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The Evolving Moran Genealogy

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  • Wirtz, Johannes
  • Wiehe, Thomas

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.

Suggested Citation

  • Wirtz, Johannes & Wiehe, Thomas, 2019. "The Evolving Moran Genealogy," Theoretical Population Biology, Elsevier, vol. 130(C), pages 94-105.
    • Handle: RePEc:eee:thpobi:v:130:y:2019:i:c:p:94-105
    DOI: 10.1016/j.tpb.2019.07.005
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    References listed on IDEAS

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    1. Pfaffelhuber, P. & Wakolbinger, A., 2006. "The process of most recent common ancestors in an evolving coalescent," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1836-1859, December.
    2. Kluth, Sandra & Baake, Ellen, 2013. "The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation," Theoretical Population Biology, Elsevier, vol. 90(C), pages 104-112.
    3. Lenz, Ute & Kluth, Sandra & Baake, Ellen & Wakolbinger, Anton, 2015. "Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution," Theoretical Population Biology, Elsevier, vol. 103(C), pages 27-37.
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    Cited by:

    1. Kaur, Gursharn & Choi, Kwok Pui & Wu, Taoyang, 2023. "Distributions of cherries and pitchforks for the Ford model," Theoretical Population Biology, Elsevier, vol. 149(C), pages 27-38.

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