Hierarchical modeling and inference in ecology : the analysis of data from populations, metapopulations and communities

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants) * Development of classical, likelihood-based procedures for inference, as well as Bayesian methods of analysis * Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS * Computing support in technical appendices in an online companion web site Cover ......Page 1 Copyright ......Page 2 Preface ......Page 3 Acknowledgements ......Page 7 1. Conceptual and Philosophical Considerations in Ecology and Statistics......Page 9 Science by Hierarchical Modeling......Page 10 Example: Modeling Replicated Counts......Page 11 Ecological Scales of Organization......Page 15 Sampling Biological Systems......Page 17 Detectability or Detection Bias......Page 18 Spatial Sampling and Spatial Variation......Page 19 The Observation-driven View......Page 21 The Process-Driven View......Page 23 The Philosophical Middle Ground: The Hierarchical View......Page 24 Probability as the Basis for Inference......Page 26 Dueling Caricatures of Bayesianism......Page 27 Our Bayesian Parody......Page 28 Parametric Inference......Page 30 Parametric Inference and The Nature of Assumptions......Page 31 The Hierarchical Rube Goldberg Device......Page 32 Summary......Page 33 Preliminaries......Page 35 Statistical Concepts......Page 36 Common Distributions and Notation......Page 38 Probability Rules for Random Variables......Page 40 The Role of Approximating Models......Page 42 Classical (Frequentist) Inference......Page 44 Maximum Likelihood Estimation......Page 45 Properties of MLEs......Page 51 Bayesian Inference......Page 58 Bayes' Theorem and the Problem of `Inverse Probability'......Page 60 Pros and Cons of Bayesian Inference......Page 62 Asymptotic Properties of the Posterior Distribution......Page 63 Modern Methods of Bayesian Computation......Page 65 Model Selection......Page 70 Inverting Tests to Estimate Confidence Intervals......Page 76 A Bayesian Approach to Model Selection......Page 78 Assessment and Comparison of Models......Page 81 Modeling Observations and Processes......Page 84 Versatility of Hierarchical Models......Page 85 Hierarchical Models in Ecology......Page 89 3. Modeling Occupancy and Occurrence Probability......Page 91 Logistic Regression Models of Occurrence......Page 93 Modeling Species Distribution: Swiss Breeding Birds......Page 95 Observation Covariates......Page 102 Bayesian Logistic Regression......Page 103 Analysis by Markov Chain Monte Carlo......Page 104 Logistic Regression in WinBUGS......Page 105 Models of Occupancy Allowing for Imperfect Observation......Page 106 Sampling Error for Binary Observations......Page 107 Importance of Detection Bias......Page 109 The Repeated Measures Design......Page 110 The Closure Assumption and Temporal Scale......Page 112 Power of the Survey Method......Page 113 Bayesian Analysis of Hierarchical Representation......Page 114 Example: Analysis of the Willow Tit Data......Page 115 Bayesian Model Selection: Calculation of Posterior Model Weights......Page 116 Occupancy Model as a Zero-Inflated Binomial......Page 119 Encounter history Formulation......Page 120 Likelihood Analysis......Page 122 Finite-Sample Inference......Page 124 Likelihood Estimation......Page 128 False-Positive Errors......Page 130 Multi-State Occupancy Models......Page 131 Summary......Page 132 4. Occupancy and Abundance......Page 134 Royle--Nichols Model Formulation......Page 136 Derived Parameters: Occupancy and Flavors of p......Page 138 Induced Heterogeneity......Page 139 Analysis by Integrated Likelihood......Page 140 Bird Point Counts......Page 141 Application to Carnivore Survey Data......Page 143 Prediction of Local Abundance......Page 145 What is N?......Page 146 Modeling Covariate Effects......Page 147 Non-binomial Detection......Page 149 Alternative Abundance Models......Page 151 Example: Analysis of the Catbird Data......Page 153 Functional Independence between P and Abundance......Page 154 Abundance and Occupancy under Independence of p and N......Page 155 Choice of Link Functions......Page 157 Assessing Functional Independence......Page 158 Illustration......Page 159 Estimating Occupancy in the Absence of Replicate Samples......Page 161 Summary......Page 162 5. Inference in Closed Populations......Page 165 Example......Page 167 Shrinking and growing multinomials by conditioning and unconditioning......Page 169 Estimating the Size of a Closed Population......Page 170 The Classic Design based on Replication......Page 171 Inference based on the Conditional Likelihood......Page 173 Analysis of the Microtus Data......Page 175 Tiger camera trapping data......Page 176 An Encounter History Formulation......Page 178 Model variations......Page 180 Pooling Robustness of the Multinomial......Page 181 Multiple Observer Sampling......Page 182 Example: Aerial Waterfowl Survey......Page 183 Removal Sampling......Page 185 Data Augmentation......Page 186 Heuristic development......Page 187 Bayesian Motivation by Analysis of M0......Page 188 Implementation......Page 189 Analysis of the Microtus Data......Page 190 Summary......Page 193 6. Models with Individual Effects......Page 197 Individual Heterogeneity Models......Page 198 Bias Induced by Heterogeneity......Page 199 Model construction......Page 200 Flavors of Mh......Page 201 Example: Flat-tailed Horned Lizard Data......Page 205 Inference About Species Richness......Page 206 Spatial Subsamples as Replicates......Page 209 Bayesian Analysis of Heterogeneity Models using Data Augmentation......Page 210 Example: Estimating Species Richness......Page 211 Of Bugs in BUGS......Page 212 Individual Covariate Models......Page 215 Background......Page 217 Model Formulation......Page 218 Bayesian Estimation by Data Augmentation......Page 219 Example: Microtus Trapping Data......Page 220 Example: Group Size in Waterfowl Surveys......Page 224 Summary......Page 227 7. Spatial Capture--Recapture Models......Page 231 A Hierarchical Model for Temporary Emigration......Page 233 Distance Sampling as an Individual Covariate Model......Page 235 Technical Formulation......Page 236 Classical Derivation......Page 238 Distance Sampling