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

Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect the propagation across the system of a signal triggered by some perturbation. However, for field experiments this method is inefficient, as the possibilities of the observer to perturb the group are limited and empirical observations must rely on rare natural perturbations. An alternative way is to use spatio-temporal correlations to assess the information transfer mechanism directly from the spontaneous fluctuations of the system, without the need to have an actual propagating signal on record. We test the approach on ground truth data provided by numerical simulations in three dimensions of two models of collective behaviour characterized by very different dynamical equations and information transfer mechanisms: the classic Vicsek model, describing an overdamped noninertial dynamics and the inertial spin model, characterized by an un- derdamped inertial dynamics. By using dynamical finite size scaling, we show that spatio-temporal correlations are able to distinguish unambiguously the diffusive information transfer mechanism of the Vicsek model from the linear mechanism of the inertial spin model.