Bayesian Population Analysis using WinBUGS. A hierarchical perspective

Bayesian Population Analysis Using WinBUGS: A Hierarchical Perspective
Copyright
Dedication
Foreword
Preface
Acknowledgments
1 Introduction
1.1 Ecology: The Study of Distribution and Abundance and of the Mechanisms Driving Their Change
1.2 Genesis of Ecological Observations
1.3 The Binomial Distribution as a Canonical Description of the Observation Process
1.4 Structure and Overview of the Contents of this Book
1.5 Benefits of Analyzing Simulated Data Sets: An Example of Bias and Precision
1.6 Summary and Outlook
1.7 Exercises
2 Brief Introduction to Bayesian Statistical Modeling
2.1 Introduction
2.2 Role of Models in Science
2.3 Statistical Models
2.4 Frequentist and Bayesian Analysis of Statistical Models
2.5 Bayesian Computation
2.6 WinBUGS
2.7 Advantages and Disadvantages of Bayesian Analyses by Posterior Sampling
2.8 Hierarchical Models
2.9 Summary and Outlook
3 Introduction to the Generalized Linear Model: The Simplest Model for Count Data
3.1 Introduction
3.2 Statistical Models: Response = Signal + Noise
3.2.1 The Noise Component
3.2.2 The Signal Component
3.2.3 Bringing the Noise and the Signal Components Together: The Link Function
3.3 Poisson GLM in R and WinBUGS for Modeling Time Series of Counts
3.3.1 Generation and Analysis of Simulated Data
3.3.2 Analysis of Real Data Set
3.4 Poisson GLM for Modeling Fecundity
3.5 Binomial GLM for Modeling Bounded Counts or Proportions
3.5.1 Generation and Analysis of Simulated Data
3.5.2 Analysis of Real Data Set
3.6 Summary and Outlook
3.7 Exercises
4 Introduction to Random Effects: Conventional Poisson GLMM for Count Data
4.1 Introduction
4.1.1 An Example
4.1.2 What Are Random Effects?
4.1.3 Why Do We Treat Batches of Effects as Random?
Scope of Inference
Assessment of Variability
Partitioning of Variability
Modeling of Correlations among Parameters
Accounting for All Random Processes in a Modeled System
Avoiding Pseudoreplication
Borrowing Strength
Random Effects as a Compromise between Pooling and No Pooling of Batched Effects
Combining Information
4.1.4 Why Should We Ever Treat a Factor as Fixed?
4.2 Accounting for Overdispersion by Random Effects-Modeling in R and WinBUGS
4.2.1 Generation and Analysis of Simulated Data
4.2.2 Analysis of Real Data
4.3 Mixed Models with Random Effects for Variability among Groups Site and Year Effects
4.3.1 Generation and Analysis of Simulated Data
4.3.2 Analysis of Real Data Set
Null or Intercept-Only Model
Fixed Site Effects
Fixed Site and Fixed Year Effects
Random Site Effects
Random Site and Random Year Effects
Random Site and Random Year Effects and First-Year Fixed Observer Effect
Random Site and Random Year Effects, First-Year Fixed Observer Effect, and Overall Linear Time Trend
The Full Model
4.4 Summary and Outlook
4.5 Exercises
5 State-Space Models for Population Counts
5.1 Introduction
5.2 A Simple Model
5.3 Systematic Bias in the Observation Process
5.4 Real Example: House Martin Population Counts in the Village of Magden
5.5 Summary and Outlook
5.6 Exercises
6 Estimation of the Size of a Closed Population from Capture?Recapture Data
6.1 Introduction
6.2 Generation and Analysis of Simulated Data with Data Augmentation
6.2.1 Introduction to Data Augmentation for the Simplest Case: Model M0
6.2.2 Time Effects: Model Mt
6.2.3 Behavioral or Memory Effects: Model Mb
6.2.4 Individual Random Effects: The Heterogeneity Model Mh
6.2.5 Combined Effects: Model Mth
6.3 Analysis of a Real Data Set: Model Mtbh for Species Richness Estimation