Remarks......Page 239 Bayesian Analysis of Distance Sampling by Data Augmentation......Page 240 Example: Analysis of Burnham's Impala Data......Page 241 Joint Distribution of the Augmented Data......Page 242 Distance Sampling with Measurement Error......Page 244 Estimating Density from Location-of-Capture Information......Page 247 Model Formulation......Page 249 Bayesian Analysis by Data Augmentation......Page 252 Analysis of the Lizard Data......Page 253 Effective Sample Area......Page 256 Remarks......Page 258 Estimating Density from Trapping Arrays......Page 259 Model Formulation......Page 261 Example......Page 265 Analysis of the Model......Page 266 Analysis of the Tiger Camera Trapping Data......Page 267 Summary......Page 270 8. Metapopulation Models of Abundance......Page 272 A Hierarchical View of the Population......Page 274 Sampling Protocols and Observation Models......Page 275 Modeling Abundance and Detection......Page 277 Binomial Mixture Models......Page 279 Multinomial Mixture Models......Page 287 Summary......Page 299 9. Occupancy Dynamics......Page 301 Background......Page 302 Occupancy State Model......Page 303 Metapopulation Summaries......Page 305 Bayesian Analysis......Page 306 A Generalized Colonization Model: Modeling Invasive Spread......Page 307 Imperfect Observation of the State Variable......Page 309 Hierarchical Formulation......Page 310 Likelihood Analysis of the Model......Page 312 Auto-Logistic Representation......Page 315 Covariate Models......Page 317 Spatial Auto-logistic Models......Page 318 The Auto-logistic Model......Page 319 Imperfect Observation of the State Variable......Page 322 Spatio-Temporal Dynamics......Page 325 Model Formulation......Page 326 Summary......Page 327 10. Modeling Population Dynamics......Page 329 Data Augmentation......Page 330 Implementation......Page 331 State-Space Parameterization of the Jolly--Seber Model......Page 332 Process Model Formulations......Page 333 Jolly--Seber Model as a Restricted Occupancy Model......Page 334 The Implied Recruitment Model......Page 336 Bayesian Analysis of the Models......Page 337 Abundance and Other Derived Parameters......Page 338 Prior Distributions for Recruitment......Page 340 Schwarz and Arnason's Formulation......Page 341 Implementation......Page 343 Models with Individual Effects......Page 344 Summary......Page 346 11. Modeling Survival......Page 350 Classical Formulation of the CJS Model......Page 351 Modeling Nest Survival......Page 353 Analysis of the Redstart Data......Page 356 Hierarchical Formulation......Page 357 Hierarchical Formulation of the CJS Model......Page 360 Bayesian Analysis......Page 361 Representation as a Constrained Jolly--Seber Model......Page 362 Modeling Avian Survival from Mist-Net Data......Page 363 CJS Model with Pre-determined Residents......Page 364 Modeling Spatial Variation in Survival......Page 367 Analysis of the MAPS Data......Page 371 Model Formulation......Page 372 Analysis of the European Dipper Data......Page 375 Model Selection......Page 376 Prior Sensitivity......Page 378 Summary......Page 379 12. Models of Community Composition and Dynamics......Page 381 Models with Known Species Richness......Page 382 Models with Unknown Species Richness......Page 385 Modeling Augmented Data......Page 388 Example: North American Breeding Bird Survey......Page 389 Covariates of Occurrence and Detection......Page 391 Modeling Avian Species in Switzerland......Page 392 Estimates of Species Richness and Geographic Distribution......Page 393 Dynamic Models......Page 394 Temporal Covariate Models......Page 398 Temporal Dependence Models......Page 399 Hybrid Models......Page 400 Summary......Page 401 The Hierarchical Modeling Philosophy......Page 403 Unifying Themes......Page 404 Bayesian Hierarchical Models......Page 405 Occupancy Models......Page 406 Metacommunity Models......Page 408 Individual Effects and Spatial Capture--Recapture......Page 409 Dynamic Models......Page 410 Occupancy/Abundance......Page 411 Dynamic Models and Related Extensions......Page 413 Compound Distributions......Page 414 Hierarchical Models for Complex Sampling Designs......Page 415 No Such Thing as a Free Lunch......Page 416 Bibliography......Page 418 Index......Page 439 A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including \* occurrence or occupancy models for estimating species distribution \* abundance models based on many sampling protocols, including distance sampling \* capture-recapture models with individual effects \* spatial capture-recapture models based on camera trapping and related methods \* population and metapopulation dynamic models \* models of biodiversity, community structure and dynamics \* Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants) \* Development of classical, likelihood-based procedures for inference, as well as Bayesian methods of analysis \* Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS \* Computing support in technical appendices in an online companion web site "This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical modeling in which a strict focus on probability models and parametric inference is adopted. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community and metacommunity systems. Many novel developments in the areas of distribution modeling, capture-recapture and community models are presented, some appearing for the first time in this book. The book provides the first synthetic treatment of many recent methodological advances in these areas, and also provides unification and synthesis of disparate and diffuse methods and procedures."--Résumé de l'éditeur "This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical modeling in which a strict focus on probability models and parametric inference is adopted. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community and metacommunity systems. Many novel developments in the areas of distribution modeling, capture-recapture and community models are presented, some appearing for the first time in this book. The book provides the first synthetic treatment of many recent methodological advances in these areas, and also provides unification and synthesis of disparate and diffuse methods and procedures."--Jacket.