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Local equilibrium in bird flocks

Nature Physics volume 12, pages 1153–1157 (2016)Cite this article

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Abstract

The correlated motion of flocks is an example of global order emerging from local interactions. An essential difference with respect to analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. This non-equilibrium characteristic has been studied theoretically, but its impact on actual animal groups remains to be fully explored experimentally. Here, we introduce a novel dynamical inference technique, based on the principle of maximum entropy, which accommodates network rearrangements and overcomes the problem of slow experimental sampling rates. We use this method to infer the strength and range of alignment forces from data of starling flocks. We find that local bird alignment occurs on a much faster timescale than neighbour rearrangement. Accordingly, equilibrium inference, which assumes a fixed interaction network, gives results consistent with dynamical inference. We conclude that bird orientations are in a state of local quasi-equilibrium over the interaction length scale, providing firm ground for the applicability of statistical physics in certain active systems.

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Figure 1: Performance of the inference methods on the predicted interaction range nc.
Figure 2: Comparison between the two relevant timescales of active matter, as inferred in 14 natural flocks using our inference method based on exact integration.
Figure 3: Inference on natural flocks.

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Acknowledgements

Work in Paris was supported European Research Council Starting Grant 306312. Work in Rome was supported by IIT-Seed Artswarm, European Research Council Starting Grant 257126, and US Air Force Office of Scientific Research Grant FA95501010250 (through the University of Maryland). F.G. acknowledges support from EU Marie Curie ITN grant n. 64256 (COSMOS) and Marie Curie CIG PCIG13-GA-2013-618399.

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Authors and Affiliations

  1. Laboratoire de physique statistique, CNRS, UPMC and École normale supérieure, 24, rue Lhomond, 75005 Paris , France

    Thierry Mora

  2. Laboratoire de physique théorique, CNRS, UPMC and École normale supérieure, 24, rue Lhomond, 75005 Paris, France

    Aleksandra M. Walczak

  3. Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy

    Lorenzo Del Castello, Stefania Melillo, Massimiliano Viale & Irene Giardina

  4. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy

    Lorenzo Del Castello, Stefania Melillo, Leonardo Parisi, Massimiliano Viale, Andrea Cavagna & Irene Giardina

  5. SUPA, Institute for Complex Systems and Mathematical Biology, Kings College, University of Aberdeen, Aberdeen, AB24 3UE, UK

    Francesco Ginelli

  6. Dipartimento di Informatica, Università Sapienza, 00198 Rome, Italy

    Leonardo Parisi

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  1. Thierry Mora
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  8. Andrea Cavagna
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  9. Irene Giardina
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Contributions

A.C., I.G., T.M. and A.M.W. designed the study. A.C., L.D.C., I.G., S.M., L.P. and M.V. acquired and processed the data. A.C., I.G., F.G., T.M. and A.M.W. developed the inference method. A.C., I.G., T.M. and A.M.W. wrote the paper.

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Correspondence to Thierry Mora.

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The authors declare no competing financial interests.

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Mora, T., Walczak, A., Del Castello, L. et al. Local equilibrium in bird flocks. Nature Phys 12, 1153–1157 (2016). https://doi.org/10.1038/nphys3846

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