Analyzing animal movement patterns using potential functions

The advent of GPS technology has made it possible to study human-wildlife interactions on large landscapes and quantify behavioral responses to recreation and other anthropogenic disturbances at increasingly fine scales. Of particular interest are the potential impacts on habitat use patterns, energetics, and cascading impacts on fecundity and other life history traits for key wildlife species that are exposed to human activities. Statistical models quantifying effects of human activity on animal movement on a heterogeneous landscape are essential for understanding these potential impacts. Here we present a statistical framework for analyzing movement data that is based on the concept of a potential surface. The potential surface is motivated by the assumption that animals are moving on a space-time surface with regions or points of attraction or of repulsion. We demonstrate the use of the technique by analyzing movement data from a long-term controlled experiment to evaluate the responses of free ranging Rocky Mountain elk (Cervus elaphus) to anthropogenic disturbances that vary in time and space. Our results demonstrated a strong avoidance of elk to all-terrain vehicles detected up to one km from the disturbance. Elk avoidance of mountain bikers was detected up to 500 m, and avoidance of hikers and horseback riders was detected to 200 m.

[1]  Hall Sawyer,et al.  Stopover ecology of a migratory ungulate. , 2011, The Journal of animal ecology.

[2]  Ian D. Jonsen,et al.  META‐ANALYSIS OF ANIMAL MOVEMENT USING STATE‐SPACE MODELS , 2003 .

[3]  Leslie M. Naylor,et al.  Behavioral Responses of North American Elk to Recreational Activity , 2009 .

[4]  Michael Dowd,et al.  Estimating behavioral parameters in animal movement models using a state-augmented particle filter. , 2011, Ecology.

[5]  Devin S Johnson,et al.  Continuous-time correlated random walk model for animal telemetry data. , 2008, Ecology.

[6]  D. Brillinger,et al.  Three months journeying of a Hawaiian monk seal , 2008, 0805.3019.

[7]  Paul R Moorcroft,et al.  Stochastic modelling of animal movement , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[8]  Prakasa Rao.  Statistical inference for diffusion type processes , 1999 .

[9]  Jon S. Horne,et al.  Identifying and prioritizing ungulate migration routes for landscape-level conservation. , 2009, Ecological applications : a publication of the Ecological Society of America.

[10]  Tarek I. Zohdi,et al.  Mechanistic modeling of swarms , 2009 .

[11]  S. Levin,et al.  Diffusion and Ecological Problems: Modern Perspectives , 2013 .

[12]  David R. Brillinger,et al.  Modelling particles moving in a potential field with pairwise interactions and an application , 2011 .

[13]  Lucas N Joppa,et al.  Understanding movement data and movement processes: current and emerging directions. , 2008, Ecology letters.

[14]  Juan M. Morales,et al.  EXTRACTING MORE OUT OF RELOCATION DATA: BUILDING MOVEMENT MODELS AS MIXTURES OF RANDOM WALKS , 2004 .

[15]  John W. Kern,et al.  DAILY AND SEASONAL MOVEMENTS AND HABITAT USE BY FEMALE ROCKY MOUNTAIN ELK AND MULE DEER , 2003 .

[16]  Dean P. Anderson,et al.  State-space models link elk movement patterns to landscape characteristics in Yellowstone National Park , 2007 .

[17]  H. Preisler,et al.  Modeling animal movements using stochastic differential equations , 2004 .

[18]  Brett T. McClintock,et al.  A general discrete‐time modeling framework for animal movement using multistate random walks , 2012 .

[19]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[20]  E A Codling,et al.  Sampling rate effects on measurements of correlated and biased random walks. , 2005, Journal of theoretical biology.

[21]  P. Turchin.  Quantitative analysis of movement : measuring and modeling population redistribution in animals and plants , 1998 .

[22]  S. Wood.  Low‐Rank Scale‐Invariant Tensor Product Smooths for Generalized Additive Mixed Models , 2006, Biometrics.

[23]  Robert A. Gitzen,et al.  Analysis of Resource Selection Using Utilization Distributions , 2006 .

[24]  Michael Sørensen,et al.  Estimating Functions for Discretely Observed Diffusions: A Review , 1997 .

[25]  E. Revilla,et al.  A movement ecology paradigm for unifying organismal movement research , 2008, Proceedings of the National Academy of Sciences.

[26]  Tarek I. Zohdi,et al.  Computational design of swarms , 2003 .

[27]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[28]  H. Preisler,et al.  Effects of off-road recreation on mule deer and elk. , 2004 .

[29]  Alan A. Ager,et al.  Statistical methods for analysing responses of wildlife to human disturbance. , 2005 .

[30]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[31]  D. Brillinger,et al.  An exploratory data analysis (EDA) of the paths of moving animals , 2004 .

[32]  H. Preisler,et al.  Site fidelity of the declining amphibian Rana sierrae (Sierra Nevada yellow-legged frog) , 2010 .

[33]  Stephen M. Krone,et al.  Analyzing animal movements using Brownian bridges. , 2007, Ecology.

[34]  D. Brillinger.  Modeling Spatial Trajectories , 2010 .

[35]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and an Introduction to Chaos , 2003 .