Ecological Models and Data in R

Ecological Models and Data in Ris 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

Benjamin M. Bolker is a theoretical ecologist in the Department of Zoology at the University of Florida.

Acknowledgments	p. ix
Introduction and Background	p. 1
Introduction	p. 1
What This Book Is Not About	p. 3
Frameworks for Modeling	p. 5
Frameworks for Statistical Inference	p. 10
Frameworks for Computing	p. 17
Outline of the Modeling Process	p. 20
R Supplement	p. 22
Exploratory Data Analysis and Graphics	p. 29
Introduction	p. 29
Getting Data into R	p. 30
Data Types	p. 34
Exploratory Data Analysis and Graphics	p. 40
Conclusion	p. 59
R Supplement	p. 59
Deterministic Functions for Ecological Modeling	p. 72
Introduction	p. 72
Finding Out about Functions Numerically	p. 73
Finding Out about Functions Analytically	p. 76
Bestiary of Functions	p. 87
Conclusion	p. 100
R Supplement	p. 100
Probability and Stochastic Distributions for Ecological Modeling	p. 103
Introduction: Why Does Variability Matter?	p. 103
Basic Probability Theory	p. 104
Bayes' Rule	p. 107
Analyzing Probability Distributions	p. 115
Bestiary of Distributions	p. 120
Extending Simple Distributions: Compounding and Generalizing	p. 137
R Supplement	p. 141
Stochastic Simulation and Power Analysis	p. 147
Introduction	p. 147
Stochastic Simulation	p. 148
Power Analysis	p. 156
Likelihood and All That	p. 169
Introduction	p. 169
Parameter Estimation: Single Distributions	p. 169
Estimation for More Complex Functions	p. 182
Likelihood Surfaces, Profiles, and Confidence Intervals	p. 187
Confidence Intervals for Complex Models: Quadratic Approximation	p. 196
Comparing Models	p. 201
Conclusion	p. 220
Optimization and All That	p. 222
Introduction	p. 222
Fitting Methods	p. 223
Markov Chain Monte Carlo	p. 233
Fitting Challenges	p. 241
Estimating Confidence Limits of Functions of Parameters	p. 250
R Supplement	p. 258
Likelihood Examples	p. 263
Tadpole Predation	p. 263
Goby Survival	p. 276
Seed Removal	p. 283
Standard Statistics Revisited	p. 298
Introduction	p. 298
General Linear Models	p. 300
Nonlinearity: Nonlinear Least Squares	p. 306
Nonnormal Errors: Generalized Linear Models	p. 308
R Supplement	p. 312
Modeling Variance	p. 316
Introduction	p. 316
Changing Variance within Blocks	p. 318
Correlations: Time-Series and Spatial Data	p. 320
Multilevel Models: Special Cases	p. 324
General Multilevel Models	p. 327
Challenges	p. 333
Conclusion	p. 334
R Supplement	p. 335
Dynamic Models	p. 337
Introduction	p. 337
Simulating Dynamic Models	p. 338
Observation and Process Error	p. 342
Process and Observation Error	p. 344
SIMEX	p. 346
State-Space Models	p. 348
Conclusions	p. 357
R Supplement	p. 360
Afterword	p. 362
Algebra and Calculus Basics	p. 363
Exponentials and Logarithms	p. 363
Differential Calculus	p. 364
Partial Differentiation	p. 364
Integral Calculus	p. 365
Factorials and the Gamma Function	p. 365
Probability	p. 365
The Delta Method	p. 366
Linear Algebra Basics	p. 366
Bibliography	p. 369
Index of R Arguments, Functions, and Packages	p. 383
General Index	p. 389
Table of Contents provided by Ingram. All Rights Reserved.

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Ecological Models and Data in R

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