Frequency-dependent fitness induces multistability in coevolutionary dynamics

TL;DR

This paper investigates how nonlinear frequency-dependent fitness influences coevolutionary dynamics, revealing the emergence of multistability and stochastic switching in systems with asymmetric mutation rates.

Contribution

It extends previous linear models by analyzing nonlinear frequency dependence, uncovering new metastable states and complex dynamics in coevolution.

Findings

Nonlinear frequency dependence induces multistability.

Asymmetric mutation rates lead to stochastic switching.

Metastable states are a generic feature in frequency-dependent systems.

Abstract

Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a fundamental aim of theoretical research. Recent works quantitatively studied coevolutionary dynamics of competing species with a focus on linearly frequency-dependent interactions, derived from a game-theoretic viewpoint. However, several aspects of evolutionary dynamics, e.g. limited resources, may induce effectively nonlinear frequency dependencies. Here we study the impact of nonlinear frequency dependence on evolutionary dynamics in a model class that covers linear frequency dependence as a special case. We focus on the simplest non-trivial setting of two genotypes and analyze the co-action of nonlinear frequency dependence with asymmetric mutation rates. We find that their co-action may induce novel metastable states as well as stochastic switching dynamics between them. Our results reveal how the different mechanisms of mutation, selection and genetic drift contribute to the dynamics and the emergence of metastable states, suggesting that multistability is a generic feature in systems with frequency-dependent fitness.