DOI: 10.1073/pnas.1118633109. Statistical mechanics for natural flocks of birds

Statistical mechanics for natural flocks of birds

10.1073/pnas.1118633109

Crossref journal-article

Proceedings of the National Academy of Sciences

Proceedings of the National Academy of Sciences (341)

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.

Bibliography

Bialek, W., Cavagna, A., Giardina, I., Mora, T., Silvestri, E., Viale, M., & Walczak, A. M. (2012). Statistical mechanics for natural flocks of birds. Proceedings of the National Academy of Sciences, 109(13), 4786â4791.

Authors 7

William Bialek (first)
Andrea Cavagna (additional)
Irene Giardina (additional)
Thierry Mora (additional)
Edmondo Silvestri (additional)
Massimiliano Viale (additional)
Aleksandra M. Walczak (additional)

References 36 Referenced 602

S Camazine, et al. Self-Organization in Biological Systems (Princeton Univ Press, Princeton, 2003). / Self-Organization in Biological Systems by Camazine S (2003)
10.1126/science.177.4047.393
10.1038/scientificamerican0879-158
10.1016/S0065-3454(03)01001-5
J Binney, NJ Dowrick, AJ Fisher, MEJ Newman The Theory of Critical Phenomena (Oxford Univ Press, Oxford, 1992). (10.1093/oso/9780198513940.001.0001) / The Theory of Critical Phenomena by Binney J (1992)
10.1103/PhysRevLett.75.1226
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10.1103/PhysRevE.58.4828
10.1103/PhysRevLett.92.025702
10.1103/PhysRev.106.620
10.1016/j.anbehav.2008.02.004
10.1016/j.anbehav.2008.02.002
10.1016/j.anbehav.2008.02.003
10.1073/pnas.0711437105
10.1103/PhysRevLett.106.090601
10.1103/PhysRevE.83.051123
10.1073/pnas.1005766107
10.1142/S0218202510004660
10.1073/pnas.1001763107
10.1073/pnas.1107583108
10.1073/pnas.1109355108
10.1038/nature04701
G Tkačik E Schneidman MJ Berry W Bialek Ising models for networks of real neurons. arXiv:q-bio/0611072. (2006).
10.1523/JNEUROSCI.1282-06.2006
10.1073/pnas.0609152103
G Tkačik Information flow in biological networks. (Princeton University Princeton NJ Dissertation. (2007).
W Bialek R Ranganathan Rediscovering the power of pairwise interactions. arXiv:0712.4397 [q-bio.QM]. (2007).
10.1523/JNEUROSCI.3359-07.2008
10.1093/cercor/bhn047
G Tkačik E Schneidman ML Berry W Bialek Spin glass models for networks of real neurons. arXiv:0912.5409 [q-bio.NC]. (2009).
10.1073/pnas.0805923106
10.1016/j.cell.2009.07.038
10.1073/pnas.1001705107
10.1103/PhysRevE.81.066119
10.1007/s10955-011-0229-4
10.1103/PhysRev.102.1217

Dates

Type	When
Created	13 years, 5 months ago (March 17, 2012, 12:20 a.m.)
Deposited	1 year, 4 months ago (April 21, 2024, 11:50 a.m.)
Indexed	4 days, 1 hour ago (Aug. 20, 2025, 9:15 a.m.)
Issued	13 years, 5 months ago (March 16, 2012)
Published	13 years, 5 months ago (March 16, 2012)
Published Online	13 years, 5 months ago (March 16, 2012)
Published Print	13 years, 4 months ago (March 27, 2012)

Funders 0

None

BibTeX

@article{Bialek_2012, title={Statistical mechanics for natural flocks of birds}, volume={109}, ISSN={1091-6490}, url={http://dx.doi.org/10.1073/pnas.1118633109}, DOI={10.1073/pnas.1118633109}, number={13}, journal={Proceedings of the National Academy of Sciences}, publisher={Proceedings of the National Academy of Sciences}, author={Bialek, William and Cavagna, Andrea and Giardina, Irene and Mora, Thierry and Silvestri, Edmondo and Viale, Massimiliano and Walczak, Aleksandra M.}, year={2012}, month=mar, pages={4786–4791} }

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