Front Cover

Occupancy Estimation and Modeling

Copyright

Contents

Preface

Acknowledgments

Part I Background and Concepts

1 Introduction

1.1 Operational Definitions

1.2 Sampling Animal Populations and Communities: General Principles

1.2.1 Why?

1.2.2 What?

1.2.3 How?

1.3 Inference About Dynamics and Causation

1.3.1 Generation of System Dynamics

1.3.2 Statics and Process vs. Pattern

1.4 Discussion

2 Occupancy Applications

2.1 Geographic Range

2.2 Habitat Relationships and Resource Selection

2.3 Metapopulation Dynamics

2.3.1 Inference Based on Single-Season Data

2.3.2 Inference Based on Multiple-Season Data

2.4 Large-Scale Monitoring

2.5 Multi-Species Occupancy Data

2.5.1 Inference Based on Static Occupancy Patterns

2.5.2 Inference Based on Occupancy Dynamics

2.6 Paleobiology

2.7 Disease Dynamics

2.8 Non-Ecological Applications

2.9 Discussion

3 Fundamental Principals of Statistical Inference

3.1 Definitions and Key Concepts

3.1.1 Random Variables, Probability Distributions, and the Likelihood Function

3.1.2 Expected Values and Variance

3.1.3 Introduction to Methods of Estimation

3.1.4 Properties of Point Estimators

Bias

Precision (Variance and Standard Error)

Accuracy (Mean Squared Error)

