Coalescent patterns in diploid exchangeable population models.
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.
Möhle
Martin
M
Eberhard Karls University of Tübingen, Mathematics Institute, 72076 Tübingen, Germany. martin.moehle@uni-tuebingen.de
Sagitov
Serik
S
D000465:Algorithms; D000818:Animals; D004171:Diploidy; D005260:Female; D005828:Genetics, Population; D005838:Genotype; D006801:Humans; D008297:Male; D008957:Models, Genetic; D010375:Pedigree; D012098:Reproduction / Q000235:genetics; D017678:Sex Distribution; D013269:Stochastic Processes