1. The Langevin diffusion as a continuous‐time model of animal movement and habitat selection
- Author
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Théo Michelot, Marie-Pierre Etienne, Pierre Gloaguen, Paul G. Blackwell, University of Sheffield [Sheffield], AgroParisTech, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Leverhulme Trust, University of St Andrews. Statistics, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
- Subjects
0106 biological sciences ,Utilization distribution ,Computer science ,potential function ,Step selection ,QH301 Biology ,habitat selection ,Langevin diffusion ,010603 evolutionary biology ,01 natural sciences ,Resource selection ,Stochastic differential equation ,QH301 ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,Statistical physics ,QA Mathematics ,QA ,step selection ,Animal movement ,Ecology, Evolution, Behavior and Systematics ,Independence (probability theory) ,Brownian motion ,Selection (genetic algorithm) ,Utilisation distribution ,utilization distribution ,continuous time ,Stationary distribution ,Stochastic process ,010604 marine biology & hydrobiology ,Ecological Modeling ,Potential function ,DAS ,resource selection ,animal movement ,utilisation distribution ,Langevin equation ,Continuous time ,[SDE]Environmental Sciences - Abstract
TM was supported by the Centre for Advanced Biological Modelling at the University of Sheffield, funded by the Leverhulme Trust, award number DS-2014-081. 1. The utilisation 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 utilisation 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). 2. 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 utilisation distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilisation) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. 3. 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). 4. Due to its continuous-time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat-dependent utilisation distribution, and it provides a rigorous framework to estimate long-term habitat selection from correlated movement data. The Langevin movement model can be approximated by linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking. Postprint
- Published
- 2019