The effect of recurrent mutations on genetic diversity in a large population of varying size

TL;DR

This paper investigates how recurrent mutations influence genetic diversity and the genetic signatures they leave in large populations with varying sizes, focusing on different mutation scales and their effects on polymorphism patterns.

Contribution

It introduces a detailed analysis of the genetic signatures caused by recurrent mutations across different mutation scales and explores the hydrodynamic limits of population dynamics.

Findings

Identifies three distinct genetic signatures based on mutation probability scales.

Derives hydrodynamic limits showing complex equilibrium patterns.

Highlights the impact of mutation frequency on genetic diversity and polymorphism.

Abstract

Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in the genetic signature left by a selective sweep induced by recurrent mutations at a given locus from an allele A to an allele a, depending on the mutation frequency. We distinguish three possible scales for the mutation probability per reproductive event, which entail distinct genetic signatures. Besides, we study the hydrodynamic limit of the A- and a-population size dynamics when mutations are frequent, and find non trivial equilibria leading to several possible patterns of polymorphism.