Basis Function Models for Animal Movement

ABSTRACT

Advances in satellite-based data collection techniques have served as a catalyst for new statistical methodology to analyze these data. In wildlife ecological studies, satellite-based data and methodology have provided a wealth of information about animal space use and the investigation of individual-based animal–environment relationships. With the technology for data collection improving dramatically over time, we are left with massive archives of historical animal telemetry data of varying quality. While many contemporary statistical approaches for inferring movement behavior are specified in discrete time, we develop a flexible continuous-time stochastic integral equation framework that is amenable to reduced-rank second-order covariance parameterizations. We demonstrate how the associated first-order basis functions can be constructed to mimic behavioral characteristics in realistic trajectory processes using telemetry data from mule deer and mountain lion individuals in western North America. Our approach is parallelizable and provides inference for heterogenous trajectories using nonstationary spatial modeling techniques that are feasible for large telemetry datasets. Supplementary materials for this article are available online.

KEYWORDS:

• Bayesian model averaging
• Continuous-time model
• Process convolution
• Stochastic differential equation
• Telemetry data

Supplementary Material

• Appendix A: Derivation of reparameterization of convolved multivariate Brownian motion.

• Appendix B: Specification and visualization of basis functions in $\tilde{\mathbf{H}}$.

• Appendix C: Sherman–Morrison–Woodbury identity for FMM.

• Appendix D: RJMCMC algorithm for fitting FMM.

• Appendix E: Simulation examples involving homogenous and heterogenous dynamics.

• Appendix F: Empirical variograms for posterior predictive residuals of mule deer and mountain lion models.

Acknowledgments

The authors thank Mat Alldredge, Frances Buderman, Marti Garlick, Ephraim Hanks, Bill Link, Brett McClintock, Leslie Mcfarlane, Juan Morales, Jim Powell, Henry Scharf, and Jay Ver Hoef for help for insightful discussions and feedback on the data and research. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Funding

Funding for this research was provided by NOAA (RWO 103), CPW (TO 1304), and NSF (DMS 1614392).