Redefining membership in animal groups.

Groups of animals-flocks, herds, shoals, and swarms-are often dynamical entities. Relative positions of group members change, and most groups divide and re-form on multiple timescales. Few studies, however, have attempted to define when an animal is or is not within a group. Most authors adopt arbitrary distance thresholds, such as the elective group size (EGS), which assume that animals closer than some threshold distance are in the same group. In the present article, we define a group-membership criterion derived from dynamical statistical considerations and based on detailed trajectories of all members of a moving group. We demonstrate the use of our criterion to track the comings and goings in shoals of zebrafish (Danio rerio) and the gradual dissolution of the shoal across multiple exposures to a testing tank. We present a novel measure of group cohesion based on our group membership criterion and demonstrate that excursions away from the shoal explain some previous observations of the dynamics of shoaling. Finally, we show that excursions away from a shoal are accompanied by an increase in swimming speed. Applying similar criteria to data from other species may clarify some of the common features of animal collective motion.