Statistical mechanics for natural flocks of birds

By William Bialek, Andrea Cavagna, Irene Giardina, Thierry Mora, Edmondo Silvestri, Massimiliano Viale, Aleksandra M. Walczak. Proceedings of the National Academy of Sciences of the United States of America, 2011

727 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/175602dd006420073d172f0c5dd3fbc2a3704c4d

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Citations in the corpus

Colloquium: Criticality and dynamical scaling in living systems (2017, methodology): “Bialek et al. (2012) applied a maximum entropy method to construct a statistical model consistent with the empirically measured correlations (see Appendix B).”
The statistical physics of active matter: From self-catalytic colloids to living cells (2017, background): “4, is also often controlled by alignment interactions [14,63].”
From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction (2012, unknown): “MaxEnt has been used to analyze many types of biological data, ranging from multi-electrode recording of neural activities [25,26], gene concentrations in genetic networks [27], bird flocking [28] etc.”
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Inverse statistical problems: from the inverse Ising problem to data science (2017, methodology): “In [27, 28], a model with pairwise interactions between the velocities of birds in a ﬂock is constructed.”
Symmetry, Thermodynamics, and Topology in Active Matter (2021, background): “[219] William Bialek, Andrea Cavagna, Irene Giardina, Thierry Mora, Edmondo Silvestri, Massimiliano Viale, and Aleksandra M Walczak, “Statistical mechanics for natural flocks”
Deciphering Interactions in Moving Animal Groups (2012, background): “argued that this is also the case for groups of three golden shiners [28] (but see [39] for the case of birds).”
Oscillators that sync and swarm (2017, background): “Fish schools, bird flocks, and insect swarms [22–26] have been illuminated by maximum entropy methods [27], agent-based simulations [28], and analytically tractable models based on self-propelled particles [29], and continuum limits [30–33].”
Griffiths phases and the stretching of criticality in brain networks (2013, background): “As a consequence, it is commonly assumed that the critical dynamics of Equation (4) at l¼ lc is dominated by the leading eigenvalue Lmax and that, at the threshold lc, qi cðLmaxÞfiðLmaxÞ: ð6Þ Then one can impose the steady-state condition _qi(t)¼ 0 and, under the fundamental assumption of equation (”
Ad hoc teamwork for leading a flock (2013, background): “Research on flocking behavior can be found in various disciplines, for example in physics [14], graphics [9], biology [2, 3], and distributed control theory [6, 7, 12].”
Tuned, driven, and active soft matter (2015, background): “rules [646, 647]: the interactions occur with a fixed number of nearest neighbors instead of all neighbors within a fixed interaction distance.”