Short-range interactions versus long-range correlations in bird flocks.
Bird flocks are a paradigmatic example of collective motion. One of the prominent traits of flocking is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the maximum entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between individuals. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance, and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.|Initiative for the Theoretical Sciences, The Graduate Center, 365 Fifth Avenue, New York, New York 10016, USA.
Andrea
A
Cavagna
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.
Lorenzo
L
Del Castello
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.
Supravat
S
Dey
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.|Initiative for the Theoretical Sciences, The Graduate Center, 365 Fifth Avenue, New York, New York 10016, USA.
Irene
I
Giardina
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.
Stefania
S
Melillo
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.|Dipartimento di Informatica, Università Sapienza, 00198 Rome, Italy.
Leonardo
L
Parisi
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.|Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.
Massimiliano
M
Viale
D000818:Animals; D001522:Behavior, Animal; D001717:Birds; D019277:Entropy; D016013:Likelihood Functions; D008954:Models, Biological