Noise and local interactions in milling whirligig beetles

A plethora of spectacular patterns of collective behaviour in animals exist in nature. Many studies analyse high-resolution data of collective motion of animal groups and infer the nature of local interactions that explain the observed behaviour. However, these studies most often ignore the role of noise. Here, we quantify the stochasticity in the time series dynamics of milling swarms of whirligig beetles (Gyrinidae dineutes) and show that it reveals insights on the local interactions that organisms follow. We apply the approach of data-driven discovery of dynamical equations to high-resolution time series data of milling beetle swarms, and obtain a stochastic differential equation (SDE) that governs the underlying dynamics. Analysis of the terms of SDE, together with analyses of agent-based models, reveal that beetles are likely changing their local interaction rules with group size. Specifically, we infer that beetles predominantly follow the simple rule of copying a randomly chosen individual at small group sizes; in larger groups, however, beetles follow a higher-order interaction rule. Furthermore, we find evidence for a simple negative interaction -- where a pair of beetles occasionally split. Our study shows the surprising possibility of inferring underlying modes of interactions between individuals via analysis of noise.