Collective States, Multistability and Transitional Behavior in Schooling Fish
Figure 4
Statistics of state transitions.
(A) Fraction of time spent in the different dynamical states shown for each group size. The error bars are showing the standard deviation measured across replicates. The group of 30 fish is predominantly in the polarized state, but less time is spent in this state with increasing group size (GLM: F1,22 = 36.21, P = 4.6e-06). As the group size increases, the groups gradually spend more time in the milling state (GLM: F1,22 = 19.31, P = 0.00023). The amount of time spent in the transition regime is high, but constant, for all group sizes (GLM: F1,22 = 0.67, P = 0.42). Across all group sizes (GLM: F1,22 = 0.053, P = 0.82) little time is spent in the swarm state. (B) Fraction of transitions from one state to another for the different groups. The error bars are showing the standard deviation measured across replicates. For all group sizes, the polar state predominantly transitions into the swarm state compared to the milling state (GLMM: F1,23 = 58.77, P<0.0001). The swarm state is dominated by transitions into the polarized state (GLMM: F1,23 = 55.69, P<0.0001). Although these transitions are consistent across group sizes, there is a significant interaction between group size and the frequencies of transitioning from the milling state to the swarm and polarized states (GLMM: F1,22 = 13.30, P = 0.0014). While the milling state tended to transition into the polar state, for 300 fish there was a roughly equal probability of transitioning to the polar or swarm states. (C) Rank plots showing the probability of being in a state longer than time Ts before moving into a different regime. There was no significant difference between group sizes in the persistence of the polar state (GLMM: F1,22 = 0.58, P = 0.45), although group size increased the persistence of the transition (F1,22 = 24.52, P = 1e-04) and milling states (F1,22 = 17.54, P = 4.0e-04), and to a lesser degree, the swarm state (F1,22 = 5.31, P = 0.031).