Hierarchical Modeling and Inference in Ecology: The Analysis of Data from Populations, Metapopulations and Communities

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