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Reflected Stochastic Differential Equation Models for Constrained Animal Movement

Author

Listed:
  • Ephraim M. Hanks

    (The Pennsylvania State University)

  • Devin S. Johnson

    (NOAA Fisheries)

  • Mevin B. Hooten

    (U.S. Geological Survey
    Colorado State University)

Abstract

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, 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.

Suggested Citation

  • Ephraim M. Hanks & Devin S. Johnson & Mevin B. Hooten, 2017. "Reflected Stochastic Differential Equation Models for Constrained Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 353-372, September.
    • Handle: RePEc:spr:jagbes:v:22:y:2017:i:3:d:10.1007_s13253-017-0291-8
    DOI: 10.1007/s13253-017-0291-8
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    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Devin S. Johnson & Dana L. Thomas & Jay M. Ver Hoef & Aaron Christ, 2008. "A General Framework for the Analysis of Animal Resource Selection from Telemetry Data," Biometrics, The International Biometric Society, vol. 64(3), pages 968-976, September.
    3. Mevin B. Hooten & Devin S. Johnson, 2017. "Basis Function Models for Animal Movement," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 578-589, April.
    4. Rex Dalton, 2005. "Is this any way to save a species?," Nature, Nature, vol. 436(7047), pages 14-16, July.
    5. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    6. Ephraim M Hanks & Mevin B Hooten & Devin S Johnson & Jeremy T Sterling, 2011. "Velocity-Based Movement Modeling for Individual and Population Level Inference," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-17, August.
    7. Ephraim M. Hanks & Mevin B. Hooten, 2013. "Circuit Theory and Model-Based Inference for Landscape Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 22-33, March.
    8. Mevin B. Hooten & Christopher K. Wikle & Robert M. Dorazio & J. Andrew Royle, 2007. "Hierarchical Spatiotemporal Matrix Models for Characterizing Invasions," Biometrics, The International Biometric Society, vol. 63(2), pages 558-567, June.
    9. Amanda R. Cangelosi & Mevin B. Hooten, 2009. "Models for Bounded Systems with Continuous Dynamics," Biometrics, The International Biometric Society, vol. 65(3), pages 850-856, September.
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    Cited by:

    1. Dhanushi A Wijeyakulasuriya & Elizabeth W Eisenhauer & Benjamin A Shaby & Ephraim M Hanks, 2020. "Machine learning for modeling animal movement," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-30, July.
    2. James C. Russell & Ephraim M. Hanks & Andreas P. Modlmeier & David P. Hughes, 2017. "Modeling Collective Animal Movement Through Interactions in Behavioral States," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 313-334, September.
    3. Elizabeth Eisenhauer & Ephraim Hanks, 2020. "A lattice and random intermediate point sampling design for animal movement," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.
    4. Mevin B. Hooten & Ruth King & Roland Langrock, 2017. "Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 224-231, September.

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