Fixation probabilities in evolutionary dynamics under weak selection

Abstract

In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on the organism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on the organism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.

42 pages; final version

References in corpus (8)

• Evolutionary games on graphs
• Stochasticity and evolutionary stability
• Social goods dilemmas in heterogeneous societies
• The duality of spatial death-birth and birth-death processes and limitations of the isothermal theorem
• Counterintuitive properties of the fixation time in network-structured populations
• Limits on amplifiers of natural selection under death-Birth updating
• The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure
• Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs

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• Effects of Stochastic Games on Evolutionary Dynamics in Structured Populations
• The coalescent in finite populations with arbitrary, fixed structure
• Effect of the degree of an initial mutant in Moran processes in structured populations
• Evolutionary Dynamics of Variable Games in Structured Populations
• Natural selection of mutants that modify population structure
• Evolutionary dynamics on sequential temporal networks