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

TL;DR

This paper analyzes how advantageous ancestors contribute genetically to a population over time under a biparental Moran model with selection, revealing the extent of their genetic influence after many generations.

Contribution

It provides a quantitative framework for understanding the genetic impact of advantaged ancestors in a biparental Moran model with finite selection.

Findings

Up to 19% of the genome can originate from advantaged ancestors under strong selection.

A small initial advantage (1%) can lead to significant genetic contribution over time.

The model quantifies the relationship between initial advantage and long-term genetic influence.

Abstract

We study a population of $N$ individuals evolving according to a biparental Moran model with two types, one being advantaged compared to the other. The advantage is conferred by a Mendelian mutation, which reduces the death probability of individuals carrying it. We assume that a proportion $a$ of individuals initially carry this mutation, which therefore eventually gets fixed with high probability. After a long time, we sample a gene uniformly from the population, at a new locus, independent of the locus under selection, and calculate the probability that this gene originated from one of the initially advantaged individuals, when the population size is large. Our theorem provides quantitative insights, such as the observation that under strong viability selection, if only $1\%$ of the individuals are initially advantaged, up to $19\%$ of the population's genome will originate from them after a long time.