Estimating Presence and Abundance of Closed Populations (Statistics for Biology and Health)

This comprehensive book covers a wide variety of methods for estimating the sizes and related parameters of closed populations. With the effect of climate change, and human territory invasion, we have seen huge species losses and a major biodiversity decline. Populations include plants, trees, various land and sea animals, and some human populations. With such a diversity of populations, an extensive variety of different methods are described with the collection of different types of data. For example, we have count data from plot sampling, which can also allow for incomplete detection. There is a large chapter on occupancy methods where a major interest is determining whether a particular species is present or not. Citizen and opportunistic survey data can also be incorporated. A related topic is species methods, where species richness and species' interactions are of interest. A variety of distance methods are discussed. One can use distances from points and lines, as wellas nearest neighbor distances. The applications are extensive, and include marine, acoustic, and aerial surveys, using multiple observers or detection devices. Line intercept measurements have a role to play such as, for example, estimating parameters relating to plant coverage. An increasingly important class of removal methods considers successive “removals" from a population, with physical removal or "removal" by capture-recapture of marked individuals. With the change-in-ratio method, removals are taken from two or more classes, e.g., males and females. Effort data used for removals can also be used. A very important method for estimating abundance is the use of capture-recapture data collected discretely or continuously and can be analysed using both frequency and Bayesian methods. Computational aspects of fitting Bayesian models are described. A related topic of growing interest is the use of spatial and camera methods. With the plethora of models there has been a corresponding development of various computational methods and packages, which are often mentioned throughout. Covariate data is being used more frequently, which can reduce the number of unknown parameters by using logistic and loglinear models. An important computational aspect is that of model selection methods. The book provides a useful list of over 1400 references. Preface Contents 1 Model Building 1.1 Introduction 1.2 Model and Design-Based Methods 1.3 Classical Frequentist or Bayesian Methods 1.4 Hierarchical Modeling 1.5 Mixture Models 1.6 Regression Models 1.6.1 Covariates 1.7 Simulation 1.8 Model Fitting and Selection 1.8.1 Frequency Models 1.8.2 Bayesian Models 1.8.3 Model Averaging 1.9 Computing 1.9.1 Model Diagnostics 1.10 General Study Design 1.11 Where to Now? 1.12 Summary 2 Plot Sampling 2.1 Absolute Density 2.2 Design Considerations 2.2.1 Plot Shape and Area 2.2.2 Proportion of Area Sampled 2.2.3 Number of Plots Sampling Method 2.2.4 Irregular Areas 2.2.5 Trees 2.2.6 Primary and Secondary Units 2.3 Stratified Sampling 2.3.1 Estimation 2.3.2 Choosing Number of Plots 2.3.3 Having a Random Distribution 2.3.4 Plot Sampling with Animals 2.4 Edge Effect 2.5 Home Range 2.6 Relative Density 2.6.1 Index Methods 2.7 Population Distribution 2.7.1 Types of Distribution 2.7.2 Negative Binomial Distribution 2.7.3 CMP Distribution 2.7.4 Taylor's Power law 2.7.5 Fairfield Smith's Variance Law 2.8 Widely Dispersed and Clustered Populations 2.9 Summary 3 Detectability 3.1 Detection Probability 3.1.1 Constant Known Detection Probability 3.2 Unknown Detection 3.2.1 Replicate Counts 3.2.2 Circular Plots 3.2.3 Double Sampling 3.2.4 Partial Repeat Sampling 3.2.5 Unequal Individual Detection Probabilities 3.2.6 Detection Model with Spatially Replicated Counts 3.2.7 Detection Methods 3.3 Adaptive Sampling with Incomplete Detectability 3.4 