By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive synthesis of the theory of population oscillations. It first reviews the conceptual tools that ecologists use to investigate population oscillations and then provides an in-depth discussion of several case studies.

Preface xi Mathematical Symbols xv Part I: THEORY 1. Introduction 3 1.1 At the Sources 3 1.1.1 The Puzzle of Population Cycles 3 1.1.2 Modeling Nature 4 1.1.3 The Balance of Nature 5 1.2 General Philosophy of the Approach 6 1.2.1 Defining the Phenomenon to Be Explained 8 1.2.2 Formalizing Hypotheses as Mathematical Models 11 1.2.3 Contrasting Models with Data 14 2. Population Dynamics from First Principles 17 2.1 Introduction 17 2.2 Exponential Growth 19 2.2.1 Derivation of the Exponential Model 20 2.2.2 Comparison with the Law of Inertia 22 2.2.3 "Laws": Postulates, Theorems, Empirical Generalizations? 25 2.3 Self-Limitation 26 2.3.1 Upper and Lower Density Bounds 26 2.3.2 Formalizing the Notion of Self-Limitation 27 2.3.3 The Logistic Model 29 2.4 Consumer-Resource Oscillations 30 2.4.1 Three More Postulates 31 2.4.2 The Lotka-Volterra Predation Model 33 2.5 Process Order 36 2.6 Synthesis 44 3. Single-Species Populations 47 3.1 Models without Population Structure 47 3.1.1 Continuous-Time Models 48 3.1.2 Discrete-Time Models 52 3.1.3 Delayed Differential Models 56 3.2 Exogenous Drivers 58 3.2.1 Stochastic Variation 60 3.2.2 Deterministic Exogenous Factors 61 3.3 Age-and Stage-Structured Models 64 3.3.1 Mathematical Frameworks 65 3.3.2 An Example: Flour Beetle Dynamics 68 3.4 Second-Order Models 70 3.4.1 Maternal Effect Hypothesis 70 3.4.2 Kin Favoritism Model 72 3.5 Synthesis 76 4. Trophic Interactions 78 4.1 Responses of Predators to Fluctuations in Prey Density 79 4.1.1 Functional Response 79 4.1.2 Aggregative Response 88 4.1.3 Numerical Response 90 4.2 Continuous-Time Models 93 4.2.1 Generalized Lotka-Volterra Models 94 4.2.2 Models Not Conforming to the LV Framework 99 4.2.3 Anatomy of a Predator-Prey Cycle 102 4.2.4 Generalist Predators 104 4.3 Discrete-Time Models: Parasitoids 108 4.3.1 Functional and Numerical Responses 109 4.3.2 Dynamical Models 111 4.4 Grazing Systems 112 4.4.1 Grazer's Functional Response 113 4.4.2 Dynamics of Vegetation Regrowth 117 4.4.3 Dynamics of Grazer-Vegetation Interactions 120 4.4.4 Plant Quality 123 4.5 Pathogens and Parasites 127 4.5.1 Transmission Rate 127 4.5.2 Microparasitism Models 128 4.5.3 Macroparasitism Models 131 4.6 Tritrophic Models 133 4.7 Synthesis 136 5. Connecting Mathematical Theory to Empirical Dynamics 137 5.1 Introduction 137 5.2 Qualitative Types of Deterministic Dynamics 139 5.2.1 Attractors 139 5.2.2 Sensitive Dependence on Initial Conditions 140 5.3 Population Dynamics in the Presence of Noise 146 5.3.1 Simple Population Dynamics 146 5.3.2 Stable Periodic Oscillations 147 5.3.3 Chaotic Oscillations 148 5.3.4 Quasi-Chaotic Oscillations 151 5.3.5 Regular Exogenous Forcing 153 5.3.6 Synthesis 153 5.4 Population Regulation 154 5.4.1 Definition of Density Dependence 155 5.4.2 Regulation: Evolution of the Concept 156 5.4.3 The Stationarity Definition of Regulation 156 5.4.4 Beyond Stationarity: Stochastic Boundedness 157 5.4.5 Synthesis 158 Part II: DATA 6. Empirical Approaches: An Overview 163 6.1 Introduction 163 6.2 Analysis of Population Fluctuations 164 6.2.1 The Structure of Density Dependence 164 6.2.2 Probes: Quantitative Measures of Time-Series Patterns 165 6.2.3 Phenomenological versus Mechanistic Approaches 167 6.3 Experimental Approaches 168 7. Phenomenological Time-Series Analysis 173 7.1 Basics 173 7.1.1 Variance Decomposition 173 7.1.2 Data Manipulations Prior to Analysis 175 7.1.3 Diagnostic Tools 178 7.2 Fitting Models to Data 183 7.2.1 General Framework 183 7.2.2 Choosing the Base Lag 186 7.2.3 Functional Forms 188 7.2.4 Model Selection by Cross-Validation 191 7.3 Synthesis 195 8. Fitting Mechanistic Models 197 8.1 Model Selection 198 8.2 Analysis of Ancillary Data 200 8.3 One-Step-Ahead Prediction 201 8.4 Trajectory Matching 203 8.5 Fitting by Nonlinear Forecasting 205 Part III: CASESTUDIES 9. Larch Budmoth 213 9.1 Introduction 213 9.2 Analysis of Time-Series Data 217 9.3 Hypotheses and Models 220 9.3.1 Plant Quality 220 9.3.2 Parasitism 229 9.3.3 Putting It All Together: A Parasitism-Plant Quality Model 235 9.4 Synthesis 237 10. Southern Pine Beetle 239 10.1 Introduction 239 10.2 Analysis of Time-Series Data 240 10.3 Hypotheses and Models 243 10.3.1 General Review of Hypotheses 243 10.3.2 Interaction with Hosts 247 10.3.3 Interaction with Parasitoids 253 10.3.4 The Predation Hypothesis 255 10.4 An Experimental Test of the Predation Hypothesis 259 10.4.1 Rationale 259 10.4.2 Results 264 10.5 Synthesis 271 11. Red Grouse 272 11.1 Numerical Patterns 273 11.2 Hypotheses and Models 281 11.2.1 Overview 281 11.2.2 Parasite-Grouse Hypothesis 282 11.2.3 Kin Favoritism Hypothesis 285 11.3 Experiments 289 11.3.1 Density Manipulation 289 11.3.2 Parasite Manipulation 291 11.4 Synthesis 294 12. Voles and Other Rodents 296 12.1 Introduction 296 12.2 Analysis of Time-Series Data 297 12.2.1 Methodological Issues 297 12.2.2 Numerical Patterns 301 12.3 Hypotheses and Models 310 12.3.1 Maternal Effect Hypothesis 311 12.3.2 Interaction with Food 316 12.3.3 Predation 317 12.4 Fitting the Predation Model by NLF 321 12.5 Lemmings 325 12.5.1 Numerical Patterns 326 12.5.2 Testing Alternative Trophic Hypotheses 328 12.5.3 Lemming-Vegetation Dynamics at Barrow 331 12.6 Synthesis 335 12.6.1 Summary of Findings 335 12.6.2 Towar a General Trophic Theory of Rodent Dynamics 339 13. Snowshoe Hare 344 13.1 Introduction 344 13.2 Numerical Patterns 345 13.3 Models 349 13.4 Experiments 356 13.5 Synthesis 362 14. Ungulates 365 14.1 Introduction 365 14.2 Interaction with Food 368 14.3 Interaction with Predators 371 14.4 Numerical Dynamics 376 14.5 Synthesis 381 15. General Conclusions 383 15.1 What Mechanisms Drive Oscillations in Nature? 383 15.2 Structure of Density Dependence 386 15.3 What about Chaos? 390 15.4 Population Ecology: A Mature Science 392 Glossary 397 References 405 Index 437

