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The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation

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  • Kluth, Sandra
  • Baake, Ellen

Abstract

We reconsider the Moran model in continuous time with population size N, two allelic types, and selection. We introduce a new particle representation, which we call the labelled Moran model, and which has the same distribution of type frequencies as the original Moran model, provided the initial values are chosen appropriately. In the new model, individuals are labelled 1,2,…,N; neutral resampling events may take place between arbitrary labels, whereas selective events only occur in the direction of increasing labels. With the help of elementary methods only, we not only recover fixation probabilities, but also obtain detailed insight into the number and nature of the selective events that play a role in the fixation process forward in time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:90:y:2013:i:c:p:104-112
    DOI: 10.1016/j.tpb.2013.09.009
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    References listed on IDEAS

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    1. Pokalyuk, Cornelia & Pfaffelhuber, Peter, 2013. "The ancestral selection graph under strong directional selection," Theoretical Population Biology, Elsevier, vol. 87(C), pages 25-33.
    2. Mano, Shuhei, 2009. "Duality, ancestral and diffusion processes in models with selection," Theoretical Population Biology, Elsevier, vol. 75(2), pages 164-175.
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    Cited by:

    1. González Casanova, Adrián & Miró Pina, Verónica & Pardo, Juan Carlos, 2020. "The Wright–Fisher model with efficiency," Theoretical Population Biology, Elsevier, vol. 132(C), pages 33-46.
    2. Wirtz, Johannes & Wiehe, Thomas, 2019. "The Evolving Moran Genealogy," Theoretical Population Biology, Elsevier, vol. 130(C), pages 94-105.
    3. Cordero, Fernando, 2017. "Common ancestor type distribution: A Moran model and its deterministic limit," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 590-621.

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