Conclusion 4 Occupancy, Abundance, and Related Topics 4.1 An Overview 4.1.1 Basic Model 4.1.2 Animal Signs 4.1.3 Some Reviews 4.1.4 Rare Species 4.1.5 Repeated Counts 4.1.6 Small Scale and Abundance 4.1.7 Invasive Species 4.2 Detection Probabilities 4.2.1 Homogeneous Detection Probabilities 4.2.2 Variable Parameters 4.2.3 Heterogeneous Detection Probabilities 4.2.4 Model Checking 4.2.5 Detectability, Covariates, and Detection-Only Data 4.2.6 Plants and Variable Plot Sizes 4.3 Some General Models 4.3.1 Using the Robust Model 4.3.2 Spatial Models 4.3.3 Penalized Likelihood 4.3.4 Testing for Occupancy Differences 4.3.5 Surveys After the First Detection? 4.4 Key Assumptions 4.4.1 Model Adequacy 4.4.2 Closure Assumption 4.5 Some Alternative Methods 4.6 Choosing Design Parameters 4.6.1 Three Designs 4.6.2 Bayesian Optimal Design 4.7 Adaptive Methods for Rare Species 4.7.1 Two-Phase Design 4.7.2 Conditional Design 4.8 Occupancy and Abundance 4.8.1 Population Trend 4.8.2 Random or Elusive Aggregated Populations 4.9 Observation Errors 4.9.1 False Positives 4.10 Further Multiple Detection Models 4.10.1 Combining Detection Types 4.10.2 Multiple Detection Devices 4.11 DNA Methods 4.11.1 eDNA 4.12 Presence-Only Data 4.12.1 Pseudo-Absence Problem 4.12.2 Poisson Point Process Models 4.12.3 Geographic Distribution 4.12.4 Using Environmental Conditions 4.12.5 Methods of Phillips & Elith, 2013 4.12.6 Combining Presence and Presence/Absence Data 4.13 Multi-Scale Models 4.14 Multispecies Models 4.15 Zero-Inflated Models 4.16 Opportunistic and Citizen Surveys 4.16.1 Two-Stage Model 4.16.2 Pro and Cons 4.16.3 Accounting for False Positives 4.16.4 Disasters 4.16.5 Bird Applications 4.16.6 General Comments 4.16.7 Citizen Presence-Only Data 4.17 Multistate Methods 4.17.1 Undetected State 4.17.2 Dynamic State Models 4.18 Disease Modeling 4.18.1 Underlying Problems 4.18.2 Multiple Data Sources 4.18.3 Dynamic Model 4.19 Multiple Data Methods 4.20 Fisheries and Marine Environments 4.21 Conclusion 5 Species Methods 5.1 Introduction 5.2 Species Distribution Models (SDMs) 5.2.1 Background and Reviews 5.2.2 Species and the Environment 5.2.3 Model Building 5.2.4 Five Challenges 5.2.5 Bayesian Models 5.2.6 Community Species 5.3 Multivariate Species Models 5.3.1 Introduction 5.3.2 Various Multivariate Models 5.3.3 Occupancy Models 5.3.4 Comparing Models 5.3.5 Spatial Models 5.3.6 Computing 5.3.7 Species Correlations 5.4 Species Interactions 5.4.1 Two Interactive Species 5.4.2 Markov Networks 5.4.3 Environmental Effects 5.4.4 Species' Counts 5.4.5 Consumer Resource Dynamical Models 5.4.6 Using Absences 5.4.7 Time-to-Detection Models 5.5 Species Richness 5.5.1 Replicate Visits 5.5.2 Data Augmentation 5.5.3 Parametric Methods 5.5.4 Nonparametric Estimates: Abundance Data 5.5.5 Nonparametric Estimates: Incidence Data 5.5.6 Rarefaction and Extrapolation Methods 5.5.7 Species Ranking 5.5.8 Second Sample Adding New Species 5.5.9 Choosing the Sample Size 5.5.10 Using eDNA 5.5.11 Biodiversity 5.5.12 Biodiversity Measures 5.5.13 Environmental Links 5.5.14 Species-Area Relationships (SARS) 5.6 Species Misidentification 5.7 Opportunistic Surveys 5.8 Summary 6 Closest Distance and Nearest Neighbor Methods 6.1 Description 6.2 Closest-Individual Distance 6.2.1 Poisson Model 6.3 The rth Closest Distance 6.3.1 The rth Nearest Neighbor 6.3.2 Nonrandom Distributions 6.4 Methods for Trees 6.4.1 Plot Methods 6.4.2 Distance Sampling for Trees 6.4.3 Three Problems with Closest Distance Methods 6.5 Summary 7 Point Counts and Point-Distance Methods 7.1 Introduction 7.2 Point-Distance Sampling 7.2.1 Theory for Point Distances Heterogeneity Bias 7.2.2 Experimental Design Sample Size 7.2.3 Measurement Errors Correction-Factor Estimators 7.2.4 Detection Functions 7.2.5 Point Sampling Along Lines 7.2.6 Cluster Sampling 7.3 Combined with Removal Method 7.4 Trapping Web 7.5 Single Trap or Lure Method 7.6 Some Model Variations 7.6.1 