"This book gives an excellent introduction to our maturing understanding of how ideas about nonlinear dynamical systems can shed light on the complex behavior of real populations. Turchin first presents the theoretical concepts, next the data, and finally brings the two together in thoughtfully presented case studies. He splendidly achieves his aim of showing how ecological problems can be illuminated by mathematical models which are—in Einstein's words—'as simple as possible, but not more so.' "—Robert M. May, President, Royal Society

"This book is a true landmark in the study of population ecology. Never before has a lucid synthesis of the basic principles and models of population dynamics been so effectively merged with insightful analyses of some of the best data for populations of insects, birds and mammals. Peter Turchin writes with admirable clarity and authority, always retaining a focus on issues that really matter for population ecology."—Ilkka Hanski, University of Helsinki

"Turchin has done an outstanding job and produced a significant milestone in our understanding of population dynamics. I have long been seeking a book like this. It is readable and accessible while going into a good depth that so many undergraduate texts fail. All people working in the field will use it, and professors will use it in courses on population dynamics. The presentation is superb—the text gallops along."—Peter Hudson, University of Stirling

This book gives an excellent introduction to our maturing understanding of how ideas about nonlinear dynamical systems can shed light on the complex behavior of real populations. Turchin first presents the theoretical concepts, next the data, and finally brings the two together in thoughtfully presented case studies. He splendidly achieves his aim of showing how ecological problems can be illuminated by mathematical models which are--in Einstein's words--'as simple as possible, but not more so.' -- Robert M. May, President, Royal Society This book is a true landmark in the study of population ecology. Never before has a lucid synthesis of the basic principles and models of population dynamics been so effectively merged with insightful analyses of some of the best data for populations of insects, birds and mammals. Peter Turchin writes with admirable clarity and authority, always retaining a focus on issues that really matter for population ecology. -- Ilkka Hanski, University of Helsinki Turchin has done an outstanding job and produced a significant milestone in our understanding of population dynamics. I have long been seeking a book like this. It is readable and accessible while going into a good depth that so many undergraduate texts fail. All people working in the field will use it, and professors will use it in courses on population dynamics. The presentation is superb--the text gallops along. -- Peter Hudson, University of Stirling