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Lines of descent in a Moran model with frequency-dependent selection and mutation

Author

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  • Baake, E.
  • Esercito, L.
  • Hummel, S.

Abstract

We study ancestral structures for the two-type Moran model with mutation and frequency-dependent selection under the nonlinear dominance or fittest-type-wins scheme. Under appropriate conditions, both lead, in distribution, to the same type-frequency process. Reasoning through the mutations on the ancestral selection graph (ASG), we develop the corresponding killed and pruned lookdown ASGs and use them to determine the present and ancestral type distributions. To this end, we establish factorial moment dualities to the Moran model and a relative. We extend the results to the diffusion limit and present applications for finite populations, as well as for moderate and weak selection limits.

Suggested Citation

  • Baake, E. & Esercito, L. & Hummel, S., 2023. "Lines of descent in a Moran model with frequency-dependent selection and mutation," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 409-457.
    • Handle: RePEc:eee:spapps:v:160:y:2023:i:c:p:409-457
    DOI: 10.1016/j.spa.2023.03.004
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    References listed on IDEAS

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    1. 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.
    2. Holger Dette & James Allen Fill & Jim Pitman & William J. Studden, 1997. "Wall and Siegmund Duality Relations for Birth and Death Chains with Reflecting Barrier," Journal of Theoretical Probability, Springer, vol. 10(2), pages 349-374, April.
    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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