Variable Circular Plot 7.6.2 Unconditional Likelihood 7.6.3 Repeated Counts Model 7.6.4 Spatially Replicated Counts Model 7.7 Double Observers 7.7.1 Theory Point Independence Dependence 7.7.2 Unreconciled Double-Observer Method 7.7.3 Aerial Counts 7.8 Components of Detectability 7.8.1 Validation and Comparison of Point Methods 7.9 Combined Methods 7.10 Summary 8 Line Transect and Distance Methods 8.1 Line Distances 8.1.1 Basic Assumptions 8.2 General Distance Theory 8.2.1 Variance Estimation 8.2.2 Encounter Rate 8.2.3 Systematic Sampling 8.2.4 Pooling Robustness 8.2.5 Detection Function Some Detection Functions 8.2.6 Group (Cluster) Sampling 8.2.7 Transects in Plots 8.3 Design Considerations 8.3.1 Some Designs 8.3.2 Choice of Transects 8.4 Transects of Random Length 8.5 Animal Signs 8.6 Line Transect Radial Distances 8.6.1 Circular Flushing Region 8.7 Plant Sampling 8.7.1 Crossed Design 8.7.2 Time Spent 8.8 Acoustic Methods 8.9 Using Presence/Absence Data 8.9.1 Log-Linear Model 8.10 Point or Line Transects? 8.11 Method of Double Observers Using Distances 8.11.1 Using Mark-Recapture and Distance 8.11.2 Allowing for Heterogeneity 8.11.3 Levels of Independence 8.11.4 Point Independence and Capture-Recapture 8.12 Aerial Censusing 8.12.1 Population Size 8.12.2 Some Examples 8.12.3 Some Model Variations 8.12.4 Supplementary Ground Counts 8.12.5 Digital Observations Using Cameras 8.13 Extension of Model-Based Methods 8.13.1 Shipboard Acoustic Surveys 8.13.2 Other Marine Surveys 8.13.3 Allowing for Movement 8.13.4 Full Model-Based Method 8.13.5 Spatial Models 8.13.6 Adaptive Sampling 8.14 Bayesian Methods 8.15 Three-Dimensional Line Transects 8.16 Summary 9 Line Intercept Methods 9.1 Line Intercept 9.1.1 Comparison of Methods 9.1.2 General Theory 9.1.3 Estimation of Coverage 9.1.4 Estimation of Particle Density 9.1.5 Kaiser's Generalization 9.2 Transects of Random Length 9.2.1 Coverage 9.2.2 Particle Density 9.2.3 Method of Kaiser 9.2.4 Line Point Intercept/Transect 9.3 Summary 10 Removal and Change-in-Ratio Methods 10.1 Basic Models 10.1.1 Constant Probability of Removal 10.1.2 Trap Reduction 10.1.3 Combined with a Mark Release 10.1.4 Regression Methods 10.1.5 Variable Catchability 10.2 Bayesian Methods 10.2.1 Random Catchability Diffuse Priors Different Techniques 10.2.2 Use of Effort Information 10.2.3 Aerial Sightings 10.2.4 Some Electrofishing Applications 10.3 Two and Three Removals 10.3.1 Three Removals 10.3.2 Two Removals 10.4 Electrofishing 10.5 Design of a Removal Experiment 10.6 Removal Methods for Subpopulations 10.6.1 Multiple Sites 10.7 Removal Methods for Point-Count Surveys 10.8 Time-to-Detection Model 10.9 Change in Ratio: Two Classes 10.9.1 Theory 10.9.2 Binomial Model Assumption (i) Assumption (ii) Assumption (iii) 10.9.3 Survival Rates 10.9.4 Removals Estimated 10.9.5 Optimum Allocation 10.9.6 Exploitation Rate 10.9.7 Subsampling 10.9.8 Continuous Case 10.10 Multiple Removals and Samples 10.11 Index-Removal Method 10.12 Known Sampling Effort 10.12.1 Several Subclasses, Removals, and Samples 10.13 Omnibus Removal Methods 10.13.1 Combining CIR and IR 10.13.2 Combining Three Methods 10.14 Summary 11 Catch-Effort Models 11.1 Types of Model 11.2 Homogeneous Models 11.2.1 Method of Estimating Functions 11.3 Heterogeneous Models 11.3.1 Using Coverage and Estimating Functions 11.4 Regression Models 11.5 Underlying Assumptions 11.5.1 Some Variable Catchability Models 11.5.2 When Is a Species Extinct? 