Geometry for a `penguin-albatross' rookery

Abstract

We introduce a simple ecological model describing the spatial organization of two interacting populations whose individuals are indifferent to conspecifics and avoid the proximity to heterospecifics. At small population densities $Φ$ a non-trivial structure is observed where clusters of individuals arrange into a rhomboidal bipartite network with an average degree of four. For $Φ\rightarrow0$ the length scale, order parameter and susceptibility of the network exhibit power-law divergences compatible with hyper-scaling, suggesting the existence of a zero density - non-trivial - critical point. At larger densities a critical threshold $Φ_{c}$ is identified above which the evolution toward a partially ordered configuration is prevented and the system becomes jammed in a fully mixed state.