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

Kranstauber B, Safi K, Bartumeus F - Mov Ecol (2014)

Bottom Line: 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 find that many of the animal trajectories do not adhere to the assumptions of the BBMM.Our novel approach is implemented and available within the "move" package for R.

View Article: PubMed Central - PubMed

Affiliation: Department for Migration and Immuno-ecology, Max Planck Institute for Ornithology, Radolfzell, Germany ; Department of Biology, University of Konstanz, Konstanz, Germany.

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.

No MeSH data available.


Related in: MedlinePlus

The median values ofσm(A),σm,o(B),σm,p(C) andId(D) and the performance index (E) in relation to the parameters of the simulated correlated random walks in separate panels. The movement scales (i.e., step sizes) are indicated on the x axis while correlation of the turning angles is on the y axis. On the upper plots colour represents the variance values, while on the lower plots colour indicates Id and the performance index. The lines represent isoclines as a visual guide for investigating the differences. Note that both axes are log transformed.
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Fig3: The median values ofσm(A),σm,o(B),σm,p(C) andId(D) and the performance index (E) in relation to the parameters of the simulated correlated random walks in separate panels. The movement scales (i.e., step sizes) are indicated on the x axis while correlation of the turning angles is on the y axis. On the upper plots colour represents the variance values, while on the lower plots colour indicates Id and the performance index. The lines represent isoclines as a visual guide for investigating the differences. Note that both axes are log transformed.

Mentions: The correlated random walk simulations showed that with increasing movement scales (step sizes) both σm,p and σm,o increase (Figure 3B, C). In addition, the orthogonal standard deviation σm,o increased as the correlation of the random walk decreased. The Brownian motion standard deviation (Figure 3A) followed largely σm,p but was more influenced by a decrease in the correlation of the correlated random walk. The index of directionality Id increased with increasing correlation but was not influenced by the movement scale (Figure 3D). Only in the region of both high correlation and small movement scales, Id became scale dependent. This was due to the effect of the location error, shown in the Additional file 1 by repeating the same analysis on the same tracks with a higher location error. The performance index increased when Id increased, at higher values for Id (0.5 and up) the performance index doubled (or more) (Figure 3E). This means that the estimated UD associated to the locations omitted for the cross validation doubled.Figure 3


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

Kranstauber B, Safi K, Bartumeus F - Mov Ecol (2014)

The median values ofσm(A),σm,o(B),σm,p(C) andId(D) and the performance index (E) in relation to the parameters of the simulated correlated random walks in separate panels. The movement scales (i.e., step sizes) are indicated on the x axis while correlation of the turning angles is on the y axis. On the upper plots colour represents the variance values, while on the lower plots colour indicates Id and the performance index. The lines represent isoclines as a visual guide for investigating the differences. Note that both axes are log transformed.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4416317&req=5

Fig3: The median values ofσm(A),σm,o(B),σm,p(C) andId(D) and the performance index (E) in relation to the parameters of the simulated correlated random walks in separate panels. The movement scales (i.e., step sizes) are indicated on the x axis while correlation of the turning angles is on the y axis. On the upper plots colour represents the variance values, while on the lower plots colour indicates Id and the performance index. The lines represent isoclines as a visual guide for investigating the differences. Note that both axes are log transformed.
Mentions: The correlated random walk simulations showed that with increasing movement scales (step sizes) both σm,p and σm,o increase (Figure 3B, C). In addition, the orthogonal standard deviation σm,o increased as the correlation of the random walk decreased. The Brownian motion standard deviation (Figure 3A) followed largely σm,p but was more influenced by a decrease in the correlation of the correlated random walk. The index of directionality Id increased with increasing correlation but was not influenced by the movement scale (Figure 3D). Only in the region of both high correlation and small movement scales, Id became scale dependent. This was due to the effect of the location error, shown in the Additional file 1 by repeating the same analysis on the same tracks with a higher location error. The performance index increased when Id increased, at higher values for Id (0.5 and up) the performance index doubled (or more) (Figure 3E). This means that the estimated UD associated to the locations omitted for the cross validation doubled.Figure 3

Bottom Line: 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 find that many of the animal trajectories do not adhere to the assumptions of the BBMM.Our novel approach is implemented and available within the "move" package for R.

View Article: PubMed Central - PubMed

Affiliation: Department for Migration and Immuno-ecology, Max Planck Institute for Ornithology, Radolfzell, Germany ; Department of Biology, University of Konstanz, Konstanz, Germany.

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.

No MeSH data available.


Related in: MedlinePlus