 17.3 Stochastic species packing with competition symmetry 207 17.3.1 Community assembly with perfectly symmetric competition 207 17.3.2 Community assembly under nearly perfectly symmetric competition 209 17.3.3 Outline of mechanism limiting competition avoidance 211 17.3.4 The distribution of invasion fitness 212 17.3.5 Competition between residents and invaders 213 17.3.6 Balance of scaled biomass during assembly 214 17.3.7 Competition avoidance 215 17.3.8 Numerical test of the theory 216 18 Random–Matrix Competition Theory 221 18.1 Asymmetric competition 221 18.1.1 Girko’s Law 221 18.1.2 Application to competitive overlap matrices 223 18.1.3 Implications for sensitivity to invaders 223 18.1.4 Relation to mean–field theory 224 18.2 Stability vs feasibility limits to species richness 225 18.2.1 The result of May (1972) 225 18.2.2 Comparison of stability and feasibility criteria 225 18.3 Partially and fully symmetric competition 226 18.4 Sparse overlap matrices 228 18.4.1 Sparse competition 228 18.4.2 Eigenvalue distributions for sparse matrices 228 18.5 Resource overlap matrices 230 18.5.1 Diffuse resource competition 230 18.5.2 Sparse resource competition: the basic problem 232 18.5.3 The effect of trophic niche–space geometry 235 18.5.4 Competition among highly specialized consumers 237 18.5.5 Resource competition for varying ratios of producer to consumer richness 237 18.5.6 Competition for competing resources 239 18.6 Comparison with data 242 18.6.1 Gall–inducing insects on plants 242 18.6.2 Freshwater ecosystems 243 18.6.3 The North Sea 244 18.6.4 Conclusions 244 19 Species Richness, Size and Trophic Level 247 19.1 Predator–prey mass ratios 247 19.2 Modelling the joint distribution of size, trophic level, and species richness 249 19.2.1 Initial considerations 249 19.2.2 Model definition 251 19.2.3 Model simulation and comparison with data 252 20 Consumer–Mediated Competition and Assembly 255 20.1 A two–level food–web assembly model 256 20.2 Analytic characterization of the model steady state 257 20.2.1 Mechanism controlling producer richness 257 20.2.2 Other characteristics of the model steady state 259 20.3 Dependence of invader impacts on dietary diversity 262 20.3.1 Formal setting 262 20.3.2 Invadibility condition 263 20.3.3 Extirpation of resources during invasion 263 20.3.4 Extirpation of resources through consumer–mediated competition 264 20.3.5 Synthesis 264 20.4 Evolution of base attack rates 266 20.4.1 Motivation 266 20.4.2 Model definition 267 20.4.3 Numerical demonstration of attack rate evolution 267 20.4.4 Attack–rate evolution and prudent predation 268 21 Food Chains and Size Spectra 271 21.1 Concepts 271 21.1.1 Community size spectra 271 21.1.2 Species size spectra 273 21.2 Power–law food chains 274 21.2.1 Infinitely long power–law food chains 274 21.2.2 Top–down and bottom–up control 276 21.2.3 Power law–food chains of finite lengths and their stability to pulse perturbations 278 21.2.4 Food chains as approximations for size spectra 279 21.2.5 Adaptation of attack rates 281 21.3 Food chains with non–linear functional responses 281 21.3.1 Loss of stability with density–independent consumption 282 21.3.2 Linearization of a generalized food chain model 283 21.3.3 Linear responses to press perturbations 284 21.3.4 Linear stability to pulse perturbations 285 21.4 What are the mechanisms controlling the scaling laws? 290 21.4.1 Arguments for biological constraints on transfer efficiency 290 21.4.2 Arguments for stability constraints on transfer efficiency 291 21.4.3 Arguments for ecological constraints on biomass imbalance 291 21.4.4 Arguments for mechanical constraints on PPMR 292 21.4.5 Arguments for dynamical constraints on PPMR 293 21.4.6 Conclusions 293 21.5 Scavengers and detrivores 294 21.5.1 The general argument 294 21.5.2 The microbial loop and other detrital channels 294 22 Structure and Dynamics of PDMM Model Communities 297 22.1 PDMM model definition 298 22.1.1 Model states 298 22.1.2 Species sampling and community assembly 298 22.1.3 Population dynamics 301 22.2 PDMM simulations 303 22.2.1 Trophic niche space and phylogenetic correlations 304 22.2.2 Steady state and invasion fitness 307 22.2.3 Diet partitioning 309 22.2.4 Resource–mediated competition 310 22.2.5 Distribution of species over body sizes and trophic levels 311 22.2.6 The size spectrum and related distributions 312 22.3 The PDMM with evolving attack rates 314 22.3.1 Modelling and tracking evolving attack rates in the PDMM 314 22.3.2 Time series of species richness, aggressivity and dietary diversity 315 22.3.3 Mutual regulation of aggressivity and dietary diversity 316 22.4 Conclusions 318 Part IV Implications 23 Scientific Implications 323 23.1 Main mechanisms identified by the theory 323 23.1.1 Two trades – one currency 323 23.1.2 Resource–mediated competition 324 23.1.3 Randomness and structure in food webs 324 23.1.4 Consumer–mediated competition and attack–rate evolution 325 23.2 Testable assumptions and predictions 325 23.2.1 Link–strength distributions and trophic niche–space geometry 325 23.2.2 Diet–partitioning statistics and sampling curves 325 23.2.3 Prey switching 326 23.2.4 Adapted attack rates 326 23.2.5 Community assembly and turnover 326 23.2.6 Patterns in link–strength matrices 327 23.3 Some unsolved problems 327 23.3.1 Large plants 327 23.3.2 Interactions between modes of competition 327 23.3.3 Absolute species richness: the role of viruses 327 23.3.4 The role of prey switching for community structure 328 23.3.5 The role of phylogenetic correlations for community dynamics 328 23.3.6 Fundamental constraints determining size–spectrum slopes 328 23.3.7 Community assembly with non–trivial attractors 328 23.3.8 Solution of the Riccati Equation for resource competition 328 23.3.9 Eigenvalues of competition matrices 329 23.3.10 Geometry and topology of trophic niche space 329 23.4 The future of community ecology 329 24 Conservation Implications 331 24.1 Assessing biodiversity 331 24.1.1 Quantifying biodiversity 331 24.1.2 Biodiversity supporting biodiversity 331 24.1.3 Assessing community turnover 332 24.2 Modelling ecological communities 333 24.2.1 Unpredictability of long–term community responses 333 24.2.2 Short–term predictions of community responses 334 24.2.3 Coarse–grained and stochastic community models 334 24.3 Managing biodiversity 334 Appendix A 337 A.1 Mathematical concepts, formulae, and jargon 337 A.1.1 Sums 337 A.1.2 Complex numbers 338 A.1.3 Vectors and matrices 339 A.1.4 Sets and functions 343 A.1.5 Differential calculus 343 A.1.6 Integrals 344 A.1.7 Differential equations 345 A.1.8 Random variables and expectation values 346 Bibliography 349 Index 365
- ISBN: 978-0-470-97355-4
- Editorial: Wiley–Blackwell
- Encuadernacion: Cartoné
- Páginas: 396
- Fecha Publicación: 26/07/2013
- Nº Volúmenes: 1
- Idioma: Inglés