Genetic contribution of an advantaged mutant in the biparental Moran model -- finite selection

TL;DR

This paper analyzes the genetic contribution of an advantageous mutant in a finite population modeled by a biparental Moran process, focusing on how initial mutation frequency influences long-term genetic contribution.

Contribution

It provides a mathematical expression for the probability that a gene sampled from the population originates from an advantaged mutant, considering finite population effects.

Findings

Derived the probability of gene origin from advantaged mutants as population size grows.

Quantified how initial mutation proportion affects long-term genetic contribution.

Provided insights into the fixation dynamics of advantageous mutations in finite populations.

Abstract

We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian way from parent to child that reduces the death probability of individuals carrying it. We assume that initially this mutation is carried by a proportion a of individuals in the population. Once the mutation is fixed, a gene is sampled uniformly in the population, at a locus independent of the locus under selection. We then give the probability that this gene initially comes from an advantaged individual, i.e. the genetic contribution of these individuals, as a function of a and when the population size is large.