Reflected Stochastic Differential Equation Models for Constrained Animal Movement

Movement for many animal species is constrained in space by barriers such as rivers, shore-lines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.

[1]  Francesca Cagnacci,et al.  Animal Movement , 1955, Nature.

[2]  Simon J. Godsill,et al.  An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo , 2007, Proceedings of the IEEE.

[3]  Murali Haran,et al.  A spatially varying stochastic differential equation model for animal movement , 2016, The Annals of Applied Statistics.

[4]  Mevin B Hooten,et al.  Animal movement constraints improve resource selection inference in the presence of telemetry error. , 2015, Ecology.

[5]  Chien-Cheng Chang.  Numerical solution of stochastic differential equations with constant diffusion coefficients , 1987 .

[6]  M. Hooten,et al.  A general science-based framework for dynamical spatio-temporal models , 2010 .

[7]  Alan A. Ager,et al.  Analyzing animal movement patterns using potential functions , 2013 .

[8]  Mevin B. Hooten,et al.  Continuous-time discrete-space models for animal movement , 2012, 1211.1992.

[9]  M. Hooten,et al.  Velocity-Based Movement Modeling for Individual and Population Level Inference , 2011, PloS one.

[10]  A. Crespi,et al.  Tracking Individuals Shows Spatial Fidelity Is a Key Regulator of Ant Social Organization , 2013, Science.

[11]  Denis S. Grebenkov,et al.  NMR survey of reflected brownian motion , 2007 .

[12]  Jonathan R. Potts,et al.  Integrated step selection analysis: bridging the gap between resource selection and animal movement , 2015, 1512.01614.

[13]  Walter Zucchini,et al.  Series of Seminars: Hidden Markov Models for Time Series , 2013 .

[14]  David R. Brillinger,et al.  Employing stochastic differential equations to model wildlife motion , 2002 .

[15]  Radu V. Craiu,et al.  Bayesian Computation Via Markov Chain Monte Carlo , 2014 .

[16]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[17]  Daniel P. Costa,et al.  Accuracy of ARGOS Locations of Pinnipeds at-Sea Estimated Using Fastloc GPS , 2010, PloS one.

[18]  T. Bekkby,et al.  SUMMER HOME RANGE AND HABITAT SELECTION OF HARBOR SEAL (PHOCA VITULINA) PUPS , 2002 .

[19]  R. Dalton.  Conservation biology: Is this any way to save a species? , 2005, Nature.

[20]  D. Lindley,et al.  Data Analysis From Statistical Foundations , 2002, The Mathematical Gazette.

[21]  Kevin Burrage,et al.  Modeling ion channel dynamics through reflected stochastic differential equations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Martin T. Wells,et al.  Exploring an Adaptive Metropolis Algorithm , 2010 .

[23]  Mevin B. Hooten,et al.  Circuit Theory and Model-Based Inference for Landscape Connectivity , 2013 .

[24]  Jacob S. Ivan,et al.  A functional model for characterizing long‐distance movement behaviour , 2016 .

[25]  J. Hoef,et al.  DIFFERENTIAL MOVEMENTS BY HARBOR SEAL PUPS IN CONTRASTING ALASKA ENVIRONMENTS , 2005 .

[26]  Devin S Johnson,et al.  A General Framework for the Analysis of Animal Resource Selection from Telemetry Data , 2008, Biometrics.

[27]  Mevin B. Hooten,et al.  Basis Function Models for Animal Movement , 2016, 1601.05408.

[28]  David R. Brillinger,et al.  Simulating constrained animal motion using stochastic differential equations , 2003 .

[29]  Mevin B Hooten,et al.  Models for Bounded Systems with Continuous Dynamics , 2009, Biometrics.

[30]  A Coulon,et al.  Genetic structure is influenced by landscape features: empirical evidence from a roe deer population , 2006, Molecular ecology.

[31]  A. Genz,et al.  Computation of Multivariate Normal and t Probabilities , 2009 .

[32]  Mevin B. Hooten,et al.  Agent-Based Inference for Animal Movement and Selection , 2010 .

[33]  Mevin B. Hooten,et al.  Dynamic social networks based on movement , 2015, 1512.07607.

[34]  Shweta Bansal,et al.  Social, spatial, and temporal organization in a complex insect society , 2015, Scientific Reports.

[35]  J. Andrew Royle,et al.  Hierarchical Spatiotemporal Matrix Models for Characterizing Invasions , 2007, Biometrics.

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

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