Annals of Applied Statistics

Continuous-time discrete-space models for animal movement

Ephraim M. Hanks, Mevin B. Hooten, and Mat W. Alldredge

Full-text: Open access

Enhanced PDF (334 KB)

Abstract

The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor) in Colorado, USA.

Article information

Source
Ann. Appl. Stat., Volume 9, Number 1 (2015), 145-165.

Dates
First available in Project Euclid: 28 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1430226088

Digital Object Identifier
doi:10.1214/14-AOAS803

Mathematical Reviews number (MathSciNet)
MR3341111

Zentralblatt MATH identifier
06446564

Keywords
Animal movement multiple imputation varying-coefficient model Markov chain

Citation

Hanks, Ephraim M.; Hooten, Mevin B.; Alldredge, Mat W. Continuous-time discrete-space models for animal movement. Ann. Appl. Stat. 9 (2015), no. 1, 145--165. doi:10.1214/14-AOAS803. https://projecteuclid.org/euclid.aoas/1430226088


Export citation

References

  • Boyce, M. S., Vernier, P. R., Nielsen, S. E. and Schmiegelow, F. K. A. (2002). Evaluating resource selection functions. Ecol. Model. 157 281–300.
  • Breed, G. A., Costa, D. P., Jonsen, I. D., Robinson, P. W. and Mills-Flemming, J. (2012). State-space methods for more completely capturing behavioral dynamics from animal tracks. Ecol. Model. 235 49–58.
  • Brillinger, D. R., Preisler, H. K., Ager, A. A. and Kie, J. G. (2001). The use of potential functions in modelling animal movement. In Data Analysis from Statistical Foundations 369–386. Nova Sci. Publ., Huntington, NY.
    Mathematical Reviews (MathSciNet): MR2034526
  • Cagnacci, F., Boitani, L., Powell, R. A. and Boyce, M. S. (2010). Animal ecology meets GPS-based radiotelemetry: A perfect storm of opportunities and challenges. Philos. Trans. R. Soc. Lond., B, Biol. Sci. 365 2157–2162.
  • Chen, Q. and Wang, S. (2011). Variable selection for multiply-imputed data with application to dioxin exposure study. Technical Report No. 217.
  • Fieberg, J., Matthiopoulos, J., Hebblewhite, M., Boyce, M. S. and Frair, J. L. (2010). Correlation and studies of habitat selection: Problem, red herring or opportunity? Philos. Trans. R. Soc. Lond., B, Biol. Sci. 365 2233–2244.
  • Forester, J. D., Im, H. K. and Rathouz, P. J. (2009). Accounting for animal movement in estimation of resource selection functions: Sampling and data analysis. Ecology 90 3554–3565.
  • Friedman, J., Hastie, T. and Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. J. Stat. Softw. 33 1–22.
  • Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian Data Analysis, 2nd ed. Chapman & Hall, Boca Raton, FL.
    Mathematical Reviews (MathSciNet): MR2027492
  • Getz, W. M. and Saltz, D. (2008). A framework for generating and analyzing movement paths on ecological landscapes. Proc. Natl. Acad. Sci. USA 105 19066–19071.
  • Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711–732.
    Mathematical Reviews (MathSciNet): MR1380810
    Digital Object Identifier: doi:10.1093/biomet/82.4.711
  • Grovenburg, T. W., Jenks, J. A., Klaver, R. W., Swanson, C. C., Jacques, C. and Todey, D. T. D. (2009). Seasonal movements and home ranges of white-tailed deer in north-central South Dakota. Can. J. Zool. 87 876–885.
  • Gurarie, E., Andrews, R. D. and Laidre, K. L. (2009). A novel method for identifying behavioural changes in animal movement data. Ecol. Lett. 12 395–408.
  • Hanks, E. M., Hooten, M. B. and Alldredge, M. W. (2015). Supplement to “Continuous-time discrete-space models for animal movement.” DOI:10.1214/14-AOAS803SUPP.
  • Hanks, E. M., Hooten, M. B., Johnson, D. S. and Sterling, J. T. (2011). Velocity-based movement modeling for individual and population level inference. PLoS ONE 6 e22795.
  • Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models. J. Roy. Statist. Soc. Ser. B 55 757–796.
    Mathematical Reviews (MathSciNet): MR1229881
  • Hooten, M. B. and Hobbs, N. T. (2015). A guide to Bayesian model selection for ecologists. Ecol. Mono. 85 3–28.
  • Hooten, M. B., Johnson, D. S., Hanks, E. M. and Lowry, J. H. (2010). Agent-based inference for animal movement and selection. J. Agric. Biol. Environ. Stat. 15 523–538.
    Mathematical Reviews (MathSciNet): MR2788638
    Digital Object Identifier: doi:10.1007/s13253-010-0038-2
  • Horne, J. S., Garton, E. O., Krone, S. M. and Lewis, J. S. (2007). Analyzing animal movements using Brownian bridges. Ecology 88 2354–2363.
  • Johnson, D. S. (2011). crawl: Fit continuous-time correlated random walk models for animal movement data. R package version 1.3-2.
  • Johnson, D. S., Hooten, M. B. and Kuhn, C. E. (2013). Estimating animal resource selection from telemetry data using point process models. J. Anim. Ecol. 82 1155–1164.
  • Johnson, D. S., London, J. M. and Kuhn, C. E. (2011). Bayesian inference for animal space use and other movement metrics. J. Agric. Biol. Environ. Stat. 16 357–370.
    Mathematical Reviews (MathSciNet): MR2843131
    Digital Object Identifier: doi:10.1007/s13253-011-0056-8
