title: The coalescence time of sampled genes in the structured coalescent model.
abstract: The aim of this article is to investigate the distribution of the coalescence time (T) for sampled genes in the structured coalescent. We obtain some exact solutions for small samples and approximate distributions for n sampled genes in strong and weak migration. We also conduct computer simulation to evaluate efficiencies of these approximations and show the dependency of the distribution of the coalescence time on the geographical structure and the intensity of migration. In a panmictic population, we prove that the conditional distribution of the coalescence time given the number of segregating sites (S) among sampled genes is given by the weighted mean of the convolution of gamma distributions. We also study the joint distribution of T and S in the structured coalescent model and show some exact solutions.
authors.affiliation: Graduate School of Natural Sciences, Nagoya City University, Mizuho, Nagoya 467-8501, Japan. noto@nsc.nagoya-cu.ac.jp
authors.forename: Morihiro
authors.initials: M
authors.lastname: Notohara
authors.forename: Takayoshi
authors.initials: T
authors.lastname: Umeda
mesh_terms: D000704:Analysis of Variance; D005075:Biological Evolution; D020090:Chromosome Segregation / Q000235:genetics; D003198:Computer Simulation; D004641:Emigration and Immigration; D018703:Founder Effect; D005787:Gene Frequency / Q000235:genetics*; D005828:Genetics, Population; D005843:Geography; D006801:Humans; D008390:Markov Chains; D008957:Models, Genetic; D009154:Mutation / Q000235:genetics; D010375:Pedigree; D016012:Poisson Distribution; D011110:Polymorphism, Genetic / Q000235:genetics; D012641:Selection, Genetic; D013997:Time Factors