Fixation probabilities in populations under demographic fluctuations

Abstract

We study the fixation probability of a mutant type when introduced into a resident population. As opposed to the usual assumption of constant pop- ulation size, we allow for stochastically varying population sizes. This is implemented by a stochastic competitive Lotka-Volterra model. The compe- tition coefficients are interpreted in terms of inverse payoffs emerging from an evolutionary game. Since our study focuses on the impact of the competition values, we assume the same birth and death rates for both types. In this gen- eral framework, we derive an approximate formula for the fixation probability ϕ of the mutant type under weak selection. The qualitative behavior of ϕ when compared to the neutral scenario is governed by the invasion dynamics of an initially rare type. Higher payoffs when competing with the resident type yield higher values of ϕ. Additionally, we investigate the influence of the remaining parameters and find an explicit dependence of ϕ on the mixed equilibrium value of the corresponding deterministic system (given that the parameter values allow for its existence).

31 pages, 7 figures

References in corpus (15)

• Evolutionary games in the multiverse
• Demographic noise can reverse the direction of deterministic selection
• Stochasticity and evolutionary stability
• Evolutionary game theory in growing populations
• The branching process with logistic growth
• Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
• Models of genetic drift as limiting forms of the Lotka-Volterra competition model
• Public goods games in populations with fluctuating size
• The limits of weak selection and large population size in evolutionary game theory
• Population Genetics with Fluctuating Population Sizes
• Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism
• A mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory
• Extinction dynamics from meta-stable coexistences in an evolutionary game
• Effects of population growth on the success of invading mutants
• Exploiting fast-variables to understand population dynamics and evolution

Cited by in corpus (1)

• Public goods games in populations with fluctuating size