Food webs and biodiversity: foundations, models, data / Axel G. Rossberg

Incluye bibliografía: páginas 349-363 e índice: páginas 365-376

Acknowledgments.. List of Symbols.. Part I Preliminaries.. 1 Introduction.. 2 Models and Theories.. 2.1 The usefulness of models.. 2.2 What models should model.. 2.3 The possibility of ecological theory.. 2.4 Theory-driven ecological research.. 3 Some Basic Concepts.. 3.1 Basic concepts of food-web studies.. 3.2 Physical quantities and dimensions.. Part II Elements of Food-Web Models.. 4 Energy and Biomass Budgets.. 4.1 Currencies of accounting.. 4.2 Rates and efficiencies.. 4.3 Energy budgets in food webs.. 5 Allometric Scaling Relationships Between Body Size and Physiological Rates.. 5.1 Scales and scaling.. 5.2 Allometric scaling.. 6 Population Dynamics.. 6.1 Basic considerations.. 6.1.1 Exponential population growth.. 6.1.2 Five complications.. 6.1.3 Environmental variability.. 6.2 Structured populations and density-dependence.. 6.2.1 The dilemma between species and stages.. 6.2.2 Explicitly stage-structured population dynamics.. 6.2.3 Communities of structured populations.. 6.3 The Quasi-Neutral Approximation.. 6.3.1 The emergence of food webs.. 6.3.2 Rana catesbeiana and its resources.. 6.3.3 Numerical test of the approximation.. 6.4 Reproductive value.. 6.4.1 The concept of reproductive value.. 6.4.2 The role of reproductive value in the QNA.. 6.4.3 Body mass as a proxy for reproductive value.. 7 From Trophic Interactions to Trophic Link Strengths.. 7.1 Functional and numerical responses.. 7.2 Three models for functional responses.. 7.2.1 Linear response.. 7.2.2 Type II response.. 7.2.3 Type II response with prey switching.. 7.2.4 Strengths and weaknesses of these models.. 7.3 Food webs as networks of trophic link strengths.. 7.3.1 The ontology of trophic link strengths.. 7.3.2 Variability of trophic link strengths.. 8 Tropic Niche Space and Trophic Traits.. 8.1 Topology and dimensionality of trophic niche space.. 8.1.1 Formal setting.. 8.1.2 Definition of trophic niche-space dimensionality

8.2 Examples and ecological interpretations.. 8.2.1 A minimal example.. 8.2.2 Is the definition of dimensionality reasonable?.. 8.2.3 Dependencies between vulnerability and foraging traits of a species.. 8.2.4 The range of phenotypes considered affects niche-space dimensionality.. 8.3 Determination of trophic niche-space dimensionality.. 8.3.1 Typical empirical data.. 8.3.2 Direct estimation of dimensionality.. 8.3.3 Iterative estimation of dimensionality.. 8.4 Identification of trophic traits.. 8.4.1 Formal setting.. 8.4.2 Dimensional reduction.. 8.5 The geometry of trophic niche space.. 8.5.1 Abstract trophic traits.. 8.5.2 Indeterminacy in abstract trophic traits.. 8.5.3 The D-dimensional niche space as a pseudo-Euclidean space.. 8.5.4 Linear transformations of abstract trophic traits.. 8.5.5 Non-linear transformations of abstract trophic traits.. 8.5.6 Standardization and interpretation of abstract trophic traits.. 8.5.7 A hypothesis and a convention.. 8.5.8 Getting oriented in trophic niche space.. 8.6 Conclusions.. 9 Community Turnover and Evolution.. 9.1 The spatial scale of interest.. 9.2 How communities evolve.. 9.3 The mutation-for-dispersion trick.. 9.4 Mutation-for-dispersion in a neutral food-web model.. 10 The Population-Dynamical Matching Model.. Part III Mechanisms and Processes.. 11 Basic Characterizations of Link-Strength Distributions.. 11.1 Modelling the distribution of logarithmic link strengths.. 11.1.1 General normally distributed trophic traits.. 11.1.2 Isotropically distributed trophic traits.. 11.2 High-dimensional trophic niche spaces.. 11.2.1 Understanding link stengths in high-dimensional trophic niche spaces.. 11.2.2 Log-normal probability distributions.. 11.2.3 The limit of log-normally distributed trophic link strength.. 11.2.4 Correlations between trophic link strengths.. 11.2.5 The distribution of the strengths of observable links.. 11.2.6 The probability of observing links (connectance

