Fig. 6.

Asynchronous switching between information processing modes among individual fish in a group and synchronous heading directions of group members. (A) Example of the simultaneous acceleration (pink)/deceleration (white) profiles of three fish in a group. BL, body length. (B) Same as in A but for the heading direction of the fish. (C, Left) Distributions of time difference (τ_max) that gave the maximum correlations between the kinematic states of pairs of fish for 1-s-long windows in a group of three (colored lines) and shuffled controls (light gray) (SI Materials and Methods). (C, Right) Peak values of the distribution of time difference (τ_max) shown in C, Left in units of SDs for pairs of fish and for shuffled data averaged over all pairs of fish within all groups of three fish (n = 6, P = 0.99, t test for matched samples). (D) Same as in C but for the distribution of time difference (τ_max) of the cross-correlation of direction of motion of pairs of fish. Here, directional correlation shows clear structure and peak times (n = 6, P < 0.0005, t test for matched samples). (E) Average empirical probability distribution P(a₁, a₂, …, a_n) of fish kinematic states (acceleration or deceleration), where a_i represents the state of fish i (solid green), and the prediction of a model assuming independence between fish p(a₁)p(a₂) … p(a_n) (dashed line); shadings represent SEM. (F) Similar to E for the distribution of heading direction P(d₁, d₂, …, d_n), where d_i is the direction of fish i discretized into six evenly sized bins (SI Materials and Methods) (solid green), and the distribution obtained under the assumption of independence p(d₁)p(d₂) … p(d_n) (dashed line).