title: Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution.
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.
authors.affiliation: Institut für Mathematik, Goethe-Universität Frankfurt, Box 111932, 60054 Frankfurt am Main, Germany. Electronic address: lenz@math.uni-frankfurt.de.
authors.forename: Ute
authors.initials: U
authors.lastname: Lenz
authors.affiliation: Faculty of Technology, Bielefeld University, Box 100131, 33501 Bielefeld, Germany. Electronic address: sandra.kluth@uni-bielefeld.de.
authors.forename: Sandra
authors.initials: S
authors.lastname: Kluth
authors.affiliation: Faculty of Technology, Bielefeld University, Box 100131, 33501 Bielefeld, Germany. Electronic address: ebaake@techfak.uni-bielefeld.de.
authors.forename: Ellen
authors.initials: E
authors.lastname: Baake
authors.affiliation: Institut für Mathematik, Goethe-Universität Frankfurt, Box 111932, 60054 Frankfurt am Main, Germany. Electronic address: wakolbin@math.uni-frankfurt.de.
authors.forename: Anton
authors.initials: A
authors.lastname: Wakolbinger
mesh_terms: D009154:Mutation; D011336:Probability; D012641:Selection, Genetic
keywords: Ancestral selection graph; Common ancestor type distribution; Lookdown graph; Pruning; Wright–Fisher diffusion with selection and mutation