Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism

TL;DR

This paper extends evolutionary game theory by incorporating fluctuating population sizes and natural growth, revealing new dynamics especially in strong mutualism scenarios that standard models overlook.

Contribution

It introduces a Lotka-Volterra model with population fluctuations, bridging the gap between classical fixed-size models and realistic growth scenarios, especially under strong mutualism.

Findings

Population size fluctuations significantly affect fixation probabilities.

Standard evolutionary game theory fails under strong mutualism with fluctuating populations.

Analytical and numerical methods quantify fixation times considering population dynamics.

Abstract

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We study a competitive Lotka-Volterra model, with number fluctuations, that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games. We show that, in an appropriate limit, the model describes standard evolutionary games with both genetic drift and overall population size fluctuations. However, there are also regimes where a varying population size can strongly influence the evolutionary dynamics. We focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results. We then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions, taking into account the population size degree of freedom. These results elucidate the interplay between population dynamics and evolutionary dynamics in well-mixed systems.