11.2.7 Estimation of link-strength spread and Pareto exponent.. 11.2.8 Empirical examples.. 12 Diet Partitioning.. 12.1 The diet partitioning function.. 12.1.1 Relation to the probability distribution of diet proportions.. 12.1.2 Another probabilistic interpretation of the DPF.. 12.1.3 The normalization property of the DPF.. 12.1.4 Empirical determination of the DPF.. 12.2 Modelling the DPF.. 12.2.1 Formal setting.. 12.2.2 Diet ratios.. 12.2.3 The DPF for high-dimensional trophic niche spaces.. 12.2.4 Gini-Simpson dietary diversity.. 12.2.5 Dependence of the DPF on niche-space dimensionality.. 12.3 Comparison with data.. 12.4 Conclusions.. 13 Multivariate Link-Strength Distributions and Phylogenetic Patterns.. 13.1 Modelling phylogenetic structure in trophic traits.. 13.1.1 Phylogenetic correlations among logarithmic link strengths.. 13.1.2 Phylogenetic correlations among link strengths.. 13.1.3 Phylogenetic patterns in binary food webs.. 13.2 The matching model.. 13.2.1 A simple model for phylogenetic structure in food webs.. 13.2.2 Definition of the matching model.. 13.2.3 Sampling steady-state matching model food webs.. 13.2.4 Alternatives to the matching model.. 13.3 Characteristics of phylogenetically structured food webs.. 13.3.1 Graphical representation of food-web topologies.. 13.3.2 Standard parameter values.. 13.3.3 Intervality.. 13.3.4 Intervality and trophic niche-space dimensionality.. 13.3.5 Degree distributions.. 13.3.6 Other phylogenetic patterns.. 13.3.7 Is phylogeny just a nuisance?.. 14 A Framework Theory for Community Assembly.. 14.1 Ecological communities as dynamical systems.. 14.2 Existence, positivity, stability, and permanence.. 14.3 Generic bifurcations in community dynamics and their ecological phenomenology.. 14.3.1 General concepts.. 14.3.2 Saddle-node bifurcations.. 14.3.3 Hopf bifurcations.. 14.3.4 Transcritical bifurcations.. 14.3.5 Bifurcations of complicated attractors

14.4 Comparison with observations.. 14.4.1 Extirpations and invasions proceed slowly.. 14.4.2 The logistic equation works quite well.. 14.4.3 IUCN Red-List criteria highlight specific extinction scenarios.. 14.4.4 Conclusion.. 14.5 Invasion fitness and harvesting resistance.. 14.5.1 Invasion fitness.. 14.5.2 Harvesting resistance: definition.. 14.5.3 Harvesting resistance: interpretation.. 14.5.4 Harvesting resistance: computation.. 14.5.5 Interpretation of h → 0.. 14.6 Community assembly and stochastic species packing.. 14.6.1 Community saturation and species packing.. 14.6.2 Invasion probability.. 14.6.3 The steady-state distribution of harvesting resistance.. 14.6.4 The scenario of stochastic species packing.. 14.6.5 A numerical example.. 14.6.6 Biodiversity and ecosystem functioning.. 15 Competition in Food Webs.. 15.1 Basic concepts.. 15.1.1 Modes of competition.. 15.1.2 Interactions in communities.. 15.2 Competition in two-level food webs.. 15.2.1 The Lotka-Volterra two-level food-web model.. 15.2.2 Computation of the equilibrium point.. 15.2.3 Direct competition among producers.. 15.2.4 Resource-mediated competition in two-level food webs.. 15.2.5 Consumer-mediated competition in two-level food webs.. 15.3 Competition in arbitrary food webs.. 15.3.1 The general Lotka-Volterra food-web model.. 15.3.2 The competition matrix for general food webs.. 15.3.3 The L-R-P formalism.. 15.3.4 Ecological interpretations of the matrices L, R, and P.. 15.3.5 Formal computation of the equilibrium point.. 15.3.6 Consumer-mediated competition in general food webs.. 15.3.7 Consumer-mediated competitive exclusion.. 15.3.8 Conclusions.. 16 Mean-Field Theory of Resource-Mediated Competition.. 16.1 Transition to scaled variables.. 16.1.1 The competitive overlap matrix.. 16.1.2 Free abundances.. 16.2 The extended mean-field theory of competitive exclusion.. 16.2.1 Assumptions.. 16.2.2 Separation of means and residuals