11.5.3 Fisheries 11.6 Summary 12 Capture-Recapture: Frequentist Methods 12.1 Introduction 12.2 Two-Sample Capture-Recapture 12.2.1 Underlying Assumptions 12.2.2 Variable Catchability 12.2.3 Two Observers with Time to Detection 12.2.4 Epidemiological Population: Two Lists 12.2.5 Epidemiological Population: Several Lists 12.2.6 Dual Record System 12.2.7 Some Individuals Stratified 12.2.8 Detection Model 12.3 Triple-Catch Method 12.4 Several Samples 12.4.1 Multinomial Model 12.4.2 Conditional Method 12.5 Pollock's Model Categories 12.5.1 Model Mt 12.5.2 Model M0 12.5.3 Model Mb 12.5.4 Model Mtb 12.5.5 Model Mh 12.5.6 Model Mth 12.5.7 Model Mbh 12.5.8 Model Mtbh 12.5.9 Choosing the Number of Samples 12.5.10 Model Selection 12.5.11 Huggins' Models 12.5.12 Test of Model Assumptions 12.6 Mixture Models 12.6.1 Models of Norris and Pollock 12.6.2 Models of Pollock and Otto 12.6.3 Identifiability 12.6.4 Model of Dorazio and Royle 12.6.5 Model of Tounkar and Rivest 12.7 Log-Linear Poisson Models 12.7.1 Using the Conditional Model 12.7.2 Pollock's Models in Log-Linear Form 12.8 Coverage Models 12.8.1 Heterogeneity 12.8.2 Coverage and Pollock's Models 12.8.3 Coverage and Dual Record System 12.9 Martingales and Estimating Functions 12.9.1 Combined with Coverage 12.10 Time-to-Detection Method 12.11 Prior Detection Effects 12.12 Using DNA Tags 12.13 Misidentification 12.14 Sampling One at a Time 12.15 Continuous-Time Models 12.15.1 Markov Model 12.15.2 General Frailty Models 12.15.3 Some Model Variations 12.15.4 Models of Schofield et al. 12.15.5 Random Removals 12.15.6 Self-Exciting (Self-Correcting) Processes 12.15.7 Single-Catch Spatial Model 12.16 Conclusion 13 Capture-Recapture: Bayesian Methods 13.1 Overview 13.2 Bayesian Statistics 13.3 Two-Sample Capture-Recapture 13.3.1 Roberts1967 13.3.2 Other Approaches 13.4 Model Mt 13.4.1 Poisson Model 13.4.2 Sequential Updating of Posterior for N 13.5 Bayesian Development of Species Distribution Models 13.6 Model Fitting with Markov Chain Monte Carlo 13.7 List Dependence 13.8 Behavior 13.9 Heterogeneity 13.9.1 Rasch Models 13.9.2 Mixture Model 13.9.3 Latent Class Model 13.9.4 Non-parametric Approaches 13.10 Estimating Abundance 13.10.1 Marginalize over p 13.10.2 Joint Update 13.10.3 Numerical Integration 13.10.4 Semi-complete Data Likelihood 13.10.5 Laplace Approximation 13.10.6 Bounding Abundance 13.10.7 Data Augmentation 13.10.8 Comparing Approaches That Bound Abundance 13.10.9 Reversible Jump Markov Chain Monte Carlo 13.11 Priors 13.11.1 Non-informative Priors for Capture-Recapture 13.11.2 Bayes Ancillarity 13.11.3 Informative Priors 13.11.4 Weakly Informative Priors 13.11.5 Hierarchical Models/Priors 13.12 Bayes in the Twenty-First Century 13.13 Conclusion 14 Spatial and Camera Methods 14.1 Spatial Recapture Models 14.1.1 Introduction 14.1.2 Description 14.1.3 A Basic Model 14.2 Some Examples 14.2.1 Multi-catch Traps 14.2.2 Passive Detector Array 14.2.3 Spatial Passive Acoustical Surveys 14.2.4 Some Miscellaneous Applications 14.2.5 Using Telemetry 14.2.6 Modeling Interactions 14.2.7 Occupancy and Spatial Combined 14.3 Bayesian Models 14.3.1 Binomial Point Process 14.3.2 Connecting Bayes and Frequency Methods of Estimation 14.4 Further Extensions 14.4.1 Stratified Populations 14.4.2 Presence-Absence Data Only 14.4.3 Viability for Introduced Species 14.4.4 SECR and Distance Sampling (DS) 14.5 Spatial Mark-Resight Models 14.5.1 Different Sightings for Marked and Unmarked 14.5.2 Lack of Individual Recognition 14.6 Camera Methods 14.6.1 Some Reviews 14.6.2 Camera Advantages 14.6.3 Design Considerations 14.6.4 Partial Identity 14.6.5 Some Applications 14.6.6 Community Method 14.6.7 Spatial Point Process Model 14.6.8 Modeling Identification Errors 14.7 Adaptive Cluster Sampling 14.8 DNA Methods 14.8.1 Comparing DNA and Camera Methods 14.8.2 Combining DNA and Camera Methods 14.9 Summary A Some General Results A.1 Poisson Process A.1.1 One-Dimensional A.1.2 Two-Dimensional A.2 N-Mixture Models A.3 Multinomial Distribution A.3.1 Some Properties A.3.2 Conditional Multinomial Distribution A.4 Delta Method A.5 Parameter-Expanded Data Augmentation A.6 Conditional Expectations A.7 Profile Likelihood Intervals A.8 Large Sample Hypothesis Tests A.8.1 Diagnostic Residuals for Frequency Models A.9 Bayesian Methods A.9.1 Sequential Updating A.9.2 Bayes Factors and Posterior Model Probabilities References Index