Modelling collective motion with simple selfish herd domain optimisation rules

One of the most prominent explanations for aggregate behaviour in animal groups is known as the selfish herd hypothesis. The selfish herd hypothesis proposes that each agent has a “domain of danger” whose area is proportional to the risk of predation. The hypothesis therefore postulates that aggregation occurs as a result of agents seeking to minimise the area of their domain. In this study, we attempt to model collective behaviours – specifically milling – using a generalisation of the original selfish herd domain optimisation principles. To do so, we investigate a model that allows agents to move towards domains of a specific (possibly non-minimal) area. Moreover, the model incorporates the lack of information that biological agents have by limiting the range of movement and field of vision of the agents. We find that the possibility of further collective motion is heavily dependent on the domain area the agents aim for — with three distinct phases of collective behaviour. In the different phases the collective motion exhibit (I) a flocculation state where the collective crystallizes, (II) a collective motion with high correlation of the agents and some milling and, finally, for too large a target area, (III) a disintegration of the collective. Thus, the model can be used as a framework in the future to achieve collective order using domain optimisation principles.