Competition of alliances in a cyclically dominant eight-species population

TL;DR

This study investigates how alliances form and compete in an eight-species population modeled by Lotka-Volterra equations, revealing conditions for stable coexistence, dominance of symmetric alliances, and finite-size effects.

Contribution

It identifies the conditions under which species alliances are stable and dominant, and explores the impact of invasion rates and system size on these dynamics.

Findings

Symmetric alliances by equally strong species are most prevalent.

Regions exist where a seven-species dominance breaks symmetry.

Finite-size effects can hinder observing the true stable solutions.

Abstract

In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures them stable coexistence against the invasion of an external species. Our principal goal is to identify those general features of a formation which determine its vitality. Therefore, we here study a traditional Lotka-Volterra model of eight-species where two four-species cycles can fight for space. Beside these formations, there are other solutions which may emerge when invasion rates are varied. The complete range of parameters is explored and we find that in most of the cases those alliances prevail which are formed by equally strong members. Interestingly, there are regions where the symmetry is broken and the system is dominated by a solution formed by seven species. Our work also highlights that serious finite-size effects may emerge which prevent observing the valid solution in a small system.