16.2.3 Mean-field theory for the mean scaled abundance.. 16.2.4 Mean-field theory for the variance of scaled abundance.. 16.2.5 The coefficient of variation of scaled abundance.. 16.2.6 Related theories.. 17 Resource-Mediated Competition and Assembly.. 17.1 Preparation.. 17.1.1 Scaled vs. unscaled variables and parameters.. 17.1.2 Mean-field vs framework theory.. 17.2 Stochastic species packing under asymmetric competition.. 17.2.1 Species richness and distribution of invasion fitness (Part I.. 17.2.2 Community response to invasion.. 17.2.3 Sensitivity of residents to invaders.. 17.2.4 Species richness and distribution of invasion fitness (Part II.. 17.2.5 Random walks of abundances driven by invasions.. 17.2.6 Further discussion of the scenario.. 17.3 Stochastic species packing with competition symmetry.. 17.3.1 Community assembly with perfectly symmetric competition.. 17.3.2 Community assembly under nearly perfectly symmetric competition.. 17.3.3 Outline of mechanism limiting competition avoidance.. 17.3.4 The distribution of invasion fitness.. 17.3.5 Competition between residents and invaders.. 17.3.6 Balance of scaled biomass during assembly.. 17.3.7 Competition avoidance.. 17.3.8 Numerical test of the theory.. 18 Random-Matrix Competition Theory.. 18.1 Asymmetric competition.. 18.1.1 Girko's Law.. 18.1.2 Application to competitive overlap matrices.. 18.1.3 Implications for sensitivity to invaders.. 18.1.4 Relation to mean-field theory.. 18.2 Stability vs feasibility limits to species richness.. 18.2.1 The result of May: páginas 972.. 18.2.2 Comparison of stability and feasibility criteria.. 18.3 Partially and fully symmetric competition.. 18.4 Sparse overlap matrices.. 18.4.1 Sparse competition.. 18.4.2 Eigenvalue distributions for sparse matrices.. 18.5 Resource overlap matrices.. 18.5.1 Diffuse resource competition.. 18.5.2 Sparse resource competition: the basic problem.. 18.5.3 The effect of trophic niche-space geometry

18.5.4 Competition among highly specialized consumers.. 18.5.5 Resource competition for varying ratios of producer to consumer richness.. 18.5.6 Competition for competing resources.. 18.6 Comparison with data.. 18.6.1 Gall-inducing insects on plants.. 18.6.2 Freshwater ecosystems.. 18.6.3 The North Sea.. 18.6.4 Conclusions.. 19 Species Richness, Size and Trophic Level.. 19.1 Predator-prey mass ratios.. 19.2 Modelling the joint distribution of size, trophic level, and species richness.. 19.2.1 Initial considerations.. 19.2.2 Model definition.. 19.2.3 Model simulation and comparison with data.. 20 Consumer-Mediated Competition and Assembly.. 20.1 A two-level food-web assembly model.. 20.2 Analytic characterization of the model steady state.. 20.2.1 Mechanism controlling producer richness.. 20.2.2 Other characteristics of the model steady state.. 20.3 Dependence of invader impacts on dietary diversity.. 20.3.1 Formal setting.. 20.3.2 Invadibility condition.. 20.3.3 Extirpation of resources during invasion.. 20.3.4 Extirpation of resources through consumer-mediated competition.. 20.3.5 Synthesis.. 20.4 Evolution of base attack rates.. 20.4.1 Motivation.. 20.4.2 Model definition.. 20.4.3 Numerical demonstration of attack rate evolution.. 20.4.4 Attack-rate evolution and prudent predation.. 21 Food Chains and Size Spectra.. 21.1 Concepts.. 21.1.1 Community size spectra.. 21.1.2 Species size spectra.. 21.2 Power-law food chains.. 21.2.1 Infinitely long power-law food chains.. 21.2.2 Top-down and bottom-up control.. 21.2.3 Power law-food chains of finite lengths and their stability to pulse perturbations.. 21.2.4 Food chains as approximations for size spectra.. 21.2.5 Adaptation of attack rates.. 21.3 Food chains with non-linear functional responses.. 21.3.1 Loss of stability with density-independent consumption.. 21.3.2 Linearization of a generalized food chain model.. 21.3.3 Linear responses to press perturbations

