Finite-size scaling as a way to probe near-criticality in natural swarms

TL;DR

This study shows that natural midge swarms adjust their size and control parameters to maintain a scaling behavior of correlations, indicating they operate near a critical point despite finite size effects.

Contribution

It provides experimental evidence that biological swarms tune their parameters to sustain near-critical correlations across different sizes.

Findings

Swarms maintain a scaling behavior of the correlation function.

Correlation length and susceptibility scale with swarm size.

Swarms exhibit near-maximal correlation at all sizes.

Abstract

Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological systems, though, are typically quite far from the thermodynamic limit, so that the value of the control parameter at which correlation and susceptibility peak depend on size. Hence, a system would need to readjust its control parameter according to its size in order to be maximally correlated. This readjustment, though, has never been observed experimentally. By gathering three-dimensional data on swarms of midges in the field we find that swarms tune their control parameter and size so as to maintain a scaling behaviour of the correlation function. As a consequence, correlation length and susceptibility scale with the system's size and swarms exhibit a near-maximal degree of correlation at all sizes.