Evolutionary game dynamics with environmental feedback in a network with two communities

TL;DR

This paper models eco-evolutionary game dynamics on a two-community network, revealing complex behaviors like bifurcations, multistability, and oscillations, and highlights the impact of community structure on population-environment feedbacks.

Contribution

It introduces a novel network-based eco-evolutionary model with environmental feedback, analyzing equilibria and stability, and exploring complex dynamical phenomena.

Findings

Rich dynamical behaviors including bifurcations and oscillations

Community structure influences eco-evolutionary dynamics

Analytical and numerical analysis of equilibria and stability

Abstract

Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying population dynamics in various manners. We propose and analyze an eco-evolutionary game dynamics model on a network with two communities such that players interact with other players in the same community and those in the opposite community at different rates. In our model, we consider two-person matrix games with pairwise interactions occurring on individual edges and assume that the environmental state depends on edges rather than on nodes or being globally shared in the population. We analytically determine the equilibria and their stability under a symmetric population structure assumption, and we also numerically study the replicator dynamics of the general model. The model shows rich dynamical behavior, such as multiple transcritical bifurcations, multistability, and anti-synchronous oscillations. Our work offers insights into understanding how the presence of community structure impacts the eco-evolutionary dynamics within and between niches.