Note: Food Webs and Biodiversity: Foundations, Models, Data -- Contents -- 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.