Geometry for a `penguin-albatross' rookery

TL;DR

This paper presents a simple ecological model explaining how two interacting populations organize spatially, forming rhomboidal clusters at low densities and becoming fully mixed at higher densities, revealing critical phenomena.

Contribution

The study introduces a minimal ecological model capturing the transition from structured clustering to a jammed mixed state in two interacting populations.

Findings

Clusters form a rhomboidal bipartite network at low densities

Power-law divergences suggest a critical point at zero density

A critical threshold density marks the transition to a fully mixed state

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 $\Phi$ a non-trivial structure is observed where clusters of individuals arrange into a rhomboidal bipartite network with an average degree of four. For $\Phi\rightarrow0$ 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 $\Phi_{c}$ is identified above which the evolution toward a partially ordered configuration is prevented and the system becomes jammed in a fully mixed state.