Statistical mechanics for natural flocks of birds

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 minim...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS Vol. 109; no. 13; p. 4786
Main Authors: Bialek, William, Cavagna, Andrea, Giardina, Irene, Mora, Thierry, Silvestri, Edmondo, Viale, Massimiliano, Walczak, Aleksandra M
Format: Journal Article
Language:English
Published: United States 27.03.2012
Subjects:
Animals
Biomechanical Phenomena
Entropy
Flight, Animal - physiology
Models, Biological
Models, Statistical
Starlings - physiology
ISSN:1091-6490, 1091-6490
Online Access:Get more information
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Summary: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.
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ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.1118633109