Noise-induced Effects in Collective Dynamics and Inferring Local Interactions from Data

In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic noise at the group level. Theory predicts that the strength of intrinsic noise is not a constant but often depends on the collective state of the group; hence, it is also called a state-dependent noise or a multiplicative noise. Surprisingly, such noise may produce collective order. However, only a few empirical studies on collective behaviour have paid attention to such effects due to the lack of methods that enable us to connect data with theory. Here, we demonstrate a method to characterise the role of stochasticity directly from high-resolution time-series data of collective dynamics. We do this by employing two well-studied individual-based toy models of collective behaviour. We argue that the group-level noise may encode important information about the underlying processes at the individual scale. In summary, we describe a method that enables us to establish connections between empirical data of animal (or cellular) collectives with the phenomenon of noise-induced states, a field that is otherwise largely limited to the theoretical literature.