Fission-fusion dynamics and group-size dependent composition in heterogeneous populations

Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups and populations consist of identical individuals. In this paper, we develop and analyse a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups. We derive a master equation for group size and compositions, and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type/species. Groups larger than the critical size are representative of the global heterogeneity, despite the propensity of heterogeneous groups to split at higher rates. Thus, our model predicts that composition of flocks are group-size dependent. We discuss the implications of our results for current methods used to infer interspecies interactions from mixed-species flock compositions. Introduction Collective phenomena and self-organisation are widespread in the animal kingdom [1–4]. Theory as well as empirical works suggest that these macroscopic behaviours often emerge from simple microscopic interactions among individuals. Much of collective behaviour theory and models assume that individuals in populations are identical. Animal populations in nature, however, are rarely homogeneous. Within conspecific social groups, heterogeneity may arise from differences in age, size, or sex. Social groups may also have dominance hierarchies including differences in behavioural tendencies such as boldness and shyness [5–7]. Heterogeneity also arises when individuals of different species interact to form groups, also called mixed-species flocks [8–13]. Given the wide prevalence