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

CAVAGNA, ANDREA; CULLA, ANTONIO; FENG, XIAO; GIARDINA, IRENE; GRIGERA, TOMAS S.; KION-CROSBY, W; MELILLO, STEFANIA; PISEGNA, GIULIA; POSTIGLIONE, LORENA; VILLEGAS, PABLO

NATURE COMMUNICATIONS

Springer Nature

Año: 2022 vol. 13 p. 2315 - 2315

2041-1723

Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamicand biomechanical constraints of flight. Yet the spatial correlations of such fluctuations arescale-free, namely they have a range as wide as the entire group, a property linked to thecapacity of the system to collectively respond to external perturbations. Scale-free correla-tions and moderate fluctuations set conflicting constraints on the mechanism controlling thespeed 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 confinementthat ignores small deviations from the natural reference value while ferociously suppressinglarger speed fluctuations, is able to reconcile scale-free correlations with biologicallyacceptable group?s speed. We validate our theoretical predictions by comparing them withfield experimental data on starling flocks with group sizes spanning an unprecedented intervalof over two orders of magnitude.