Interface networks in models of competing alliances

TL;DR

This paper investigates the formation and properties of interface networks in models of competing alliances among species, combining stochastic simulations, mean field analysis, and a novel topological soliton approach to understand biodiversity patterns.

Contribution

It introduces a topological soliton model to describe stable interfaces in competing alliances, validated by stochastic simulations and mean field solutions.

Findings

Alliances form spatial domains separated by interfaces.

Stationary interface profiles exhibit topological properties.

The soliton model aligns with stochastic simulation results.

Abstract

We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical stochastic simulations, we show that alliances compete each other forming spatial domains bounded by inter- faces of empty sites. We solve numerically the mean field equations associated to the stochastic model in one and two spatial dimensions. We demonstrate that the stationary interface profile presents topological properties which are related to the asymptotic spa- tial distribution of species of enemy alliances far away from the interface core. Finally, we introduce a theoretical approach to model the formation of stable interfaces using spontaneous breaking of a discrete symmetry. We show that all the results provided by the soliton topological model, presented here for the very first time, are in agreement with the stochastic simulations and may be used as a tool for understanding the complex biodiversity in Nature.