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
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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 -