The Evolving Moran Genealogy

TL;DR

This paper models the evolution of population genealogies in the Moran Model using Yule trees, revealing properties like time reversal and insights into the Most Recent Common Ancestor process.

Contribution

It introduces a tree-valued Markov process for Moran genealogies and explores its properties, including time reversal and ancestral lineage analysis.

Findings

Process admits time reversal

Aligns with infinite-population Moran results

Provides insights into the Most Recent Common Ancestor

Abstract

We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise to a process with a state space consisting of the finite set of Yule trees of a certain size. We derive a number of properties of this process, and show that they are in agreement with existing results on the infinite-population limit of the Moran Model. Most importantly, this process admits time reversal, which gives rise to another tree-valued Markov Chain and allows for a thorough investigation of the Most Recent Common Ancestor process.