  • Johnson, D. S., Thomas, D. L., Ver Hoef, J. M. and Christ, A. (2008a). A general framework for the analysis of animal resource selection from telemetry data. Biometrics 64 968–976.
  • Johnson, D. S., London, J. M., Lea, M.-A. and Durban, J. W. (2008b). Continuous-time correlated random walk model for animal telemetry data. Ecology 89 1208–1215.
  • Jonsen, I. D., Flemming, J. M. and Myers, R. A. (2005). Robust state-space modeling of animal movement data. Ecology 86 2874–2880.
  • Knopff, K. H., Knopff, A. A., Warren, M. B. and Boyce, M. S. (2009). Evaluating global positioning system telemetry techniques for estimating cougar predation parameters. J. Wildl. Manag. 73 586–597.
  • Lele, S. R., Nadeem, K. and Schmuland, B. (2010). Estimability and likelihood inference for generalized linear mixed models using data cloning. J. Amer. Statist. Assoc. 105 1617–1625.
    Mathematical Reviews (MathSciNet): MR2796576
    Digital Object Identifier: doi:10.1198/jasa.2010.tm09757
  • Lima, S. L. (2002). Putting predators back into behavioral predator–prey interactions. Trends Ecol. Evol. 17 70–75.
  • Manly, B. F., McDonald, L. and Thomas, D. L. (2002). Resource Selection by Animals: Statistical Design and Analysis for Field Studies. Chapman & Hall, London.
  • McClintock, B. T., King, R., Thomas, L., Matthiopoulos, J., McConnell, B. J. and Morales, J. M. (2012). A general discrete-time modeling framework for animal movement using multi-state random walks. Ecol. Mono. 82 335–349.
  • Merrill, E., Sand, H., Zimmermann, B., McPhee, H., Webb, N., Hebblewhite, M., Wabakken, P. and Frair, J. L. (2010). Building a mechanistic understanding of predation with GPS-based movement data. Philos. Trans. R. Soc. Lond. B, Biol. Sci. B 365 2279–2288.
  • Morales, J. M., Haydon, D. T., Frair, J., Holsinger, K. E. and Fryxell, J. M. (2004). Extracting more out of relocation data: Building movement models as mixtures of random walks. Ecology 85 2436–2445.
  • Nathan, R., Getz, W. M., Revilla, E., Holyoak, M., Kadmon, R., Saltz, D. and Smouse, P. E. (2008). A movement ecology paradigm for unifying organismal movement research. Proc. Natl. Acad. Sci. USA 105 19052–19059.
  • Park, T. and Casella, G. (2008). The Bayesian lasso. J. Amer. Statist. Assoc. 103 681–686.
    Mathematical Reviews (MathSciNet): MR2524001
    Digital Object Identifier: doi:10.1198/016214508000000337
  • Potts, J. R., Mokross, K. and Lewis, M. A. (2014). A unifying framework for quantifying the nature of animal interactions. J. R. Soc. Interface 11 20140333.
  • R Core Team (2013). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
  • Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley, New York.
    Mathematical Reviews (MathSciNet): MR899519
  • Rubin, D. B. (1996). Multiple imputation after 18+ years. J. Amer. Statist. Assoc. 91 473–489.
  • Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B. Stat. Methodol. 71 319–392.
    Mathematical Reviews (MathSciNet): MR2649602
    Digital Object Identifier: doi:10.1111/j.1467-9868.2008.00700.x
  • Stephens, M. (2000). Bayesian analysis of mixture models with an unknown number of components—an alternative to reversible jump methods. Ann. Statist. 28 40–74.
    Mathematical Reviews (MathSciNet): MR1762903
    Digital Object Identifier: doi:10.1214/aos/1016120364
    Project Euclid: euclid.aos/1016120364
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
    Mathematical Reviews (MathSciNet): MR1379242
  • Tracey, J. A., Zhu, J. and Crooks, K. (2005). A set of nonlinear regression models for animal movement in response to a single landscape feature. J. Agric. Biol. Environ. Stat. 10 1–18.
  • Van Moorter, B., Visscher, D., Benhamou, S., Börger, L., Boyce, M. S. and Gaillard, J.-M. (2009). Memory keeps you at home: A mechanistic model for home range emergence. Oikos 118 641–652.
  • Warton, D. I. and Shepherd, L. C. (2010). Poisson point process models solve the “pseudo-absence problem” for presence-only data in ecology. Ann. Appl. Stat. 4 1383–1402.
    Mathematical Reviews (MathSciNet): MR2758333
    Digital Object Identifier: doi:10.1214/10-AOAS331
    Project Euclid: euclid.aoas/1287409378
  • Wood, S. N. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 3–36.
    Mathematical Reviews (MathSciNet): MR2797734
    Digital Object Identifier: doi:10.1111/j.1467-9868.2010.00749.x
  • Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B. Stat. Methodol. 68 49–67.
    Mathematical Reviews (MathSciNet): MR2212574
    Digital Object Identifier: doi:10.1111/j.1467-9868.2005.00532.x

Supplemental materials

  • Alternate path imputation distribution.: This supplement contains details of a Brownian bridge path imputation distribution and its use with our CTDS approach to modeling animal movement.
    Digital Object Identifier: doi:10.1214/14-AOAS803SUPP
    Supplemental PDF (155 KB)

The Institute of Mathematical Statistics

Annals of Applied Statistics

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more