Applied Hierarchical Modeling in Ecology: Analysis of Distribution, Abundance and Species Richness in R and Bugs, Volume 1: Prelude and Static Models

About this book

Applied Hierarchical Modeling in Ecology: Distribution, Abundance, Species Richness offers a new synthesis of the state-of-the-art of hierarchical models for plant and animal distribution, abundance, and community characteristics such as species richness using data collected in metapopulation designs. These types of data are extremely widespread in ecology and its applications in such areas as biodiversity monitoring and fisheries and wildlife management.

This first volume explains static models/procedures in the context of hierarchical models that collectively represent a unified approach to ecological research, taking the reader from design, through data collection, and into analyses using a very powerful class of models. Applied Hierarchical Modeling in Ecology, Volume 1 serves as an indispensable manual for practicing field biologists, and as a graduate-level text for students in ecology, conservation biology, fisheries/wildlife management, and related fields.

Contents

    Dedication
    Foreword
    Preface
    Acknowledgments
    Part 1. Prelude
        Chapter 1. Distribution, Abundance, and Species Richness in Ecology
            1.1. Point Processes, Distribution, Abundance, and Species Richness
            1.2. Meta-population Designs
            1.3. State and Rate Parameters
            1.4. Measurement Error Models in Ecology
            1.5. Hierarchical Models for Distribution, Abundance, and Species Richness
            1.6. Summary and Outlook
            Exercises
        Chapter 2. What Are Hierarchical Models and How Do We Analyze Them?
            2.1. Introduction
            2.2. Random Variables, Probability Density Functions, Statistical Models, Probability, and Statistical Inference
            2.3. Hierarchical Models (HMs)
            2.4. Classical Inference Based on Likelihood
            2.5. Bayesian Inference
            2.6. Basic Markov Chain Monte Carlo (MCMC)
            2.7. Model Selection and Averaging
            2.8. Assessment of Model Fit
            2.9. Summary and Outlook
            Exercises
        Chapter 3. Linear Models, Generalized Linear Models (GLMs), and Random Effects Models: The Components of Hierarchical Models
            3.1. Introduction
            3.2. Linear Models
            3.3. Generalized Linear Models (GLMs)
            3.4. Random Effects (Mixed) Models
            3.5. Summary and Outlook
            Exercises
        Chapter 4. Introduction to Data Simulation
            4.1. What Do We Mean by Data Simulation, and Why Is It So Tremendously Useful?
            4.2. Generation of a Typical Point Count Data Set
            4.3. Packaging Everything in a Function
            4.4. Summary and Outlook
            Exercises
        Chapter 5. Fitting Models Using the Bayesian Modeling Software BUGS and JAGS
            5.1. Introduction
            5.2. Introduction to BUGS Software: WinBUGS, OpenBUGS, and JAGS
            5.3. Linear Model with Normal Response (Normal GLM): Multiple Linear Regression
            5.4. The R Package rjags
            5.5. Missing values (NAs) in a Bayesian Analysis
            5.6. Linear Model with Normal Response (Normal GLM): Analysis of Covariance (ANCOVA)
            5.7. Proportion of Variance Explained (R2)
            5.8. Fitting a Model with Nonstandard Likelihood Using the Zeros or the Ones Tricks
            5.9. Poisson GLM
            5.10. GoF Assessment: Posterior Predictive Checks and the Parametric Bootstrap
            5.11. Binomial GLM (Logistic Regression)
            5.12. Moment-Matching in a Binomial GLM to Accommodate Underdispersion
            5.13. Random-Effects Poisson GLM (Poisson GLMM)
            5.14. Random-Effects Binomial GLM (Binomial GLMM)
            5.15. General Strategy of Model Building with BUGS
            5.16. Summary and Outlook
            Exercises
    Part 2. Models for Static Systems
        Chapter 6. Modeling Abundance with Counts of Unmarked Individuals in Closed Populations: Binomial N-mixture Models
            6.1. Introduction to the Modeling of Abundance
            6.2. An Exercise in Hierarchical Modeling: Derivation of Binomial N-mixture Models from First Principles
            6.3. Simulation and Analysis of the Simplest Possible N-mixture Model
            6.4. A Slightly More Complex N-mixture Model with Covariates
            6.5. A Very General Data Simulation Function for N-mixture Models: simNmix
            6.6. Study Design, Bias, and Precision of the Binomial N-mixture Model Estimator
            6.7. Study of Some Assumption Violations Using Function simNmix
            6.8. Goodness-of-Fit (GoF)
            6.9. Abundance Mapping of Swiss Great Tits with unmarked
            6.10. The Issue of Space, or: What Is Your Effective Sample Area?
            6.11. Bayesian Modeling of Swiss Great Tits with BUGS
            6.12. Time-for-Space Substitution
            6.13. The Royle-Nichols Model and Other Nonstandard N-mixture Models
            6.14. Multiscale N-mixture Models
            6.15. Summary and Outlook
            Exercises
