scholarly journals Modeling interdependent animal movement in continuous time

Biometrics ◽  
2016 ◽  
Vol 72 (2) ◽  
pp. 315-324 ◽  
Author(s):  
Mu Niu ◽  
Paul G. Blackwell ◽  
Anna Skarin
Keyword(s):  
Continuous Time ◽  
Animal Movement

scholarly journals Using approximate Bayesian inference for a “steps and turns” continuous-time random walk observed at regular time intervals

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8452
Author(s):  
Sofia Ruiz-Suarez ◽  
Vianey Leos-Barajas ◽  
Ignacio Alvarez-Castro ◽  
Juan Manuel Morales
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Time Scale ◽  
Animal Movement ◽  
State Space Model ◽  
Movement Direction ◽  
Time Intervals ◽  
Space Model ◽  
Regular Time ◽  
Approximate Bayesian

The study of animal movement is challenging because movement is a process modulated by many factors acting at different spatial and temporal scales. In order to describe and analyse animal movement, several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. That is, at any time there is a non-zero probability of making a change in movement direction. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be intractable yet simulating data is straightforward, we conduct inference using different variations of Approximate Bayesian Computation (ABC). We explore the applicability of this approach as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. Simulation results suggest that the model parameters can be recovered if the observation time scale is moderately close to the average time between changes in movement direction. Good estimates were obtained when the scale of observation was up to five times that of the scale of changes in direction. We demonstrate the application of this model to a trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols. In principle, ABC methods allow to make inferences about movement processes defined in continuous time but in terms of easily interpreted steps and turns.

scholarly journals A Continuous-Time Semi-Markov Model for Animal Movement in a Dynamic Environment

2018 ◽  
Author(s):  
Devin S. Johnson ◽  
Noel A. Pelland ◽  
Jeremy T. Sterling
Keyword(s):  
Model Selection ◽  
Continuous Time ◽  
Animal Movement ◽  
Dynamic Environment ◽  
Likelihood Approximation ◽  
Fur Seal ◽  
Posterior Model Probability ◽  
Model Probability ◽  
Dynamic Habitat ◽  
Selection Methodology

AbstractWe consider an extension to discrete-space continuous-time models animal movement that have previously be presented in the literature. The extension from a continuous-time Markov formulation to a continuous-time semi-Markov formulation allows for the inclusion of temporally dynamic habitat conditions as well as temporally changing movement responses by animals to that environment. We show that with only a little additional consideration, the Poisson likelihood approximation for the Markov version can still be used within the multiple imputation framework commonly employed for analysis of telemetry data. In addition, we consider a Bayesian model selection methodology with the imputation framework. The model selection method uses a Laplace approximation to the posterior model probability to provide a computationally feasible approach. The full methodology is then used to analyze movements of 15 northern fur seal (Callorhinus ursinus) pups with respect to surface winds, geostrophic currents, and sea surface temperature. The highest posterior model probabilities belonged to those models containing only winds and current, SST did not seem to be a significant factor for modeling their movement.

scholarly journals Continuous-time discrete-space models for animal movement

2015 ◽  
Vol 9 (1) ◽  
pp. 145-165 ◽  
Author(s):  
Ephraim M. Hanks ◽  
Mevin B. Hooten ◽  
Mat W. Alldredge
Keyword(s):  
Continuous Time ◽  
Animal Movement ◽  
Discrete Space

scholarly journals ExactBayesian inference for animal movement in continuous time

2015 ◽  
Vol 7 (2) ◽  
pp. 184-195 ◽  
Author(s):  
Paul G. Blackwell ◽  
Mu Niu ◽  
Mark S. Lambert ◽  
Scott D. LaPoint
Keyword(s):  
Continuous Time ◽  
Animal Movement

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

2019 ◽  
Vol 10 (11) ◽  
pp. 1894-1907
Author(s):  
Théo Michelot ◽  
Pierre Gloaguen ◽  
Paul G. Blackwell ◽  
Marie‐Pierre Étienne
Keyword(s):  
Habitat Selection ◽  
Continuous Time ◽  
Animal Movement ◽  
Continuous Time Model ◽  
Time Model ◽  
Langevin Diffusion

Flexible continuous-time modelling for heterogeneous animal movement

2013 ◽  
Vol 255 ◽  
pp. 29-37 ◽  
Author(s):  
Keith J. Harris ◽  
Paul G. Blackwell
Keyword(s):  
Continuous Time ◽  
Animal Movement

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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