Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism

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.

Updated Version, Published in Phys. Rev. E 92, 022718 on 20 August 2015

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Cited by in corpus (9)

• Demographic noise can reverse the direction of deterministic selection
• Fixation probabilities in populations under demographic fluctuations
• Population Genetics with Fluctuating Population Sizes
• Spatial population genetics with fluid flow
• Effects of population growth on the success of invading mutants
• Immigration-induced phase transition in a regulated multispecies birth-death process
• Exploiting fast-variables to understand population dynamics and evolution
• The advantage of being slow: the quasi-neutral contact process
• Fixation in Competing Populations: Diffusion and Strategies for Survival