Social interactions dominate speed control in driving natural flocks toward criticality

TL;DR

This study shows that bird flocks operate near a critical point, with social interactions driving long-range correlations in movement, which enhances collective coordination with minimal speed fluctuations.

Contribution

The paper introduces maximum entropy models that accurately predict scale-free correlations in bird flocks, linking collective behavior to criticality in statistical physics.

Findings

Correlations in bird flocks are scale-free and proportional to flock size.

Models accurately reproduce observed velocity correlations.

Flocks operate near a critical point for optimal coordination.

Abstract

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.