Acknowledgments

1 Introduction and Background

1.1  Introduction

1.2  What This Book Is Not About

1.3  Frameworks for Modeling

1.4  Frameworks for Statistical Inference

1.5  Frameworks for Computing

1.6  Outline of the Modeling Process

1.7  R Supplement

2 Exploratory Data Analysis and Graphics

2.1  Introduction

2.2  Getting Data into R

2.3  Data Types

2.4  Exploratory Data Analysis and Graphics

2.5  Conclusion

2.6  R Supplement

3 Deterministic Functions for Ecological Modeling

3.1  Introduction

3.2  Finding Out about Functions Numerically

3.3  Finding Out about Functions Analytically

3.4  Bestiary of Functions

3.5  Conclusion

3.6  R Supplement

4 Probability and Stochastic Distributions for Ecological Modeling

4.1  Introduction: Why Does Variability Matter?

4.2  Basic Probability Theory

4.3  Bayes' Rule

4.4  Analyzing Probability Distributions

4.5  Bestiary of Distributions

4.6  Extending Simple Distributions: Compounding and Generalizing

4.7  R Supplement

5 Stochastic Simulation and Power Analysis

5.1  Introduction

5.2  Stochastic Simulation

5.3  Power Analysis

6 Likelihood and All That

6.1  Introduction

6.2  Parameter Estimation: Single Distributions

6.3  Estimation for More Complex Functions

6.4  Likelihood Surfaces, Profiles, and Confidence Intervals

6.5  Confidence Intervals for Complex Models: Quadratic Approximation

6.6  Comparing Models

6.7  Conclusion

7 Optimization and All That

7.1  Introduction

7.2  Fitting Methods

7.3  Markov Chain Monte Carlo

7.4  Fitting Challenges

7.5  Estimating Confidence Limits of Functions of Parameters

7.6  R Supplement

8 Likelihood Examples

8.1  Tadpole Predation

8.2  Goby Survival

8.3  Seed Removal

9 Standard Statistics Revisited

9.1  Introduction

9.2  General Linear Models

9.3  Nonlinearity: Nonlinear Least Squares

9.4  Nonnormal Errors: Generalized Linear Models

9.5  R Supplement

10 Modeling Variance

10.1  Introduction

10.2  Changing Variance within Blocks

10.3  Correlations: Time-Series and Spatial Data

10.4  Multilevel Models: Special Cases

10.5  General Multilevel Models

10.6  Challenges

10.7  Conclusion

10.8  R Supplement

11 Dynamic Models

11.1  Introduction

11.2  Simulating Dynamic Models

11.3  Observation and Process Error

11.4  Process and Observation Error

11.5  SIMEX

11.6  State-Space Models

11.7  Conclusions

11.8  R Supplement

12 Afterword

Appendix Algebra and Calculus Basics

A.1  Exponentials and Logarithms

A.2  Differential Calculus

A.3  Partial Differentiation

A.4  Integral Calculus

A.5  Factorials and the Gamma Function

A.6  Probability

A.7  The Delta Method

A.8  Linear Algebra Basics

 

Bibliography

Index of  R Arguments, Functions, and Packages

General Index