6.4 Capture?Recapture Models with Individual Covariates: Model Mt+X
6.4.1 Individual Covariate Model for Species Richness Estimation
6.4.2 Individual Covariate Model for Population Size Estimation
6.5 Summary and Outlook
6.6 Exercises
7 Estimation of Survival from Capture?Recapture Data Using the Cormack?Jolly?Seber Model
7.1 Introduction
7.2 The CJS Model as a State-Space Model
7.3 Models with Constant Parameters
7.3.1 Inclusion of Information about Latent State Variable
7.4 Models with Time-Variation
7.4.1 Fixed Time Effects
7.4.2 Random Time Effects
7.4.3 Temporal Covariates
7.5 Models with Individual Variation
7.5.1 Fixed Group Effects
7.5.2 Random Group Effects
7.5.3 Individual Random Effects
7.6 Models with Time and Group Effects
7.6.1 Fixed Group and Time Effects
7.6.2 Fixed Group and Random Time Effects
7.7 Models with Age Effects
7.8 Immediate Trap Response in Recapture Probability
7.9 Parameter Identifiability
7.10 Fitting the CJS to Data in the M-Array Format: the Multinomial Likelihood
7.10.1 Introduction
7.10.2 Time-Dependent Models
7.10.3 Age-Dependent Models
7.11 Analysis of a Real Data Set: Survival of Female Leisler’s Bats
7.12 Summary and Outlook
7.13 Exercises
8 Estimation of Survival Using Mark-Recovery Data
8.1 Introduction
8.2 The Mark-Recovery Model as a State-Space Model
8.2.1 Simulation of Mark-Recovery Data
8.2.2 Analysis of a Model with Constant Parameters
8.3 The Mark-Recovery Model Fitted with the Multinomial Likelihood
8.3.1 Constant Parameters
8.3.2 Age-Dependent Parameters
8.4 Real-Data Example: Age-Dependent Survival in Swiss Red Kites
8.5 Summary and Outlook
8.6 Exercises
9 Estimation of Survival and Movement from Capture?Recapture Data Using Multistate Models
9.1 Introduction
9.2 Estimation of Movement between Two Sites
9.2.1 Model Description
9.2.2 Generation of Simulated Data
9.2.3 Analysis of the Model
9.3 Accounting for Temporary Emigration
9.3.1 Model Description
9.3.2 Generation of Simulated Data
9.3.3 Analysis of the Model
9.4 Estimation of Age-Specific Probability of First Breeding
9.4.1 Model Description
9.4.2 Generation of Simulated Data
9.4.3 Analysis of the Model
9.5 Joint Analysis of Capture?Recapture and Mark-Recovery Data
9.5.1 Model Description
9.5.2 Generation of Simulated Data
9.5.3 Analysis of the Model
9.6 Estimation of Movement among Three Sites
9.6.1 Model Description
9.6.2 Generation of Simulated Data
9.6.3 Analysis of the Model
9.7 Real-Data Example: The Showy Lady’s Slipper
9.8 Summary and Outlook
9.9 Exercises
10 Estimation of Survival, Recruitment, and Population Size from Capture?Recapture Data Using the Jolly?Seber Model
10.1 Introduction
10.2 The JS Model as a State-Space Model
10.3 Fitting the JS Model with Data Augmentation
10.3.1 The JS Model as a Restricted Dynamic Occupancy Model
10.3.2 The JS Model as a Multistate Model
10.3.3 The Superpopulation Parameterization
10.4 Models with Constant Survival and Time-Dependent Entry
10.4.1 Analysis of the JS Model as a Restricted Occupancy Model
10.4.2 Analysis of the JS Model as a Multistate Model
10.4.3 Analysis of the JS Model Under the Superpopulation Parameterization
10.4.4 Comparison of Estimates
10.5 Models with Individual Capture Heterogeneity
10.6 Connections between Parameters, Further Quantities and Some Remarks on Identifiability
10.7 Analysis of a Real Data Set: Survival, Recruitment and Population Size of Leisler’s Bats
10.8 Summary and Outlook
10.9 Exercises
11 Estimation of Demographic Rates, Population Size, and Projection Matrices from Multiple Data Types Using Integrated ...
