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Swarming, schooling, milling : phase diagram of a data-driven fish school model

par Clément Sire - 14 mai 2014

Toutes les versions de cet article : English , français

The phase diagram of a model derived from actual experiments (at CRCA Toulouse) reproduces the swarming, schooling, and milling (photo) phases observed generically in fish schools, along with a rare but observed elongated phase.

Abstract of the article : 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 behavioral 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 individual parameters. We also show that milling does not occur for arbitrarily large groups, mainly due to a distance dependence interaction of the model and information propagation delays in the school, which cause conflicting reactions for large groups. We finally discuss the biological significance of our findings, especially the dependence of behavioural transitions on social interactions, which were reported by Gautrais et al. to be adaptive in the experimental conditions.

This work involves biologists from the CRCA, and physicists from the SPEC (CEA-Saclay), and the LPT.

Reference : Daniel Calovi, Ugo Lopez, Sandrine Ngo, Clément Sire, Hugues Chaté and Guy Theraulaz, New J. Phys. 16, 015026 (2014) (including a video abstract)