Skip to main content
Log in

Abstract

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Brillinger, D. R. Modeling spatial trajectories. In Gelfand, A. E., P. J. Diggle, M. Fuentes, and P. Guttorp, editors, Handbook of Spatial Statistics, chapter 26, pages 463—-475. Chapman & Hall/CRC, Boca Raton, Florida, USA, 2010.

    Chapter  Google Scholar 

  • Brillinger, D. R. and B. S. Stewart. 1998. Elephant-seal movements: Modelling migration. Canadian Journal of Statistics, 26(3):431–443.

    Article  MATH  Google Scholar 

  • Brost, B. M., M. B. Hooten, E. M. Hanks, and R. J. Small. 2015. Animal movement constraints improve resource selection inference in the presence of telemetry error. Ecology, 96(10):2590–2597.

    Article  PubMed  Google Scholar 

  • Buderman, F. E., M. B. Hooten, J. S. Ivan, and T. M. Shenk. 2016. A functional model for characterizing long-distance movement behaviour. Methods in Ecology and Evolution, 7(3):264–273.

    Article  Google Scholar 

  • Fleming, C. H., W. F. Fagan, T. Mueller, K. A. Olson, P. Leimgruber, and J. M. Calabrese. 2015. Estimating where and how animals travel: An optimal framework for path reconstruction from autocorrelated tracking data. Ecology, pages 15–1607.1.

  • Gelfand, A. E. and A. F. M. Smith. 1990. Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85(410):398–409.

    Article  MathSciNet  MATH  Google Scholar 

  • Hanks, E. M., M. B. Hooten, and M. W. Alldredge. 2015. Continuous-time discrete-space models for animal movement. The Annals of Applied Statistics, 9(1):145–165.

    Article  MathSciNet  MATH  Google Scholar 

  • Hanks, E. M., M. B. Hooten, D. S. Johnson, and J. T. Sterling. 2011. Velocity-Based movement modeling for individual and population level inference. PLoS ONE, 6(8):e22795.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • Hanks, E. M. and D. A. Hughes. 2016. Flexible discrete space models of animal movement.

  • Hefley, T. J., K. M. Broms, B. M. Brost, F. E. Buderman, S. L. Kay, H. R. Scharf, J. R. Tipton, P. J. Williams, and M. B. Hooten. 2017. The basis function approach for modeling autocorrelation in ecological data. Ecology, 98(3):632–6446.

    Article  PubMed  Google Scholar 

  • Hooten, M. B., F. E. Buderman, B. M. Brost, E. M. Hanks, and J. S. Ivan. 2016. Hierarchical animal movement models for population-level inference. Environmetrics, 27(6):322–333.

    Article  MathSciNet  Google Scholar 

  • Hooten, M. B. and D. S. Johnson. In Press. Basis function models for animal movement. Journal of the American Statistical Association.

  • Hooten, M. B., D. S. Johnson, E. M. Hanks, and J. H. Lowry. 2010. Agent-based inference for animal movement and selection. Journal of Agricultural, Biological, and Environmental Statistics, 15(4):523–538.

    Article  MathSciNet  MATH  Google Scholar 

  • Hooten, M. B., D. S. Johnson, B. T. McClintock, and J. M. Morales. 2017. Animal Movement: Statistical Models for Telemetry Data. Chapman & Hall/CRC, Boca Raton, Florida, USA.

    Book  Google Scholar 

  • Johnson, D. S., M. B. Hooten, and C. E. Kuhn. 2013. Estimating animal resource selection from telemetry data using point process models. Journal of Animal Ecology, 82(6):1155–1164.

    Article  PubMed  Google Scholar 

  • Johnson, D. S., J. M. London, M.-A. Lea, and J. W. Durban. 2008. Continuous-time correlated random walk model for animal telemetry data. Ecology, 89(5):1208–15.

    Article  PubMed  Google Scholar 

  • Kays, R., M. C. Crofoot, W. Jetz, and M. Wikelski. 2015. Terrestrial animal tracking as an eye on life and planet. Science, 348(6240).

  • Langrock, R., R. King, J. Matthiopoulos, L. Thomas, D. Fortin, and J. M. Morales. 2012. Flexible and practical modeling of animal telemetry data: Hidden Markov models and extensions. Ecology, 93(11):2336–2342.

    Article  PubMed  Google Scholar 

  • Little, R. J. A. and D. B. Rubin. 1987. Statistical Analysis with Missing Data. John Wiley & Sons, New York, New York, USA.

    MATH  Google Scholar 

  • McClintock, B. T. 2017. Incorporating Telemetry Error into Hidden Markov Models of Animal Movement Using Multiple Imputation. Journal of Agricultural, Biological and Environmental Statistics.

  • McClintock, B. T., D. S. Johnson, M. B. Hooten, J. M. Ver Hoef, and J. M. Morales. 2014. When to be discrete: the importance of time formulation in understanding animal movement. Movement Ecology, 2(1):21.

    Article  PubMed  PubMed Central  Google Scholar 

  • McClintock, B. T., J. M. London, M. F. Cameron, and P. L. Boveng. 2015. Modelling animal movement using the Argos satellite telemetry location error ellipse. Methods in Ecology and Evolution, 6(3):266–277.

    Article  Google Scholar 

  • McClintock, B. T., D. J. F. Russell, J. Matthiopoulos, and R. King. 2013. Combining individual animal movement and ancillary biotelemetry data to investigate population-level activity budgets. Ecology, 94(4):838–849.

    Article  Google Scholar 

  • Nelson, E. 1967. Dynamical Theories of Brownian Motion. Princeton University Press, Princeton, New Jersey.

    MATH  Google Scholar 

  • Ormerod, J. T. and M. P. Wand. 2010. Explaining variational approximations. The American Statistician, 64(2):140–153.

    Article  MathSciNet  MATH  Google Scholar 

  • Rubin, D. B. 1996. Multiple imputation after 18+ years. Journal of the American Statistical Association, 91(434):473–489.

    Article  MATH  Google Scholar 

  • —— 2004. Multiple Imputation for Nonresponse in Surveys.John Wiley & Sons, New York, New York, USA.

    MATH  Google Scholar 

  • Scharf, H. R., M. B. Hooten, B. K. Fosdick, D. S. Johnson, J. M. London, and J. W. Durban. 2016. Dynamic social networks based on movement. Annals of Applied Statistics, 10(4):2182–2202.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank Ephraim Hanks for early insights and discussions about the research. Funding for this research was provided by NOAA (RWO 103), CPW (TO 1304), and NSF (DMS 1614392). Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Henry Scharf.

Electronic supplementary material

Below is the link to the electronic supplementary material.

13253_2017_294_MOESM1_ESM.pdf

Supplement A: Implementation details This document contains implementation details and additional results for both simulation studies and the appllication to the movement of a Northern fur seal. (PDF 3.91MB)

13253_2017_294_MOESM2_ESM.zip

Supplement B: Application vignette This vignette shows how the two-stage process imputation procedure was implemented for the application to the movement of a Norther fur seal. (ZIP 3.38MB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Scharf, H., Hooten, M.B. & Johnson, D.S. Imputation Approaches for Animal Movement Modeling. JABES 22, 335–352 (2017). https://doi.org/10.1007/s13253-017-0294-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13253-017-0294-5

Keywords

Navigation