Marginal speed confinement resolves the conflict between correlation and control in collective behaviour

Andrea Cavagna, Antonio Culla (), Xiao Feng, Irene Giardina, Tomas S. Grigera, Willow Kion-Crosby, Stefania Melillo, Giulia Pisegna, Lorena Postiglione and Pablo Villegas
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Andrea Cavagna: UOS Sapienza
Antonio Culla: UOS Sapienza
Xiao Feng: UOS Sapienza
Irene Giardina: UOS Sapienza
Tomas S. Grigera: UOS Sapienza
Willow Kion-Crosby: UOS Sapienza
Stefania Melillo: UOS Sapienza
Giulia Pisegna: UOS Sapienza
Lorena Postiglione: UOS Sapienza
Pablo Villegas: IMT Institute for Advanced Studies

Nature Communications, 2022, vol. 13, issue 1, 1-11

Abstract: 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.

Date: 2022
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DOI: 10.1038/s41467-022-29883-4

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