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arXiv · 1808.10809

The Evolving Moran Genealogy

Johannes Wirtz·Thomas Wiehe
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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.

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Johannes Wirtz, Thomas Wiehe. 2018-08-31. The Evolving Moran Genealogy. https://arxiv.org/abs/1808.10809

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