Hierarchical societies exhibit diverse swarming transitions

Social hierarchy is central to decision-making such as the coordinated movement of many swarming species. Here we propose a hierarchical swarm model for collective motion in the spirit of the Vicsek model of self-propelled particles. We show that, as the hierarchy becomes important, the swarming transition changes dramatically from the weak first-order transition observed for egalitarian populations, to a stronger first-order transition for intermediately strong hierarchies, and finally to a second-order phase transition when approaching to the extremely despotic societies. Associated to this we observe that the spatial structure of the swarm, as measured by the correlation between the density and velocity fields, is strongly mediated by the hierarchy. A vectorial network model is developed that provides a correct explanation. A two-group model and vectorial noise are also studied to verify the robustness of the observations. Our results imply that diverse type of swarming transitions is possible, depending on the impact of hierarchy of the species under study.