Ecological Models and Data in R

Acknowledgments ix Chapter 1: Introduction and Background 1 1.1 Introduction 1 1.2 What This Book Is Not About 3 1.3 Frameworks for Modeling 5 1.4 Frameworks for Statistical Inference 10 1.5 Frameworks for Computing 17 1.6 Outline of the Modeling Process 20 1.7 R Supplement 22 Chapter 2: Exploratory Data Analysis and Graphics 29 2.1 Introduction 29 2.2 Getting Data into R 30 2.3 Data Types 34 2.4 Exploratory Data Analysis and Graphics 40 2.5 Conclusion 59 2.6 R Supplement 59 Chapter 3: Deterministic Functions for Ecological Modeling 72 3.1 Introduction 72 3.2 Finding Out about Functions Numerically 73 3.3 Finding Out about Functions Analytically 76 3.4 Bestiary of Functions 87 3.5 Conclusion 100 3.6 R Supplement 100 Chapter 4: Probability and Stochastic Distributions for Ecological Modeling 103 4.1 Introduction: Why Does Variability Matter? 103 4.2 Basic Probability Theory 104 4.3 Bayes' Rule 107 4.4 Analyzing Probability Distributions 115 4.5 Bestiary of Distributions 120 4.6 Extending Simple Distributions: Compounding and Generalizing 137 4.7 R Supplement 141 Chapter 5: Stochastic Simulation and Power Analysis 147 5.1 Introduction 147 5.2 Stochastic Simulation 148 5.3 Power Analysis 156 Chapter 6: Likelihood and All That 169 6.1 Introduction 169 6.2 Parameter Estimation: Single Distributions 169 6.3 Estimation for More Complex Functions 182 6.4 Likelihood Surfaces, Profiles, and Confidence Intervals 187 6.5 Confidence Intervals for Complex Models: Quadratic Approximation 196 6.6 Comparing Models 201 6.7 Conclusion 220 Chapter 7: Optimization and All That 222 7.1 Introduction 222 7.2 Fitting Methods 223 7.3 Markov Chain Monte Carlo 233 7.4 Fitting Challenges 241 7.5 Estimating Confidence Limits of Functions of Parameters 250 7.6 R Supplement 258 Chapter 8: Likelihood Examples 263 8.1 Tadpole Predation 263 8.2 Goby Survival 276 8.3 Seed Removal 283 Chapter 9: Standard Statistics Revisited 298 9.1 Introduction 298 9.2 General Linear Models 300 9.3 Nonlinearity: Nonlinear Least Squares 306 9.4 Nonnormal Errors: Generalized Linear Models 308 9.5 R Supplement 312 Chapter 10: Modeling Variance 316 10.1 Introduction 316 10.2 Changing Variance within Blocks 318 10.3 Correlations: Time-Series and Spatial Data 320 10.4 Multilevel Models: Special Cases 324 10.5 General Multilevel Models 327 10.6 Challenges 333 10.7 Conclusion 334 10.8 R Supplement 335 Chapter 11: Dynamic Models 337 11.1 Introduction 337 11.2 Simulating Dynamic Models 338 11.3 Observation and Process Error 342 11.4 Process and Observation Error 344 11.5 SIMEX 346 11.6 State-Space Models 348 11.7 Conclusions 357 11.8 R Supplement 360 Chapter 12: Afterword 362 Appendix Algebra and Calculus Basics 363 A.1 Exponentials and Logarithms 363 A.2 Differential Calculus 364 A.3 Partial Differentiation 364 A.4 Integral Calculus 365 A.5 Factorials and the Gamma Function 365 A.6 Probability 365 A.7 The Delta Method 366 A.8 Linear Algebra Basics 366 Bibliography 369 Index of R Arguments, Functions, and Packages 383 General Index 389