Cyclical interactions with alliance-specific heterogeneous invasion rates

TL;DR

This paper investigates a six-species predator-prey system on lattices, revealing complex alliance survival dynamics influenced by invasion rates, with implications for understanding stability in ecological and social systems.

Contribution

It introduces a model with heterogeneous invasion rates in a six-species system and demonstrates non-monotonous alliance survival behavior through simulations and mean-field analysis.

Findings

Alliance survival shows non-monotonous dependence on invasion rate differences.

Mean-field approximation qualitatively reproduces simulation results.

Study highlights complex stability issues in multi-species competition.

Abstract

We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend on the predator-prey pair, whereby cyclic symmetries within the two three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected non-monotonous dependence of alliance survival on the difference of alliance-specific invasion rates. This behavior is qualitatively reproduced by a four-point mean-field approximation. The study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences.