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1.3.4.1. Definition of metrics

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Our aim is to identify different activities within a trajectory. In this case, we wish to distinguish between foraging behaviors (associated with rapid changes in direction) and, for example, direct movement toward a point of interest, which results in a straighter trajectory. In this case, turning angle and step length appear to be the most relevant metrics. Biological knowledge concerning the movement of these birds supports the use of these metrics to distinguish between different behaviors.

In this example, we have chosen to adjust two models, which differ in the way in which they treat step length and turning angles (and thus in the associated emission distributions). The two pairs of metrics considered here are as follows:

 – Step length and turning angle: a classic choice, as presented by Morales et al. (2004): the emission distributions in this case are a gamma distribution for step length and a circular (von Mises) distribution for angles. This model will be labeled length/angle in our figures.

 – Bivariate velocity change metric (Gurarie et al. 2009): the emission distributions in this case are two independent normal distributions. This model will be labeled bivariate speed in our figures.

Statistical Approaches for Hidden Variables in Ecology

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