title: Statistical mechanics for natural flocks of birds.
abstract: Flocking is a typical example of emergent collective behavior, where interactions between individuals produce collective patterns on the large scale. Here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data. We construct the minimally structured (maximum entropy) model consistent with experimental correlations in large flocks of starlings. The maximum entropy model shows that local, pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings, with no free parameters. We also find that the number of interacting neighbors is independent of flock density, confirming that interactions are ruled by topological rather than metric distance. Finally, by comparing flocks of different sizes, the model correctly accounts for the observed scale invariance of long-range correlations among the fluctuations in flight direction.
authors.affiliation: Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA.
authors.forename: William
authors.initials: W
authors.lastname: Bialek
authors.forename: Andrea
authors.initials: A
authors.lastname: Cavagna
authors.forename: Irene
authors.initials: I
authors.lastname: Giardina
authors.forename: Thierry
authors.initials: T
authors.lastname: Mora
authors.forename: Edmondo
authors.initials: E
authors.lastname: Silvestri
authors.forename: Massimiliano
authors.initials: M
authors.lastname: Viale
authors.forename: Aleksandra M
authors.initials: AM
authors.lastname: Walczak
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D019277:Entropy; D005426:Flight, Animal / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D046749:Starlings / Q000502:physiology*