Speed fluctuations of individual birds within natural flocks are moderate, as it is natural to expect given the aerodynamic, energetic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations  have a range as wide as the entire group : the speed change of a bird influences and is influenced by that of birds on the other side of the flock. Long-range correlations and limited speed fluctuations set conflicting constraints on the mechanism controlling the individual speed of each bird, as the factors boosting correlations also tend to amplify speed fluctuations and vice versa. Here, building on experimental field data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude, we develop a novel type of speed control mechanism that generates scale-free correlations yet allowing for biologically plausible values of the flocks' speed. The bare-bones hallmark of this new control is a strongly nonlinear speed-restoring force that ignores small deviations of the individual speed from its natural reference value , while ferociously suppressing larger speed fluctuations. Numerical simulations of self-propelled particles flocks in the same size range as the empirical data fully support our theoretical results . The match of field empirical data , theory and simulations over such an extensive range of sizes suggests that the novel speed control we propose is the most economic theoretical mechanism able to reproduce all key experimental traits of real flocks .
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 .
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building on experimental field data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude, we develop a novel type of speed control mechanism that generates scale-free correlations yet allowing for biologically plausible values of the flocks' speed. The bare-bones hallmark of this new control is a strongly nonlinear speed-restoring force that
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flocks in the same size range as the empirical data fully support our theoretical results . The match of field empirical data , theory and simulations over such an extensive range of sizes suggests that the novel speed control we propose is the most economic theoretical mechanism able to reproduce all key experimental traits of real flocks
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