Metrics for describing dyadic movement: a review

In movement ecology, the few works that have taken collective behaviour into account are data-driven and rely on simplistic theoretical assumptions, relying in metrics that may or may not be measuring what is intended. In the present paper, we focus on pairwise joint-movement behaviour, where individuals move together during at least a segment of their path. We investigate the adequacy of twelve metrics introduced in previous works for assessing joint movement by analysing their theoretical properties and confronting them with contrasting case scenarios. Two criteria are taken into account for review of those metrics: 1) practical use, and 2) dependence on parameters and underlying assumptions. When analysing the similarities between the metrics as defined, we show how some of them can be expressed using general mathematical forms. In addition, we evaluate the ability of each metric to assess specific aspects of joint-movement behaviour: proximity (closeness in space-time) and coordination (synchrony) in direction and speed. We found that some metrics are better suited to assess proximity and others are more sensitive to coordination. To help readers choose metrics, we elaborate a graphical representation of the metrics in the coordination and proximity space based on our results, and give a few examples of proximity and coordination focus in different movement studies. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1186/s40462-018-0144-2) contains supplementary material, which is available to authorized users.