Ecological Models and Data in R
Benjamin M. Bolker

http://press.princeton.edu/titles/8709.html

Ecological Models and Data in R is the first truly practical introduction to modern statistical methods for ecology. In step-by-step detail, the book teaches ecology graduate students and researchers everything they need to know in order to use maximum likelihood, information-theoretic, and Bayesian techniques to analyze their own data using the programming language R. Drawing on extensive experience teaching these techniques to graduate students in ecology, Benjamin Bolker shows how to choose among and construct statistical models for data, estimate their parameters and confidence limits, and interpret the results. The book also covers statistical frameworks, the philosophy of statistical modeling, and critical mathematical functions and probability distributions. It requires no programming background--only basic calculus and statistics.

Practical, beginner-friendly introduction to modern statistical techniques for ecology using the programming language R
Step-by-step instructions for fitting models to messy, real-world data
Balanced view of different statistical approaches
Wide coverage of techniques--from simple (distribution fitting) to complex (state-space modeling)
Techniques for data manipulation and graphical display
Companion Web site with data and R code for all examples


TABLE OF CONTENTS:


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

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