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Zbl 0981.92020
Slade, Paul F.
Simulation of `hitch-hiking' genealogies. (English)
[J] J. Math. Biol. 42, No.1, 41-70 (2001). ISSN 0303-6812; ISSN 1432-1416/e

Summary: An ancestrial influence graph is derived, an analogue of the coalescent and a composite of {\it R.C. Griffiths'} [IMS Lect. Notes, Monogr. Ser. 18, 100-117 (1991; Zbl 0781.92022)] two-locus ancestral graph and {\it S.M. Krone} and {\it C. Neuhauser's} [Theor. Popul. Biol. 51, No. 3, 210-237 (1997; Zbl 0910.92024)] ancestral selection graph. This generalizes their use of branching-coalescing random graphs so as to incorporte both selection and recombination into gene genealogies. Qualitative understanding of a `hitch-hiking' effect on genealogies is pursued via diagrammatic representation of the genealogical process in a two-locus, two-allele haploid model.\par Extending the simulation technique of {\it R.C. Griffiths} and {\it S. Tavaré} [Math. Comput. Modelling 23, No. 8-9, 141-158 (1996; Zbl 0853.92014)], computational estimations of expected times to the most recent common ancestor of samples of $n$ genes under recombination and selection in two-locus, two-allele haploid and diploid models are presented. Such times are conditional on sample configuration. Monte Carlo simulations show that `hitch-hiking' is a subtle effect that alters the conditional expected depth of the genealogy at the linked neutral locus depending on a mutation-selection-recombination balance.

MSC 2000:: *92D15 Problems related to evolution
92D10 Genetics
05C90 Appl. of graph theory

Keywords: population genetics; selection; recombination; gene genealogies; Monte Carlo inference; random graphs

Citations: Zbl 0781.92022; Zbl 0910.92024; Zbl 0853.92014

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