A data-driven method for reconstructing and modelling social interactions in moving animal groups

Group-living organisms that collectively migrate range from cells and bacteria to human crowds, and include swarms of insects, schools of fish and flocks of birds or ungulates. Unveiling the behavioural and cognitive mechanisms by which these groups coordinatetheir movements is a challenging task. These mechanisms take place at the individual scale and they can be described as a combination ofpairwise interactions between individuals and interactions between these individuals and the physical obstacles in the environment.Thanks to the development of novel tracking techniques that provide large and accurate data sets, the main characteristics of indivi\-dual and collective behavioural patterns can be quantified with an unprecedented level of precision. However, in a large number of works, social interactions are usually described by force map methods that only have a limited capacity of explanation and prediction, being rarely suitable for a direct implementation in a concise and explicit mathematical model. Here, we present a general method to extract the interactions between individuals that are involved in the coordination of collective movements in groups of organisms. We then apply this method to characterize social interactions in two species of shoaling fish, the rummy-nose tetra (Hemigrammus rhodostomus) and the zebrafish (Danio rerio),which both present a burst-and-coast motion. The detailed quantitative description of microscopic individual-level interactions thus provides predictive models of the emergent dynamics observed at the macroscopic group-level. This method can be applied to a wide range of biological and social systems