Instability of defensive alliances in the predator-prey model on complex networks

TL;DR

This paper investigates the stability of defensive alliances in a six-species predator-prey model on complex networks, revealing different phase transition types under temporal and spatial randomness, with analytical and numerical insights.

Contribution

It introduces a detailed analysis of alliance stability in a six-species food web on complex networks, highlighting the effects of network topology and mutation rate on phase transitions.

Findings

Alliance-breaking transition is continuous and in the 2D Ising universality class with temporal disorder.

Spatial randomness causes a discontinuous phase transition.

The mean-field solution aligns with numerical results and reveals dynamic behaviors.

Abstract

A model of six-species food web is studied in the viewpoint of spatial interaction structures. Each species has two predators and two preys, and it was previously known that the defensive alliances of three cyclically predating species self-organize in two-dimensions. The alliance-breaking transition occurs as either the mutation rate is increased or interaction topology is randomized in the scheme of the Watts-Strogatz model. In the former case of temporal disorder, via the finite-size scaling analysis the transition is clearly shown to belong to the two-dimensional Ising universality class. In contrast, the geometric or spatial randomness for the latter case yields a discontinuous phase transition. The mean-field limit of the model is analytically solved and then compared with numerical results. The dynamic universality and the temporally periodic behaviors are also discussed.