  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.
