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Information transfer is an essential factor in determining the robustness ofcollective behaviour in biological systems with distributed control. The mostdirect way to study the information transfer mechanisms is to experimentallydetect the propagation across the system of a signal triggered by someperturbation. However, for field experiments this method is inefficient, as thepossibilities of the observer to perturb the group are limited and empiricalobservations must rely on rare natural perturbations. An alternative way is touse spatio-temporal correlations to assess the information transfer mechanismdirectly from the spontaneous fluctuations of the system, without the need tohave an actual propagating signal on record. We test the approach on groundtruth data provided by numerical simulations in three dimensions of two modelsof collective behaviour characterized by very different dynamical equations andinformation transfer mechanisms: the classic Vicsek model, describing anoverdamped noninertial dynamics and the inertial spin model, characterized byan un- derdamped inertial dynamics. By using dynamical finite size scaling, weshow that spatio-temporal correlations are able to distinguish unambiguouslythe diffusive information transfer mechanism of the Vicsek model from thelinear mechanism of the inertial spin model.

Spatio-temporal correlations in models of collective motion ruled by different dynamical laws