21.3.4 Linear stability to pulse perturbations.. 21.4 What are the mechanisms controlling the scaling laws?.. 21.4.1 Arguments for biological constraints on transfer efficiency.. 21.4.2 Arguments for stability constraints on transfer efficiency.. 21.4.3 Arguments for ecological constraints on biomass imbalance.. 21.4.4 Arguments for mechanical constraints on PPMR.. 21.4.5 Arguments for dynamical constraints on PPMR.. 21.4.6 Conclusions.. 21.5 Scavengers and detrivores.. 21.5.1 The general argument.. 21.5.2 The microbial loop and other detrital channels.. 22 Structure and Dynamics of PDMM Model Communities.. 22.1 PDMM model definition.. 22.1.1 Model states.. 22.1.2 Species sampling and community assembly.. 22.1.3 Population dynamics.. 22.2 PDMM simulations.. 22.2.1 Trophic niche space and phylogenetic correlations.. 22.2.2 Steady state and invasion fitness.. 22.2.3 Diet partitioning.. 22.2.4 Resource-mediated competition.. 22.2.5 Distribution of species over body sizes and trophic levels.. 22.2.6 The size spectrum and related distributions.. 22.3 The PDMM with evolving attack rates.. 22.3.1 Modelling and tracking evolving attack rates in the PDMM.. 22.3.2 Time series of species richness, aggressivity and dietary diversity.. 22.3.3 Mutual regulation of aggressivity and dietary diversity.. 22.4 Conclusions.. Part IV Implications.. 23 Scientific Implications.. 23.1 Main mechanisms identified by the theory.. 23.1.1 Two trades - one currency.. 23.1.2 Resource-mediated competition.. 23.1.3 Randomness and structure in food webs.. 23.1.4 Consumer-mediated competition and attack-rate evolution.. 23.2 Testable assumptions and predictions.. 23.2.1 Link-strength distributions and trophic niche-space geometry.. 23.2.2 Diet-partitioning statistics and sampling curves.. 23.2.3 Prey switching.. 23.2.4 Adapted attack rates.. 23.2.5 Community assembly and turnover.. 23.2.6 Patterns in link-strength matrices.. 23.3 Some unsolved problems

23.3.1 Large plants.. 23.3.2 Interactions between modes of competition.. 23.3.3 Absolute species richness: the role of viruses.. 23.3.4 The role of prey switching for community structure.. 23.3.5 The role of phylogenetic correlations for community dynamics.. 23.3.6 Fundamental constraints determining size-spectrum slopes.. 23.3.7 Community assembly with non-trivial attractors.. 23.3.8 Solution of the Riccati Equation for resource competition.. 23.3.9 Eigenvalues of competition matrices.. 23.3.10 Geometry and topology of trophic niche space.. 23.4 The future of community ecology.. 24 Conservation Implications.. 24.1 Assessing biodiversity.. 24.1.1 Quantifying biodiversity.. 24.1.2 Biodiversity supporting biodiversity.. 24.1.3 Assessing community turnover.. 24.2 Modelling ecological communities.. 24.2.1 Unpredictability of long-term community responses.. 24.2.2 Short-term predictions of community responses.. 24.2.3 Coarse-grained and stochastic community models.. 24.3 Managing biodiversity.. Appendix A.. A.1 Mathematical concepts, formulae, and jargon.. A.1.1 Sums.. A.1.2 Complex numbers.. A.1.3 Vectors and matrices.. A.1.4 Sets and functions.. A.1.5 Differential calculus.. A.1.6 Integrals.. A.1.7 Differential equations.. A.1.8 Random variables and expectation values.. Bibliography.. Index

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. eng