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The ancestral selection graph under strong directional selection

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  • Pokalyuk, Cornelia
  • Pfaffelhuber, Peter

Abstract

The ancestral selection graph (ASG) was introduced by Neuhauser and Krone (1997) in order to study populations of constant size which evolve under selection. Coalescence events, which occur at rate 1 for every pair of lines, lead to joint ancestry. In addition, splitting events in the ASG at rate α, the scaled selection coefficient, produce possible ancestors, such that the real ancestor depends on the ancestral alleles. Here, we use the ASG in the case without mutation in order to study fixation of a beneficial mutant. Using our main tool, a reversibility property of the ASG, we provide a new proof of the fact that a beneficial allele fixes roughly in time (2logα)/α if α is large.

Suggested Citation

  • Pokalyuk, Cornelia & Pfaffelhuber, Peter, 2013. "The ancestral selection graph under strong directional selection," Theoretical Population Biology, Elsevier, vol. 87(C), pages 25-33.
    • Handle: RePEc:eee:thpobi:v:87:y:2013:i:c:p:25-33
    DOI: 10.1016/j.tpb.2012.09.005
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    References listed on IDEAS

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    1. Wakeley, John & Sargsyan, Ori, 2009. "The conditional ancestral selection graph with strong balancing selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 355-364.
    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. Pokalyuk, Cornelia & Wakolbinger, Anton, 2020. "Maintenance of diversity in a hierarchical host–parasite model with balancing selection and reinfection," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1119-1158.
    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. 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.
    4. Bossert, S. & Pfaffelhuber, P., 2018. "The fixation probability and time for a doubly beneficial mutant," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4018-4050.
    5. 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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