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

Speed fluctuations of individual birds within natural flocks are moderate, due to the aerodynamic, energetic 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. Scale-free correlations and limited fluctuations set conflicting constraints on the mechanism controlling the speed of each bird, as the factors boosting correlations tend to amplify fluctuations, and vice versa. Here, using a field-theoretical approach, we demonstrate that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger fluctuations, is the only mechanism reconciling scale-free correlations with biologically acceptable flocks' speed, a result that we confirm through numerical simulations on self-propelled particles in three dimensions. We validate the theoretical as well as the numerical predictions of this analysis by comparing our results with field experimental data on starling flocks having group sizes spanning an unprecedented interval of over two orders of magnitude.