The probability of fixation of a single mutant in an exchangeable selection model |
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Authors: | Sabin Lessard Véronique Ladret |
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Institution: | (1) Département de mathématiques et de statistique, Université de Montréal, Montréal, QC, H3C 3J7, Canada |
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Abstract: | The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability
of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this
probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula
is expressed in terms of mean coalescence times under neutrality assuming that the coefficient of selection for the mutant
type has a derivative with respect to the intensity of selection that takes a polynomial form with respect to the frequency
of the mutant type. An approximation is obtained in the case where this derivative is a continuous function of the mutant
frequency and the population size is large. This approximation is consistent with a diffusion approximation under moment conditions
on the number of descendants of a single individual in one time step. Applications to evolutionary game theory in finite populations
are presented.
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Keywords: | Exchangeable model Coalescence times Diffusion approximation Evolutionary game theory Fixation probability |
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