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

Abstract: 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.