Coalescent patterns in diploid exchangeable population models |
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Authors: | Email author" target="_blank">Martin?M?hleEmail author Serik?Sagitov |
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Institution: | (1) Eberhard Karls University of Tübingen, Mathematics Institute, 72076 Tübingen, Germany;(2) Chalmers University of Technology and Göteborg University, School of Mathematical and Computing Sciences, S-41296 Göteborg, Sweden |
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Abstract: | A class of two-sex population models is considered with N females and equal number N of males constituting each generation. Reproduction is assumed to undergo three stages: 1) random mating, 2) exchangeable reproduction, 3) random sex assignment. Treating individuals as pairs of genes at a certain locus we introduce the diploid ancestral process (the past genealogical tree) for n such genes sampled in the current generation. Neither mutation nor selection are assumed. A convergence criterium for the diploid ancestral process is proved as N goes to infinity while n remains unchanged. Conditions are specified when the limiting process (coalescent) is the Kingman coalescent and situations are discussed when the coalescent allows for multiple mergers of ancestral lines.Work supported by the Bank of Sweden Tercentenary Foundation.Mathematics Subject Classification (2000):Primary 92F25, 60J70; Secondary 92D15, 60F17 |
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Keywords: | Ancestral process" target="_blank">gif" alt="ensp" align="MIDDLE" BORDER="0">Ancestral process Coalescent Diploid model Exchangeability Generator Neutrality Population genetics Two-sex model Weak convergence |
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