TY - JOUR
T1 - Social interactions dominate speed control in poising natural flocks near criticality
AU - Bialek, William
AU - Cavagna, Andrea
AU - Giardina, Irene
AU - Mora, Thierry
AU - Pohl, Oliver
AU - Silvestri, Edmondo
AU - Viale, Massimiliano
AU - Walczak, Aleksandra M.
PY - 2014/5/20
Y1 - 2014/5/20
N2 - Flocks of birds exhibit a remarkable degree of coordination and collective response. It is not just that thousands of individuals fly, on average, in the same direction and at the same speed, but that even the fluctuations around the mean velocity are correlated over long distances. Quantitative measurements on flocks of starlings, in particular, show that these fluctuations are scale-free, with effective correlation lengths proportional to the linear size of the flock. Here we construct models for the joint distribution of velocities in the flock that reproduce the observed local correlations between individuals and their neighbors, as well as the variance of flight speeds across individuals, but otherwise have as little structure as possible. These minimally structured or maximum entropy models provide quantitative, parameter-free predictions for the spread of correlations throughout the flock, and these are in excellent agreement with the data. These models are mathematically equivalent to statistical physics models for ordering in magnets, and the correct prediction of scale-free correlations arises because the parameters- completely determined by the data-are in the critical regime. In biological terms, criticality allows the flock to achieve maximal correlation across long distances with limited speed fluctuations.
AB - Flocks of birds exhibit a remarkable degree of coordination and collective response. It is not just that thousands of individuals fly, on average, in the same direction and at the same speed, but that even the fluctuations around the mean velocity are correlated over long distances. Quantitative measurements on flocks of starlings, in particular, show that these fluctuations are scale-free, with effective correlation lengths proportional to the linear size of the flock. Here we construct models for the joint distribution of velocities in the flock that reproduce the observed local correlations between individuals and their neighbors, as well as the variance of flight speeds across individuals, but otherwise have as little structure as possible. These minimally structured or maximum entropy models provide quantitative, parameter-free predictions for the spread of correlations throughout the flock, and these are in excellent agreement with the data. These models are mathematically equivalent to statistical physics models for ordering in magnets, and the correct prediction of scale-free correlations arises because the parameters- completely determined by the data-are in the critical regime. In biological terms, criticality allows the flock to achieve maximal correlation across long distances with limited speed fluctuations.
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U2 - 10.1073/pnas.1324045111
DO - 10.1073/pnas.1324045111
M3 - Article
C2 - 24785504
AN - SCOPUS:84900993138
SN - 0027-8424
VL - 111
SP - 7212
EP - 7217
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 20
ER -