## Bivariate Gaussian bridges : directional factorization of diffusion in Brownian bridge models

2014
##### Authors
Bartumeus, Frederic
Journal article
Published
##### Published in
Movement Ecology ; 2 (2014). - 5. - BioMed Central. - eISSN 2051-3933
##### Abstract
Background
In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion.

Results
Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk.

Conclusion
We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the “move” package for R.
##### Subject (DDC)
570 Biosciences, Biology
##### Keywords
Dynamic Bivariate Gaussian bridge, Dynamic Brownian bridge movement model, Utilisation distribution, Animal tracking, GPS, Home range and space use modelling
##### Cite This
ISO 690KRANSTAUBER, Bart, Kamran SAFI, Frederic BARTUMEUS, 2014. Bivariate Gaussian bridges : directional factorization of diffusion in Brownian bridge models. In: Movement Ecology. BioMed Central. 2, 5. eISSN 2051-3933. Available under: doi: 10.1186/2051-3933-2-5
BibTex
@article{Kranstauber2014Bivar-52040,
year={2014},
doi={10.1186/2051-3933-2-5},
title={Bivariate Gaussian bridges : directional factorization of diffusion in Brownian bridge models},
volume={2},
journal={Movement Ecology},
author={Kranstauber, Bart and Safi, Kamran and Bartumeus, Frederic},
note={Article Number: 5}
}

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<dcterms:abstract xml:lang="eng">Background&lt;br /&gt;In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion.&lt;br /&gt;&lt;br /&gt;Results&lt;br /&gt;Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk.&lt;br /&gt;&lt;br /&gt;Conclusion&lt;br /&gt;We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the “move” package for R.</dcterms:abstract>
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Yes