The Evolving Moran Genealogy
Populations and Evolution
2019-02-08 v2 Probability
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.
Cite
@article{arxiv.1808.10809,
title = {The Evolving Moran Genealogy},
author = {Johannes Wirtz and Thomas Wiehe},
journal= {arXiv preprint arXiv:1808.10809},
year = {2019}
}