Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution

Ute Lenz, Sandra Kluth, Ellen Baake and Anton Wakolbinger

Theoretical Population Biology, 2015, vol. 103, issue C, 27-37

Abstract: In a (two-type) Wright–Fisher diffusion with directional selection and two-way mutation, let x denote today’s frequency of the beneficial type, and given x, let h(x) be the probability that, among all individuals of today’s population, the individual whose progeny will eventually take over in the population is of the beneficial type. Fearnhead (2002) and Taylor (2007) obtained a series representation for h(x). We develop a construction that contains elements of both the ancestral selection graph and the lookdown construction and includes pruning of certain lines upon mutation. Besides being interesting in its own right, this construction allows a transparent derivation of the series coefficients of h(x) and gives them a probabilistic meaning.

Keywords: Common ancestor type distribution; Ancestral selection graph; Lookdown graph; Pruning; Wright–Fisher diffusion with selection and mutation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:103:y:2015:i:c:p:27-37

DOI: 10.1016/j.tpb.2015.01.005

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