Imputation Approaches for Animal Movement Modeling

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.

[1]  Roland Langrock,et al.  Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions. , 2012, Ecology.

[2]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

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

[4]  Jacob S. Ivan,et al.  Hierarchical animal movement models for population‐level inference , 2016, 1606.09585.

[5]  Brett T McClintock,et al.  When to be discrete: the importance of time formulation in understanding animal movement , 2014, Movement Ecology.

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

[7]  Brett T. McClintock,et al.  Combining individual animal movement and ancillary biotelemetry data to investigate population-level activity budgets , 2013 .

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

[9]  Brett T. McClintock,et al.  Incorporating Telemetry Error into Hidden Markov Models of Animal Movement Using Multiple Imputation , 2017 .

[10]  Edward Nelson Dynamical Theories of Brownian Motion , 1967 .

[11]  D. Brillinger Modeling Spatial Trajectories , 2010 .

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

[13]  Mevin B Hooten,et al.  The basis function approach for modeling autocorrelation in ecological data. , 2016, Ecology.

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

[15]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[16]  D. Rubin Multiple Imputation After 18+ Years , 1996 .

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

[18]  Brett T. McClintock,et al.  Modelling animal movement using the Argos satellite telemetry location error ellipse , 2015 .

[19]  David A. Hughes,et al.  Flexible discrete space models of animal movement , 2016, 1606.07986.

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

[21]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[22]  D. Rubin Multiple imputation for nonresponse in surveys , 1989 .

[23]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[24]  D. Brillinger,et al.  Elephant-seal movements : Modelling migration * , 1998 .

[25]  Mevin B Hooten,et al.  Estimating animal resource selection from telemetry data using point process models. , 2013, The Journal of animal ecology.

[26]  M. Wand,et al.  Explaining Variational Approximations , 2010 .

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

[28]  R. Kays,et al.  Terrestrial animal tracking as an eye on life and planet , 2015, Science.

[29]  Brett T. McClintock,et al.  Animal Movement: Statistical Models for Telemetry Data , 2017 .

[30]  C H Fleming,et al.  Estimating where and how animals travel: an optimal framework for path reconstruction from autocorrelated tracking data. , 2015, Ecology.