Marginal speed confinement resolves the conflict between correlation and control in natural flocks of birds

TL;DR

This paper introduces a marginal speed confinement mechanism that explains how bird flocks maintain scale-free correlations in speed fluctuations while keeping individual speeds within biologically acceptable limits, supported by field data.

Contribution

It proposes a novel statistical field theory model for bird flock speed control that reconciles scale-free correlations with moderate individual speed fluctuations.

Findings

The model predicts scale-free correlations in bird speeds.

Field data from starling flocks support the model's predictions.

Speed fluctuations are confined to biologically feasible ranges.

Abstract

Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations are scale-free, namely they have a range as wide as the entire group, a property linked to the capacity of the system to collectively respond to external perturbations. Scale-free correlations and moderate fluctuations set conflicting constraints on the mechanism controlling the speed of each agent, as the factors boosting correlation amplify fluctuations, and vice versa. Here, using a statistical field theory approach, we suggest that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations, is able to reconcile scale-free correlations with biologically acceptable group's speed. We validate our theoretical predictions by comparing them with field experimental data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude.