Animal movement

STATISTICAL MODELS FOR

TELEMETRY DATA

Animal

Movement

Cervus canadensis Phoca largha; Dave

Withrow), and mountain lion (Puma concolor; Jacob Ivan, Colorado Parks and Wildlife).

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Library of Congress Cataloging-in-Publication Data

Names: Hooten, Mevin B., 1976-

Title: Animal movement : statistical models for telemetry data / Mevin

B. Hooten [and three others].

Description: Boca Raton : CRC Press, 2017. | Includes bibliographical

references and indexes.

Identifiers: LCCN 2016034976 | ISBN 9781466582149 (hardback : alk. paper)

Subjects: LCSH: Animal behavior--Mathematical models. | Home range (Animal

geography)--Mathematical models. | Biotelemetry.

Classification: LCC QL751.65.M3 A55 2017 | DDC 591.501/5118--dc23

LC record available at https://lccn.loc.gov/2016034976

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Contents

Preface ..................................................................................ix

Acknowledgments ......................................................................xi

Authors................................................................................ xiii

Chapter 1 Introduction .............................................................. 1

1.1 Background on Animal Movement ............................. 1

1.1.1 Population Dynamics ................................... 3

1.1.2 Spatial Redistribution ................................... 4

1.1.3 Home Ranges, Territories, and Groups ................ 6

1.1.4 Group Movement and Dynamics....................... 7

1.1.5 Informed Dispersal and Prospecting ................... 8

1.1.6 Memory ................................................. 8

1.1.7 Individual Condition .................................... 9

1.1.8 Energy Balance ........................................ 10

1.1.9 Food Provision ......................................... 10

1.1.10 Encounter Rates and Patterns ......................... 10

1.2 Telemetry Data .................................................. 12

1.3 Notation ......................................................... 14

1.4 Statistical Concepts ............................................. 15

1.5 Additional Reading ............................................. 17

Chapter 2 Statistics for Spatial Data .............................................. 19

2.1 Point Processes.................................................. 19

2.1.1 Homogeneous SPPs.................................... 21

2.1.2 Density Estimation..................................... 23

2.1.3 Parametric Models ..................................... 25

2.2 Continuous Spatial Processes .................................. 28

2.2.1 Modeling and Parameter Estimation .................. 29

2.2.2 Prediction............................................... 34

2.2.3 Restricted Maximum Likelihood...................... 35

2.2.4 Bayesian Geostatistics ................................. 36

2.3 Discrete Spatial Processes ...................................... 39

2.3.1 Descriptive Statistics................................... 40

2.3.2 Models for Discrete Spatial Processes ................ 43

2.4 Spatial Confounding ............................................ 47

2.5 Dimension Reduction Methods ................................ 48

2.5.1 Reducing Necessary Calculations..................... 48

2.5.2 Reduced-Rank Models ................................ 49

2.5.3 Predictive Processes ................................... 51

2.6 Additional Reading ............................................. 54

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vi Contents

Chapter 3 Statistics for Temporal Data ........................................... 55

3.1 Univariate Time Series.......................................... 55

3.1.1 Descriptive Statistics................................... 57

3.1.2 Models for Univariate Temporal Data ................ 60

3.1.2.1 Autoregressive Models...................... 60

3.1.2.2 Moving Average Models.................... 65

3.1.2.3 Backshift Notation .......................... 66

3.1.2.4 Differencing in Time Series Models ....... 68

3.1.2.5 Fitting Time Series Models................. 68

3.1.3 Forecasting ............................................. 71

3.1.4 Additional Univariate Time Series Notes............. 73

3.1.5 Temporally Varying Coefficient Models ............. 74

3.1.6 Temporal Point Processes ............................. 77

3.2 Multivariate Time Series........................................ 83

3.2.1 Vector Autoregressive Models ........................ 83

3.2.2 Implementation ........................................ 87

3.3 Hierarchical Time Series Models .............................. 88

3.3.1 Measurement Error .................................... 89

3.3.2 Hidden Markov Models ............................... 91

3.3.3 Upscaling............................................... 92

3.3.3.1 Implementation: Kalman

Approaches .................................. 94

3.3.3.2 Implementation: Bayesian

Approaches .................................. 96

3.4 Additional Reading ............................................. 98

Chapter 4 Point Process Models .................................................. 99

