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by Benjamin M. Bolker
Ecological Models and Data in R
Cover Page
Title Page
Copyright Page
Contents
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
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