Social interactions dominate speed control in poising natural flocks near criticality.
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.
Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544; wbialek@princeton.edu.
William
W
Bialek
Unità Operativa di Supporto (UOS) Sapienza, Istituto Sistemi Complessi-Consiglio Nazionale delle Ricerche, 00185 Rome, Italy;Dipartimento di Fisica, Sapienza Universitá di Roma, 00185 Rome, Italy;
Andrea
A
Cavagna
Unità Operativa di Supporto (UOS) Sapienza, Istituto Sistemi Complessi-Consiglio Nazionale delle Ricerche, 00185 Rome, Italy;Dipartimento di Fisica, Sapienza Universitá di Roma, 00185 Rome, Italy;
Irene
I
Giardina
Laboratoire de Physique Statistique de l'École Normale Supérieure, Centre National de la Recherche Scientifique and Universités Paris VI and Paris VII, 75231 Paris Cedex 05, France; and.
Thierry
T
Mora
Unità Operativa di Supporto (UOS) Sapienza, Istituto Sistemi Complessi-Consiglio Nazionale delle Ricerche, 00185 Rome, Italy;Dipartimento di Fisica, Sapienza Universitá di Roma, 00185 Rome, Italy;
Oliver
O
Pohl
Unità Operativa di Supporto (UOS) Sapienza, Istituto Sistemi Complessi-Consiglio Nazionale delle Ricerche, 00185 Rome, Italy;Dipartimento di Fisica, Sapienza Universitá di Roma, 00185 Rome, Italy;
Edmondo
E
Silvestri
Unità Operativa di Supporto (UOS) Sapienza, Istituto Sistemi Complessi-Consiglio Nazionale delle Ricerche, 00185 Rome, Italy;Dipartimento di Fisica, Sapienza Universitá di Roma, 00185 Rome, Italy;
Massimiliano
M
Viale
Laboratoire de Physique Théorique de l'École Normale Supérieure, Centre National de la Recherche Scientifique and Université Paris VI, 75231 Paris Cedex 05, France.
Aleksandra M
AM
Walczak
D000818:Animals; D001522:Behavior, Animal; D019277:Entropy; D005426:Flight, Animal / Q000502:physiology*; D008962:Models, Theoretical; D009068:Movement; D012919:Social Behavior; D046749:Starlings / Q000502:physiology*
collective behavior; statistical mechanics