Fig. 5

Phenotypic groups emerge by clustering individual fish based on their behavioral dynamics. (A) Pairwise distance matrix between the transition matrices of individual fish at . We find structure across multiple scales, with prey exposure being an important source of variability. (B) We use a constant shift embedding (CSE) to map distances onto an Euclidean space that preserves the pairwise distances among individual fish (gray dots). We plot the first two dimensions of the transition matrix space with example matrices displayed for two individuals (red dots). We test whether two fish behave significantly differently over the experimental timescale by re-estimating transition matrices from finite simulations of each fish?s and calculating the distance between the re-estimated and original transition matrices (blue area around example fish). Averaging these distances sets an effective scale (blue area around example fish) within which neighboring fish are indistinguishable from each other (SI Appendix). (C) Left, illustration of our clustering approach as a tree diagram, with the distance matrix organized according to the cluster assignment. We structure the phenotypic space through a top?down subdivision of a multiplicative diffusion process [hierarchical multiplicative diffusive (HMD) clustering] where distances are rescaled by . At each iteration , the group of fish that is most separable is subdivided so that the ordering of subdivisions is indicative of the relative scale separation among fish from different groups. We stop the clustering at the point beyond which the effective distances between fish within clusters stop decreasing ( , 7 clusters, vertical dashed line; see SI Appendix, Fig. S6B). The widths of the branches of the tree are proportional to the number of fish in each cluster. (C) Right, individual fish are color-coded by their most likely phenotypic group , where . Dot size indicates the posterior probability . (D) Clustering reveals different phenotypic groups : Groups exhibit a bias toward fast cruising (with also exhibiting fast wandering and also exhibiting slow cruising and wandering) while groups share a bias toward slow cruising and wandering (with exhibiting also faster cruising) and groups use mostly fast wandering, with some slow cruising and wandering also for . (E) Probability of either hunting (E1) or detecting (E2) resources for the phenotypic groups, as in Fig. 3B (SI Appendix, Fig. S5). (E1) Probability of hunting prey within 3 bouts (SI Appendix, Fig. S5A), at a distance of (41) and within a cone of ahead of the fish (40): group , which biased toward slow cruising and wandering strategies, is the most effective at gathering prey. (E2) Probability of detecting uniformly distributed resources with a radius : groups are effective for short to meso-length scale search, while are most effective at large scale dispersal. Group is approximately equally efficient across a broad range of length scales (black line, average of all groups).