4.1 Space Use ....................................................... 99

4.1.1 Home Range ..........................................101

4.1.2 Core Areas ............................................103

4.2 Resource Selection Functions .................................107

4.2.1 Implementation of RSF Models......................110

4.2.2 Efficient Computation of RSF Integrals .............113

4.3 Resource Utilization Functions................................117

4.4 Autocorrelation ................................................121

4.5 Population-Level Inference ....................................123

4.6 Measurement Error ............................................127

4.7 Spatio-Temporal Point Process Models.......................131

4.7.1 General Spatio-Temporal Point Processes...........132

4.7.2 Conditional STPP Models for Telemetry

Data ....................................................134

4.7.3 Full STPP Model for Telemetry Data................138

4.7.4 STPPs as Spatial Point Processes ....................141

4.8 Additional Reading ............................................145

Contents vii

Chapter 5 Discrete-Time Models................................................ 147

5.1 Position Models ................................................147

5.1.1 Random Walk .........................................147

5.1.2 Attraction..............................................150

5.1.3 Measurement Error ...................................150

5.1.4 Temporal Alignment (Irregular Data)................153

5.1.5 Heterogeneous Behavior..............................153

5.2 Velocity Models................................................158

5.2.1 Modeling Movement Parameters.....................162

5.2.2 Generalized State-Switching Models ................168

5.2.3 Response to Spatial Features .........................175

5.2.4 Direct Dynamics in Movement Parameters..........176

5.2.5 Patch Transitions......................................178

5.2.6 Auxiliary Data ........................................182

5.2.7 Population-Level Inference...........................186

5.3 Additional Reading ............................................187

Chapter 6 Continuous-Time Models ............................................ 189

6.1 Lagrangian versus Eulerian Perspectives .....................189

6.2 Stochastic Differential Equations .............................192

6.3 Brownian Bridges..............................................195

6.4 Attraction and Drift ............................................197

6.5 Ornstein–Uhlenbeck Models ..................................199

6.6 Potential Functions.............................................202

6.7 Smooth Brownian Movement Models ........................211

6.7.1 Velocity-Based Stochastic Process Models .........212

6.7.2 Functional Movement Models and Covariance......217

6.7.3 Implementing Functional Movement Models .......219

6.7.4 Phenomenological Functional Movement

Models.................................................220

6.7.5 Velocity-Based Ornstein–Uhlenbeck Models .......223

6.7.6 Resource Selection and Ornstein–Uhlenbeck

Models.................................................229

6.7.7 Prediction Using Ornstein–Uhlenbeck

Models.................................................231

6.8 Connections among Discrete and

Continuous Models ............................................235

6.9 Additional Reading ............................................238

Chapter 7 Secondary Models and Inference .................................... 239

7.1 Multiple Imputation............................................239

7.2 Transitions in Discrete Space..................................241

7.3 Transitions in Continuous Space ..............................246

7.4 Generalized Models for Transitions in Discrete Space.......253

viii Contents

7.5 Connections with Point Process Models......................256

7.5.1 Continuous-Time Models ............................256

7.5.2 Discrete-Time Models ................................263

7.6 Additional Reading ............................................267

Glossary ............................................................................. 269

References........................................................................... 273

Author Index........................................................................ 291

Subject Index ....................................................................... 299

Preface

With the field of animal movement modeling evolving so rapidly, navigating the

expanding literature is challenging. It may be impossible to provide an exhaustive

summary of animal movement concepts, biological underpinnings, and behavioral

theory; thus, we view this book as a starting place to learn about the fundamen￾tal suite of statistical modeling tools available for providing inference concerning

individual-based animal movement.

Notice that the title is focused on “statistical models for telemetry data.” The set of

existing literature related to animal movement is massive, with thousands of individ￾ual papers related to the general topic. All of this information cannot be synthesized

in a single volume; thus, we focus on the subset of literature mainly concerned with

parametric statistical modeling (i.e., statistical approaches for inverse modeling based

on data and known probability distributions, mainly using likelihood and Bayesian

methods). There are many other approaches for simulating animal movement and

visualizing telemetry data; we leave most of those for another volume.

Our intention is that this book reads more like a reference than a cookbook. It pro￾vides insight about the statistical aspects of animal movement modeling. We expect

two types of readers: (1) a portion of readers will use this book as a companion ref￾erence for obtaining the background necessary to read scientific papers about animal

movement, and (2) the other portion of readers will use the book as a foundation for

creating and implementing their own statistical animal movement models.

We designed this book such that it opens with an overview of animal movement

data and a summary of the progression of the field over the years. Then we provide

a series of chapters as a review of important statistical concepts that are relevant for

the more advanced animal movement models that follow. Chapter 4 covers point pro￾cess models for learning about animal movement; many of these rely on uncorrelated

telemetry data, but Section 4.7 addresses spatio-temporal point processes. Chapters 5

through 6 are concerned with dynamic animal movement models of both the discrete￾and continuous-time flavors. Finally, Chapter 7 describes approaches to use mod￾els in sequence, properly accommodating the uncertainty from first-stage models in

second-stage inference.

