The Evolving Moran Genealogy

Johannes Wirtz; Thomas Wiehe

doi:10.1016/j.tpb.2019.07.005

The Evolving Moran Genealogy

Theor Popul Biol. 2019 Dec:130:94-105. doi: 10.1016/j.tpb.2019.07.005. Epub 2019 Jul 19.

Authors

Johannes Wirtz¹, Thomas Wiehe²

Affiliations

¹ Institut für Genetik, Universität zu Köln, Germany. Electronic address: wirtzj0@uni-koeln.de.
² Institut für Genetik, Universität zu Köln, Germany. Electronic address: twiehe@uni-koeln.de.

PMID: 31330138
DOI: 10.1016/j.tpb.2019.07.005

Abstract

We study the evolution of the population genealogy in the classic neutral Moran Model of finite size n∈N 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 on a state space consisting of n-sized binary increasing trees. 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 makes it possible to simplify the mechanisms determining state changes, and allows for a thorough investigation of the Most Recent Common Ancestorprocess.

Keywords: Kingman Coalescent; Markov chains; Moran model; Time reversal; Yule model.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Biological Evolution*
Genealogy and Heraldry*
Genetics, Population*
Markov Chains
Models, Genetic