Evolution of the most recent common ancestor of a population with no selection

TL;DR

This paper models the evolution of the time to the most recent common ancestor in a neutral population, analyzing its dynamics and correlation with genetic diversity using a Markov process.

Contribution

It introduces a simple Markov process model to describe the evolution of the coalescence time in a neutral population and explores its properties.

Findings

Derived characteristics of the coalescence time evolution.

Analyzed the correlation between coalescence time and genetic diversity.

Provided insights into the stochastic dynamics of ancestral lineage convergence.

Abstract

We consider the evolution of a population of fixed size with no selection. The number of generations $G$ to reach the first common ancestor evolves in time. This evolution can be described by a simple Markov process which allows one to calculate several characteristics of the time dependence of $G$. We also study how $G$ is correlated to the genetic diversity.