Pattern Formation in Populations with Density-Dependent Movement and Two Interaction Scales

TL;DR

This paper investigates how populations with movement influenced by two different spatial scales form diverse patterns, including clusters and labyrinths, through simulations and mathematical modeling.

Contribution

It introduces a novel model combining short-range clustering and long-range dispersal behaviors, leading to complex pattern formation analysis.

Findings

Patterns include labyrinths and periodic clusters.

Clusters often form ring-like structures.

The model explains biological clustering behaviors.

Abstract

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological organisms (like mussels) that tend to cluster at short ranges as a defensive strategy, and strongly disperse if there is a high population pressure at large ranges for optimizing foraging. We perform stochastic simulations of a particle-level model of the system, and derive and analyze a continuous density description (a nonlinear diffusion equation). In both cases we show that this interplay of scale-dependent-behaviors gives rise to a rich formation of spatial patterns ranging from labyrinths to periodic cluster arrangements. In most cases these clusters have the very peculiar appearance of ring-like structures, i.e., organisms arranging in the perimeter of the clusters, that we discuss in detail.