Continuous‐time Correlated Random Walk Model for Animal Telemetry Data

Abstract

We propose a continuous-time version of the correlated random walk model for animal telemetry data. The continuous-time formulation allows data that have been nonuniformly collected over time to be modeled without subsampling, interpolation, or aggregation to obtain a set of locations uniformly spaced in time. The model is derived from a continuous-time Ornstein-Uhlenbeck velocity process that is integrated to form a location process. The continuous-time model was placed into a state-space framework to allow parameter estimation and location predictions from observed animal locations. Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are possible. A harbor seal data set was analyzed with a model that incorporates the proportion of each hour spent on land. Also, a northern fur seal pup data set was analyzed with a random drift component to account for directed travel and ocean currents.

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

“…The behavioural process leads to a flexible range of movement patterns, whilst the continuous-time formulation allows missing and irregular observations to be handled with ease. Movement within a behaviour has some similarities with the velocity-based continuous-time model of Johnson et al (2008a) but is more intuitive, enabling a separation of speed and direction that matches empirical observations well. Parameter interpretation is simpler when separated in this way, describing aspects of movement such as a mean travelling speed and a volatility to the direction of movement.…”

“…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.…”

“…The ability to incorporate behavioural switching, however, is limited, either being highly restricted [setting velocity to zero for a stationary state at known times based on additional tag information (Johnson et al 2008a)], or simplifying to a discrete-time behavioural process (Hanks et al 2011;McClintock et al 2014) or movement process (Breed et al 2012). Similarly, the correlated and biased movement models of Kranstauber et al (2014) use discrete-time methods for estimating the behavioural process.…”

“…An alternative approach to those above is given by Hanks et al (2015) in which movement is defined in discrete space, using a Markov chain to model location switches. The inference method they propose, however, requires imputing continuous-time movement paths via some other movement model [examples include Johnson et al (2008a) and Buderman et al (2016)], therefore inheriting such a model's associated assumptions and limitations.…”

Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”

“…Integrating the sequence of steps results in a stochastic process with long-range structure, and formal specifications of such processes are referred to as Wiener processes or Brownian motion . Johnson et al (2008) imposed additional smoothness on the resulting stochastic processes by letting a stationary form of Brownian motion (i.e., the Ornstein-Uhlenbeck process) describe the velocity process and then integrating it a second time to result in the position process. This idea to use an integrated form of Brownian motion inspired a class of generalized models using basis function specifications to yield different amounts and types of smoothness in the process to model more realistic animal movement trajectories (Hooten and Johnson 2017b).…”