A spatially varying stochastic differential equation model for animal movement

Russell, James C.; Hanks, Ephraim M.; Haran, Murali; Hughes, David A.

doi:10.1214/17-aoas1113

Cited by 22 publications

(52 citation statements)

References 53 publications

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“…In this paper, we used the Euler discretization scheme to obtain pseudo maximum likelihood estimators. This scheme is the most widely used method to carry out inference for discretely observed diffusion processes, when the transition density is not analytically tractable (see Brillinger, 2010;Preisler et al, 2004;Russell, Hanks, Haran, & Hughes, 2018, for applications in ecology). There exist other pseudo-likelihood approaches, and Gloaguen et al (2018) argued that better inferences could be obtained with more refined schemes.…”

Section: Discussionmentioning

confidence: 99%

The Langevin diffusion as a continuous‐time model of animal movement and habitat selection

et al. 2019

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The utilization distribution of an animal describes the relative probability of space use. It is natural to think of it as the long‐term consequence of the animal's short‐term movement decisions: it is the accumulation of small displacements which, over time, gives rise to global patterns of space use. However, many estimation methods for the utilization distribution either assume the independence of observed locations and ignore the underlying movement (e.g. kernel density estimation), or are based on simple Brownian motion movement rules (e.g. Brownian bridges). We introduce a new continuous‐time model of animal movement, based on the Langevin diffusion. This stochastic process has an explicit stationary distribution, conceptually analogous to the idea of the utilization distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilization) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. Standard approximation techniques can be used to derive the pseudo‐likelihood of the Langevin diffusion movement model, and to estimate habitat preference and movement parameters from tracking data. We investigate the performance of the method on simulated data, and discuss its sensitivity to the time scale of the sampling. We present an example of its application to tracking data of Steller sea lions Eumetopias jubatus. Due to its continuous‐time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat‐dependent utilization distribution, and it provides a rigorous framework to estimate long‐term habitat selection from correlated movement data. The Langevin movement model can be written as a linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking.

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Section: Discussionmentioning

confidence: 99%

The Langevin diffusion as a continuous‐time model of animal movement and habitat selection

et al. 2019

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“…Animal movement models have also been developed to account for more mechanistic interactions among individuals (e.g., Russell et al, 2016;Scharf et al, 2015), and while we did not address those specifically, the approach we presented may also be beneficial in those settings. Furthermore, Bayesian animal movement models have been fit using integrated nested Laplace approximation (INLA; Rue et al, 2009;Illian et al, 2012;Illian et al, 2013;Ruiz-Cárdenas et al, 2012;Jonsen, 2016), and one could use INLA to fit the hierarchical point process model in our first example.…”

Section: Resultsmentioning

confidence: 99%

Hierarchical animal movement models for population‐level inference

et al. 2016

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Summary: New methods for modeling animal movement based on telemetry data are developed regularly.With advances in telemetry capabilities, animal movement models are becoming increasingly sophisticated.Despite a need for population-level inference, animal movement models are still predominantly developed for individual-level inference. Most efforts to upscale the inference to the population-level are either post hoc or complicated enough that only the developer can implement the model. Hierarchical Bayesian models provide an ideal platform for the development of population-level animal movement models but can be challenging to fit due to computational limitations or extensive tuning required. We propose a two-stage procedure for fitting hierarchical animal movement models to telemetry data. The two-stage approach is statistically rigorous and allows one to fit individual-level movement models separately, then resample them using a secondary MCMC algorithm. The primary advantages of the two-stage approach are that the first stage is easily parallelizable and the second stage is completely unsupervised, allowing for a completely automated fitting procedure in many cases. We demonstrate the two-stage procedure with two applications of animal movement models. The first application involves a spatial point process approach to modeling telemetry data and the second involves a more complicated continuous-time discrete-space animal movement model. We fit these models to simulated data and real telemetry data arising from a population of monitored Canada lynx in Colorado, USA.

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“…The form of φ in (3.7) defines the expected drift as descending (or ascending if α < 0) along the gradient of the SST field, with a velocity that depends both on the temperature at the present location and a scalar α. This is somewhat similar to the varying motility surface used by Russell et al (2018) in an stochastic differential equation (SDE) model to allow the magnitude of the velocity vector to depend on the location. More specifically, we can view the latent field S as a scaled potential surface in which the gradient of S directs the expected movement with a velocity that also depends on the value of S at that location.…”

Section: A Preferential Movement Modelmentioning

confidence: 91%

Modelling ocean temperatures from bio-probes under preferential sampling

Dinsdale¹,

Salibián‐Barrera²

2019

Ann. Appl. Stat.

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In the last 25 years there has been an important increase in the amount of data collected from animal-mounted sensors (bio-probes), which are often used to study the animals' behaviour or environment. We focus here on an example of the latter, where the interest is in sea surface temperature (SST), and measurements are taken from sensors mounted on Elephant Seals in the Southern Indian ocean. We show that standard geostatistical models may not be reliable for this type of data, due to the possibility that the regions visited by the animals may depend on the SST. This phenomenon is know in the literature as preferential sampling, and, if ignored, it may affect the resulting spatial predictions and parameter estimates. Research on this topic has been mostly restricted to stationary sampling locations such as monitoring sites. The main contribution of this manuscript is to extend this methodology to observations obtained by devices that move through the region of interest, as is the case with the tagged seals. More specifically, we propose a flexible framework for inference on preferentially sampled fields, where the process that generates the sampling locations is stochastic and moving over time through a 2dimensional space. Our simulation studies confirm that predictions obtained from the preferential sampling model are more reliable when this phenomenon is present, and they compare very well to the standard ones when there is no preferential sampling. Finally, we note that the conclusions of our analysis of the SST data can change considerably when we incorporate preferential sampling in the model.

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A spatially varying stochastic differential equation model for animal movement

Cited by 22 publications

References 53 publications

The Langevin diffusion as a continuous‐time model of animal movement and habitat selection

The Langevin diffusion as a continuous‐time model of animal movement and habitat selection

Hierarchical animal movement models for population‐level inference

Modelling ocean temperatures from bio-probes under preferential sampling

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