11.1 Introduction
11.2 Developing an Integrated Population Model IPM
11.2.1 First Step: Define the Link between Changes in Population Size and Demographic Rates
11.2.2 Second Step: Define the Likelihoods of Each Individual Data Set
Likelihood of the Population Count Data
Likelihood of the Capture–Recapture Data
Likelihood of Reproductive Success Data
11.2.3 Third Step: Formulate the Joint Likelihood
11.3 Example of a Simple IPM Counts, Capture?Recapture, Reproduction
11.3.1 Load Data
11.3.2 Analysis of the Model
11.4 Another Example of an IPM: Estimating Productivity without Explicit Productivity Data
11.5 IPMs for Population Viability Analysis
11.6 Real Data Example: Hoopoe Population Dynamics
11.7 Summary and Outlook
11.8 Exercises
12 Estimation of Abundance from Counts in Metapopulation Designs Using the Binomial Mixture Model
12.1 Introduction
12.2 Generation and Analysis of Simulated Data
12.2.1 The Simplest Case with Constant Parameters
12.2.2 Introducing Covariates
12.3 Analysis of Real Data: Open-Population Binomial Mixture Models
12.3.1 Simple Poisson Model
12.3.2 Zero-Inflated Poisson Binomial Mixture Model ZIP Binomial Mixture Model
12.3.3 Binomial Mixture Model with Overdispersion in Both Abundance and Detection
12.4 Summary and Outlook
12.5 Exercises
13 Estimation of Occupancy and Species Distributions from Detection/Nondetection Data in Metapopulation Designs Using ...
13.1 Introduction
13.2 What Happens When p < 1 and Constant and p is Not Accounted for in a Species Distribution Model?
13.3 Generation and Analysis of Simulated Data for Single-Season Occupancy
13.3.1 The Simplest Possible Site-Occupancy Model
13.3.2 Site-Occupancy Models with Covariates
13.4 Analysis of Real Data Set: Single-Season Occupancy Model
13.5 Dynamic Multiseason Site-Occupancy Models
13.5.1 Generation and Analysis of Simulated Data
13.5.2 Dynamic Occupancy Modeling in a Real Data Set
13.6 Multistate Occupancy Models
13.7 Summary and Outlook
13.8 Exercises
14 Concluding Remarks
14.1 The Power and Beauty of Hierarchical Models
14.1.1 Hierarchical Models Make the Fitting of Complex Statistical Models Easier
14.1.2 Hierarchical Models Foster a Synthetic Understanding of a Large Array of Models
14.1.3 Hierarchical Models Lead to Cleaner Thinking
14.1.4 Hierarchical Models Lead to a Step-Up Approach in Tackling a Problem
14.1.5 What Kind of Hierarchical Model? Primary Model Selection in WinBUGS
14.1.6 Secondary Model Selection: Hierarchical Models and Variable Selection
14.1.7 Hierarchical Models and MARK, unmarked, E-SURGE, and PRESENCE
14.1.8 Hierarchical Models and Study Design
14.2 The Importance of the Observation Process
14.3 Where Will We Go?
14.3.1 Combination of Information
14.3.2 Population and Community Models for Metapopulation Designs
14.3.3 Spatial Models
14.3.4 Relaxing the Closure Assumption
14.3.5 More Flexible Covariate Modeling
14.3.6 Accounting for Misclassification Error
14.4 The Importance of Population Analysis for Conservation and Management
Appendix 1 A List of WinBUGS Tricks
Appendix 2 Two Further Useful Multistate Capture–Recapture Models
2.1 Estimation of Age-Specific Survival Probabilities
2.1.1 Model Description
2.1.2 Generation of Simulated Data
2.1.3 Analysis of the Model
2.2 Accounting for Immediate Trap Response
2.2.1 Model Description
2.2.2 Generation of Simulated Data
2.2.3 Analysis of the Model
References
Index
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