        Chapter 7. Modeling Abundance Using Multinomial N-Mixture Models
            7.1. Introduction
            7.2. Multinomial N-Mixture Models in Ecology
            7.3. Simulating Multinomial Observations in R
            7.4. Likelihood Inference for Multinomial N-Mixture Models
            7.5. Example 1: Bird Point Counts Based on Removal Sampling
            7.6. Bayesian Analysis in BUGS Using the Conditional Multinomial (Three-Part) Model
            7.7. Building Custom Multinomial Models in unmarked
            7.8. Spatially Stratified Capture-Recapture Models
            7.9. Example 3: Jays in the Swiss MHB
            7.10. Summary and Outlook
            Exercises
        Chapter 8. Modeling Abundance Using Hierarchical Distance Sampling
            8.1. Introduction
            8.2. Conventional Distance Sampling
            8.3. Bayesian Conventional Distance Sampling
            8.4. Hierarchical Distance Sampling (HDS)
            8.5. Bayesian HDS
            8.6. Summary
            Exercises
        Chapter 9. Advanced Hierarchical Distance Sampling
            9.1. Introduction
            9.2. Distance Sampling (DS) with Clusters, Groups, or Other Individual Covariates
            9.3. Time-Removal and DS Combined
            9.4. Mark-Recapture/Double-Observer DS
            9.5. Open HDS Models: Temporary Emigration
            9.6. Open HDS Models: Implicit Dynamics
            9.7. Open HDS Models: Modeling Population Dynamics
            9.8. Spatial Distance Sampling: Modeling Within-Unit Variation in Density
            9.9. Summary
            Exercises
        Chapter 10. Modeling Static Occurrence and Species Distributions Using Site-occupancy Models
            10.1. Introduction to the Modeling of Occurrence—Including Species Distributions
            10.2. Another Exercise in Hierarchical Modeling: Derivation of the Site-Occupancy Model
            10.3. Simulation and Analysis of the Simplest Possible Site-Occupancy Model
            10.4. A Slightly More Complex Site-Occupancy Model with Covariates
            10.5. A General Data Simulation Function for Static Occupancy Models: simOcc
            10.6. A Model with Lots of Covariates: Use of R Function model.matrix with BUGS
            10.7. Study Design, and Bias and Precision of Site-Occupancy Estimators
            10.8. Goodness-of-Fit
            10.9. Distribution Modeling and Mapping of Swiss Red Squirrels
            10.10. Multiscale Occupancy Models
            10.11. Space-for-Time Substitution
            10.12. Models for Data along Transects: Poisson, Exponential, Weibull, and Removal Observation Models
            10.13. Occupancy Modeling of a Community of Species
            10.14. Modeling Wiggly Covariate Relationships: Penalized Splines in Hierarchical Models
            10.15. Summary and Outlook
            Exercises
        Chapter 11. Hierarchical Models for Communities
            11.1. Introduction
            11.2. Simulation of a Metacommunity
            11.3. Metacommunity Data from the Swiss Breeding Bird Survey MHB
            11.4. Overview of Some Models for Metacommunities
            11.5. Community Models That Ignore Species Identity
            11.6. Community Models that Fully Retain Species Identity
            11.7. The Dorazio/Royle (DR) Community Occupancy Model with Data Augmentation (DA)
            11.8. Inferences Based on the Estimated Z Matrix: Similarity among Sites and Species
            11.9. Species Richness Maps and Species Accumulation Curves
            11.10. Community N-mixture (or Dorazio/Royle/Yamaura - DRY) Models
            11.11. Summary and Outlook
            Exercises
    Summary and Conclusion
    References
    Author Index
    Subject Index

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Biography

Dr Marc Kéry is a Population Ecologist with the Swiss Ornithological Institute and a courtesy professor ("Privatdozent") at the University of Zürich/Switzerland, from where he received his PhD in Ecology in 2000. He is an expert in the estimation and modeling of abundance, distribution and species richness in "metapopulation designs" (i.e., collections of replicate sites). For most of his work, he uses the Bayesian model fitting software BUGS and JAGS, about which he has published two books with Academic Press (2010 and 2012). He has authored/coauthored 70 peer-reviewed articles and four book chapters. Since 2007, and for a total of 103 days, he has taught 23 statistical modeling workshops about the methods in the proposed book at research institutes and universities all over the world.

Dr J. Royle is currently a Research Statistician at the U.S. Geological Survey's Patuxent Wildlife Research Center. His research is focused on the application of probability and statistics to ecological problems, especially those related to animal sampling and demographic modeling. Much of his research over the last 10 years has been devoted to the development of methods illustrated in our new book. He has authored or coauthored more than 100 journal articles, and co-authored the books Spatial Capture Recapture, Hierarchical Modeling and Inference in Ecology and Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence, all published by Academic Press.