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.
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Work supported by the Bank of Sweden Tercentenary Foundation.
Mathematics Subject Classification (2000): Primary 92F25, 60J70; Secondary 92D15, 60F17
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Möhle, M., Sagitov, S. Coalescent patterns in diploid exchangeable population models. J. Math. Biol. 47, 337–352 (2003). https://doi.org/10.1007/s00285-003-0218-6
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DOI: https://doi.org/10.1007/s00285-003-0218-6