Statistical mechanics for natural flocks of birds

William Bialek, Andrea Cavagna, Irene Giardina, Thierry Mora, Edmondo Silvestri, Massimiliano Viale, Aleksandra M. Walczak

Research output: Contribution to journalArticlepeer-review

483 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4786-4791
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number13
StatePublished - Mar 27 2012

All Science Journal Classification (ASJC) codes

  • General


  • Animal groups
  • Statistical inference


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