TY - JOUR

T1 - Statistical mechanics for natural flocks of birds

AU - Bialek, William

AU - Cavagna, Andrea

AU - Giardina, Irene

AU - Mora, Thierry

AU - Silvestri, Edmondo

AU - Viale, Massimiliano

AU - Walczak, Aleksandra M.

PY - 2012/3/27

Y1 - 2012/3/27

N2 - 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.

AB - 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.

KW - Animal groups

KW - Statistical inference

UR - http://www.scopus.com/inward/record.url?scp=84859455508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859455508&partnerID=8YFLogxK

U2 - 10.1073/pnas.1118633109

DO - 10.1073/pnas.1118633109

M3 - Article

C2 - 22427355

AN - SCOPUS:84859455508

SN - 0027-8424

VL - 109

SP - 4786

EP - 4791

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 13

ER -