Short-range interaction vs long-range correlation in bird flocks

TL;DR

This paper uses the Maximum Entropy approach to analyze bird flock data, revealing that effective interactions between birds decay exponentially over short distances despite long-range velocity correlations, highlighting the method's ability to identify minimal interaction parameters.

Contribution

It advances previous studies by retrieving the full functional dependence of bird interactions on distance, demonstrating the effectiveness of ME in distinguishing relevant interaction information.

Findings

Interactions decay exponentially over a few individuals

Long-range correlations do not imply long-range interactions

Method captures anisotropy in mutual interactions

Abstract

Bird flocks are a paradigmatic example of collective motion. One of the prominent experimental traits discovered about flocks 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 birds. 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.