Exact Bayesian inference for animal movement in continuous time

Abstract

Summary1. It is natural to regard most animal movement as a continuous-time process, generally observed at discrete times. Most existing statistical methods for movement data ignore this; the remainder mostly use discrete-time approximations, the statistical properties of which have not been widely studied, or are limited to special cases. We aim to facilitate wider use of continuous-time modelling for realistic problems. 2. We develop novel methodology which allows exact Bayesian statistical analysis for a rich class of movement models with behavioural switching in continuous time, without any need for time discretization error. We represent the times of changes in behaviour as forming a thinned Poisson process, allowing exact simulation and Markov chain Monte Carlo inference. The methodology applies to data that are regular or irregular in time, with or without missing values. 3. We apply these methods to GPS data from two animals, a fisher (Pekania [Martes] pennanti) and a wild boar (Sus scrofa), using models with both spatial and temporal heterogeneity. We are able to identify and describe differences in movement behaviour across habitats and over time. 4. Our methods allow exact fitting of realistically complex movement models, incorporating environmental information. They also provide an essential point of reference for evaluating other existing and future approximate methods for continuous-time inference.

Classification of Animal Movement Behavior through Residence in Space and Time

“…Analysis of the high-resolution fisher track ( R = 40 m) through an urban habitat, reflects discrete and clustered locations of periodic short-term resting places [29], with more dispersed searching/foraging locations interspersed with relatively linear transit segments (Fig 6a). RST classification of resting/stationary behavior states in this fisher track was not influenced by the less frequent GPS sampling caused by accelerometer-informed data loggers because RT is a cumulative measure of time spent within circle of radius R and therefore a resting fisher would accumulate the same RT value regardless of GPS sampling frequency.…”

Bayesian Inference for Multistate ‘Step and Turn’ Animal Movement in Continuous Time

“…on (x, y) locations (Johnson et al 2008a;Blackwell et al 2015) could be applied, with postprocessing to determine the distribution of speed and bearing, the covariance structure of such distributions, and hence the implicit shapes of the paths, will not be the same as that presented here. Ecological justification for such a covariance structure may be difficult or lacking, whereas our model is directly defined by these quantities and therefore initially motivated by ecological ideas.…”

“…Depending on the duration of study, it may also be useful to allow varying rates with time, perhaps periodically to reflect daily or annual cycles. Both these extensions could be addressed, without any additional approximation, using the framework in Blackwell et al (2015), applied there to movement models directly based on location (rather than velocity or steps and turns) with heterogeneity in both space and time. More generally, we could capture some more of the complexity of behaviour by including an additional 'resting' state, likely to occur at particular times of the day, with low or zero speed and perhaps a high volatility to represent the 'forgetting' of bearing whilst resting.…”

“…To reflect the changing behaviours of an animal over time, a switching model is employed, with different movement characteristics for each state (Blackwell 1997;Morales et al 2004;McClintock et al 2012;Blackwell et al 2015). The behavioural process is taken to be a continuous-time Markov chain with switching rates λ and probabilities q (Guttorp 1995).…”

“…Similarly, the correlated and biased movement models of Kranstauber et al (2014) use discrete-time methods for estimating the behavioural process. Blackwell et al (2015) overcome these limitations by modelling location and allowing for a rich class of behavioural processes dependent on both environmental covariates and time via continuous-time Markov chains. A set of models able to incorporate a range of movement assumptions including the home range movement of Blackwell et al (2015) are given in Fleming et al (2014), basing inference on the semivariance function of the underlying movement.…”