Swarming, schooling, milling: phase diagram of a data-driven fish school model
We determine the basic phase diagram of the fish school model derived from data by Gautrais et al (2012 PLoS Comput. Biol. 8 e1002678), exploring its parameter space beyond the parameter values determined experimentally on groups of barred flagtails (Kuhlia mugil) swimming in a shallow tank. A modified model is studied alongside the original one, in which an additional frontal preference is introduced in the stimulus/response function to account for the angular weighting of interactions. Our study, mostly limited to groups of moderate size (in the order of 100 individuals), focused not only on the transition to schooling induced by increasing the swimming speed, but also on the conditions under which a school can exhibit milling dynamics and the corresponding behavioural transitions. We show the existence of a transition region between milling and schooling, in which the school exhibits multistability and intermittence between schooling and milling for the same combination of 7