Impact of network structure on a model of diffusion and competitive interaction

TL;DR

This paper investigates how complex network structures influence species diffusion, competition, and coexistence, revealing that scale-free networks promote biodiversity while regular and Erdos-Renyi graphs tend to favor single-species dominance.

Contribution

It introduces a model linking network topology with species dynamics, highlighting the impact of degree distribution, clustering, and community structure on species survival and coexistence.

Findings

Scale-free networks support species coexistence.

Regular and Erdos-Renyi graphs favor invasion by a single species.

Network structure critically influences stability and diversity.

Abstract

We consider a model in which agents of different species move over a complex network, are subject to reproduction and compete for resources. The complementary roles of competition and diffusion produce a variety of fixed points, whose stability depends on the structure of the underlying complex network. The survival and death of species is influenced by the network degree distribution, clustering, degree-degree correlations and community structures. We found that the invasion of all the nodes by just one species is possible only in Erdos-Renyi and regular graphs, while networks with scale--free degree distribution, as those observed in real social, biological and technological systems, guarantee the co-existence of different species and therefore help enhancing species diversity.