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