The Evolving Moran Genealogy

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

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