We devote a great deal of space to spatial and temporal statistics in general because

this is an area that many animal ecologists have received no formal training in. These

subjects are critical for animal movement modeling and we recommend at least a light

reading of Chapters 2 and 3 for everyone. However, we recognize that readers already

familiar with the basics of telemetry data, as well as spatial and temporal statistics,

may be tempted to skip ahead to Chapter 4, only referring back to Chapters 2 and 3

for reference.

Finally, despite the rapid evolution of animal movement modeling approaches,

no single method has risen to the top as a gold standard. This lack of a universally

accepted framework for analyzing all types of telemetry data is somewhat unique in

the field of quantitative animal ecology and can be daunting for new researchers just

ix

x Preface

wanting to do the right thing. On the other hand, it is an exciting time in animal ecol￾ogy because we can ask and answer new questions that are fundamental to the biology,

ecology, and conservation of wildlife. Each new statistical approach for analyzing

telemetry data brings potential for new inference into the scientific understanding of

critical processes inherent to living systems.

Acknowledgments

The authors acknowledge the following funding sources: NSF DMS 1614392,

CPW T01304, NOAA AKC188000, PICT 2011-0790, and PIP 112-201101-58. The

authors are grateful to (in alphabetical order) Mat Alldredge, Chuck Anderson, David

Anderson, Ali Arab, Randy Boone, Mike Bower, Randy Brehm, Brian Brost, Franny

Buderman, Paul Conn, Noel Cressie, Kevin Crooks, Marìa del Mar Delgado, Bob

Dorazio, Tom Edwards, Gabriele Engler, John Fieberg, James Forester, Daniel Fortin,

Marti Garlick, Brian Gerber, Eli Gurarie, Ephraim Hanks, Dan Haydon, Trevor

Hefley, Tom Hobbs, Jennifer Hoeting, Gina Hooten, Jake Ivan, Shea Johnson, Gwen

Johnson, Layla Johnson, Matt Kaufman, Bill Kendall, Carey Kuhn, Josh London,

John Lowry, Jason Matthiopoulos, Joe Margraf, Leslie McFarlane, Josh Millspaugh,

Ryan Neilson, Joe Northrup, Otso Ovaskainen, Jim Powell, Andy Royle, Henry

Scharf, Tanya Shenk, John Shivik, Bob Small, Jeremy Sterling, David Theobald, Len

Thomas, Jay Ver Hoef, Lance Waller, David Warton, Gary White, Chris Wikle, Perry

Williams, Ken Wilson, Ryan Wilson, Dana Winkelman, George Wittemyer, Jamie

Womble, Jun Zhu, and Jim Zidek for various engaging discussions about animal

movement, assistance, collaboration, and support during this project. The findings

and conclusions in this book by the NOAA authors do not necessarily represent the

views of the National Marine Fisheries Service, NOAA. Any use of trade, firm, or

product names is for descriptive purposes only and does not imply endorsement by

the U.S. Government.

xi

Authors

Mevin B. Hooten is an associate professor in the Departments of Fish, Wildlife, and

Conservation Biology, and Statistics at Colorado State University. He is also assistant

unit leader in the U.S. Geological Survey, Colorado Cooperative Fish and Wildlife

Research Unit. Dr. Hooten earned a PhD in statistics at the University of Missouri.

His research focuses on the development of statistical methodology for spatial and

spatio-temporal ecological processes.

Devin S. Johnson is a statistician at the National Oceanic and Atmospheric Admin￾istration, National Marine Fisheries Service. Dr. Johnson earned a PhD in statistics at

Colorado State University. His research focuses on the development and application

of statistical models for ecological data, with special focus on marine mammals. He

is also the creator and maintainer of the “crawl” R package.

Brett T. McClintock is a statistician at the National Oceanic and Atmospheric

Administration, National Marine Fisheries Service. Dr. McClintock earned a PhD

in wildlife biology and MS in statistics at Colorado State University. His research

focuses on the development and application of statistical models for ecological data

with a primary focus on marine mammals.

Juan M. Morales is a researcher from CONICET (Consejo Nacional de Investiga￾ciones Cientıficas y Tecnicas–National Scientific and Technical Research Council) ´

and a professor at Universidad Nacional del Comahue in Bariloche, Argentina. Dr.

Morales earned a PhD in ecology at the University of Connecticut and his research

focus is on animal movement and spatial ecology.

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