3.1.5 Computer Intensive Methods

3.2 Maximum Likelihood Estimation Methods

3.2.1 Maximum Likelihood Estimators

3.2.2 Properties of Maximum Likelihood Estimators

3.2.3 Variance, Covariance (and Standard Error) Estimation

3.2.4 Confidence Interval Estimators

3.2.5 Multiple Maxima

3.2.6 Observed and Complete Data Likelihood

3.3 Bayesian Estimation

3.3.1 Theory

3.3.2 Computing Methods

3.4 Modeling Predictor Variables

3.4.1 The Logit Link Function

3.4.2 Interpretation

3.4.3 Estimation

3.5 Hypothesis Testing

3.5.1 Background and Definitions

3.5.2 Likelihood Ratio Tests

3.5.3 Goodness of Fit Tests

3.6 Model Selection

3.6.1 Akaike's Information Criterion (AIC)

3.6.2 Goodness of Fit and Overdispersion

3.6.3 Quasi-AIC

3.6.4 Model Averaging and Model Selection Uncertainty

3.6.5 Bayesian Assessment of Model Fit

3.6.6 Bayesian Model Selection

3.7 Discussion

Part II Single-Species, Single-Season Occupancy Models

4 Basic Presence/Absence Situation

4.1 The Sampling Situation

4.2 Estimation of Occupancy if Probability of Detection Is 1 or Known Without Error

4.3 Two-Step Ad Hoc Approaches

4.3.1 Geissler-Fuller Method

4.3.2 Azuma-Baldwin-Noon Method

4.3.3 Nichols-Karanth Method

4.4 Model-Based Approach

4.4.1 Building a Model

Observed Data Likelihood

Complete Data Likelihood

4.4.2 Estimation

4.4.3 Constant Detection Probability Model

4.4.4 Survey-Specific Detection Probability Model

4.4.5 Probability of Occupancy Given Species Not Detected at a Unit

4.4.6 Example: Blue-Ridge Two-Lined Salamanders

Maximum Likelihood Estimation

Bayesian Estimation

4.4.7 Missing Observations

4.4.8 Covariate Modeling

4.4.9 Violations of Model Assumptions

Violation of Closure

Heterogeneity in Occupancy Probability

Heterogeneity in Detection Probability

Lack of Independence

Species Misidentification

4.4.10 Assessing Model Fit

4.4.11 Diagnostic Plots

4.4.12 Examples

Pronghorn Antelope

Mahoenui Giant Weta

Mahoenui Giant Weta: A Bayesian Analysis

Swiss Willow Tit

4.5 Case Study: Troll Distribution in Middle Earth

4.6 Discussion

5 Beyond Two Occupancy States

5.1 The Sampling Situation

5.2 Model Based Approach

5.2.1 Observed Data Likelihood

5.2.2 Matrix Formulation

5.3 Alternative Parameterizations

5.4 Missing Observations

5.5 Covariates and Predictor Variables

5.6 Model Assumptions

5.7 Examples

5.7.1 California Spotted Owl Reproduction

5.7.2 Breeding Success of Grizzly Bears

5.8 Discussion

6 Extensions to Basic Approaches

6.1 Estimating Occupancy for a Finite Population or Small Area

6.1.1 Prediction of Unobserved Occupancy State

A Non-Bayesian Approach

A Bayesian Approach

6.1.2 Example: Blue Ridge Two-Lined Salamanders Revisited

6.1.3 Consequences of a Finite Population

6.1.4 A Related Issue

6.2 Accounting for False Positive Detections

6.2.1 Modeling Misclassification for a Single Season

A General Approach

Terminology

Unit Confirmation Design

Calibration Design

Observation Confirmation Design

Selecting an Approach

6.2.2 Discussion

6.3 Multi-Scale Occupancy

6.3.1 Model Definition

6.3.2 Example: Striped Skunks

6.3.3 Discussion

6.4 Autocorrelated Surveys

6.4.1 Model Description

6.4.2 Example: Tigers on Trails

6.4.3 Discussion

6.5 Staggered Entry-Departure Model

6.5.1 Model Description

6.5.2 Example: Maryland Amphibians

6.5.3 Discussion

6.6 Spatial Autocorrelation in Occurrence

6.6.1 Covariates

6.6.2 Conditional Auto-Regressive Model

6.6.3 Autologistic Model

6.6.4 Kriging

6.6.5 Restricted Spatial Regression

6.7 Discussion

7 Modeling Heterogeneous Detection Probabilities

7.1 Occupancy Models with Heterogeneous Detection

7.1.1 General Formulation

7.1.2 Finite Mixtures

7.1.3 Continuous Mixtures

7.1.4 Abundance-Induced Heterogeneity Models

7.1.5 Evaluation of Model Fit

7.2 Example: Breeding Bird Point Count Data

7.3 Modeling Covariate Effects on Detection

7.4 Example: Anuran Calling Survey Data

7.5 On the Identifiability of ψ

7.6 Discussion

Part III Single-Species, Multiple-Season Occupancy Models

8 Basic Presence/Absence Situation

8.1 Basic Sampling Scheme

8.2 An Implicit Dynamics Model

8.3 Modeling Dynamic Changes Explicitly

8.3.1 Modeling Dynamic Processes when Detection Probability is 1

8.3.2 Conditional Modeling of Dynamic Processes

8.3.3 Unconditional Modeling of Dynamic Processes

8.3.4 Missing Observations

8.3.5 Including Covariate Information

8.3.6 Alternative Parameterizations

8.3.7 Example: House Finch Expansion in North America

8.4 Violations of Model Assumptions

8.5 Discussion

9 More than Two Occupancy States

9.1 Basic Sampling Scheme

9.2 Defining an Explicit Dynamics Model

9.3 Modeling Data and Parameter Estimation

9.4 Covariates and `Missing' Observations

9.5 Model Assumptions

9.6 Examples

9.6.1 Maryland Green Frogs

9.6.2 California Spotted Owls

9.7 Discussion

10 Further Topics

10.1 False Positive Detections

10.1.1 Confirmation Designs

Two Detection Types

Two Detection Methods

Example Analysis

10.1.2 More Observation and Occupancy States: General Approach

10.1.3 Discussion

10.2 Autocorrelated Within-Season Detections

10.3 Spatial Correlation in Dynamics

10.4 Investigating Occupancy Dynamics

10.4.1 Markovian, Random, and No Changes in Occupancy

10.4.2 Equilibrium

10.4.3 Example: Northern Spotted Owl

10.4.4 Further Insights

Inferring Population Trajectory from Dynamic Parameters

Time-Invariant Dynamic Parameters Can Induce an Apparent Trend

10.4.5 Chronological Order of Surveys

10.4.6 Discussion

10.5 Sensitivity of Occupancy to Dynamic Processes

10.5.1 Two-State Situation

10.5.2 General Situation

10.6 Modeling Heterogeneous Detection Probabilities

10.7 Discussion

Part IV Study Design

11 Design of Single-Season Occupancy Studies

11.1 Defining the Population of Interest

11.2 Defining a Sampling Unit

11.3 Unit Selection

11.4 Defining a `Season'

11.5 Conducting Repeat Surveys

11.5.1 General Considerations

11.5.2 Special Note on Using Spatial Replication

11.6 Allocation of Effort, Number of Sites vs. Number of Surveys

11.6.1 Standard Design

No Consideration of Cost

Including Survey Cost

11.6.2 Double Sampling Design

11.6.3 Removal Sampling Design

11.6.4 More Units vs. More Surveys

11.6.5 Finite Population

11.7 Discussion

12 Multiple-Season Study Design

12.1 Time Interval Between Seasons

12.2 Same vs. Different Units Each Season

12.3 More Units vs. More Seasons

12.4 More on Unit Selection

12.5 Discussion

Part V Advanced Topics

13 Integrated Modeling of Habitat and Occupancy Dynamics

13.1 Introduction

13.2 Basic Sampling Situation

13.3 Model Development and Estimation

13.3.1 Missing Observations

13.3.2 Covariates

13.4 Biological Questions of Interest

13.4.1 Effect of Habitat Change on Occupancy Dynamics

13.4.2 Effect of Species Presence on Habitat Dynamics

13.5 System Summaries

13.6 Model Extensions

13.7 Example

13.7.1 Patuxent Spotted Salamanders

13.8 Discussion

14 Species Co-Occurrence

14.1 Detection Probability and Inferences About Species Co-Occurrence

14.2 A Single-Season Model

14.2.1 General Sampling Situation

14.2.2 Statistical Model

14.2.3 Derived Parameters and Alternative Parameterizations

14.2.4 Covariates

14.2.5 Missing Observations

14.3 Addressing Biological Hypotheses

14.4 Example: Terrestrial Salamanders in Great Smoky Mountains National Park

14.5 Extension to Multiple Seasons

14.6 Example: Barred and Northern Spotted Owls

14.7 Study Design Issues

14.8 Generalizing to More than Two Species

14.9 Discussion

15 Occupancy in Community-Level Studies

15.1 Investigating the Community at a Single Unit

15.1.1 Fraction of Species Present in a Single Season

15.1.2 Changes in the Fraction of Species Present over Time or Space

15.2 Investigating the Community at Multiple Units

15.2.1 Single-Season Studies: Modeling Occupancy and Detection

15.2.2 Single-Season Studies: Multi-Species Occupancy Models (MSOMs)

15.2.3 Example of the Dorazio-Royle Multi-Species Occupancy Model

15.3 The Yamaura Extensions: Multi-Species Abundance Models

15.4 Multiple-Season Multi-Species Occupancy Models

15.5 Discussion

16 Final Comments

Appendix

A.1 Notation for Summations and Products

A.2 Vectors and Matrices

A.2.1 Vectors

A.2.2 Matrices

A.2.3 Vector and Matrix Manipulation

A.3 Differentiation and Integration

Bibliography

Index

Back Cover