List of Figures and Tables xi Acknowledgments xv Chapter 1: Complexity in Ecological Systems 1 The Newtonian Paradigm in Physics 2 Dynamics and Thermodynamics 6 Emergent Properties 10 Ecosystems as Complex Adaptive Systems 13 Chapter 2: Nonlinear Dynamics 17 The Balance of Nature?17 Population Cycles 19 Catastrophes and Breakpoints 27 Deterministic Chaos 31 Evidence of Bifurcations in Nature 34 Unpredictability and Forecasting 42 The Ecology of Universality 48 Evidence of Chaos in Nature 50 Criticisms of Chaos 58 Complex Dynamics:The Interplay between Noise and Nonlinearities 61 Chapter 3: Spatial Self-Organization:From Pattern to Process 65 Space:The Missing Ingredient 65 Turing Instabilities 68 Coupled Map Lattice Models 84 Looking for Self-Organizing Spatial Patterns in Nature 95 Dispersal and Complex Dynamics 98 Spatial Synchrony in Population Cycles 108 When Is Space Relevant?A Trade-Off between Simplicity and Realism 117 Coevolution and Diffusion in Phenotype Space 123 Chapter 4: Scaling and Fractals in Ecology 127 Scaling and Fractals 127 Fractal Time Series 137 Percolation 139 Nonequilibrium Phase Transitions 144 The Branching Process 146 The Contact Process:Complexity Made Simple 149 Random Walks and Levy Flights in Population Dynamics 151 Percolation and Scaling in Random Graphs 156 Ecological Multifractals 162 Self-Organized Critical Phenomena 165 Complexity from Simplicity 168 Chapter 5: Habitat Loss and Extinction Thresholds 171 Habitat Loss and Fragmentation 171 Extinction Thresholds in Metapopulation Models 173 Extinction Thresholds in Metacommunity Models 178 Food Web Structure and Habitat Loss 186 Percolation in Spatially Explicit Landscapes 191 Extinction Thresholds in Spatially Explicit Models 195 Analytical Models of Correlated Landscapes 199 More Realistic Models of Extinction Thresholds 206 Chapter 6: Complex Ecosystems:From Species to Networks 215 Stability and Complexity 215 N-Species Lotka-Volterra Models 218 Topological and Dynamic Constraints 223 Indirect Effects 226 Keystone Species and Evolutionary Dynamics 231 Complexity and Fragility in Food Webs 237 Community Assembly:The Importance of History 251 Scaling in Ecosystems:A Stochastic Quasi-Neutral Model 254 Chapter 7: Complexity in Macroevolution 263 Extinction and Diversification 263 Internal and External Factors 264 Scaling in the Fossil Recor 270 Competition and the Fossil Recor 276 Red Queen Dynamics 279 Evolution on Fitness Landscapes 282 Extinctions and Coherent Noise 292 NetworkModels of Macroevolution 295 Ecology as It Would Be: Artificial Life 304 Recovery after Mass Extinction 308 Implications for Current Ecologies 313 Appendix 1.Lyapunov Exponents for ID Maps 317 Appendix 2.Renormalization Group Analysis 319 Appendix 3.Stochastic Multispecies Model 321 References 325 Index 359.