title: When and where was the most recent common ancestor?
abstract: The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = tau, the distribution of Z is Gaussian with mean zero and variance 2tau. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension.
authors.affiliation: Department of Ecology and Evolution, The University of Chicago, Illinois 60637-1573, USA.
authors.forename: Thomas
authors.initials: T
authors.lastname: Nagylaki
mesh_terms: D000818:Animals; D004641:Emigration and Immigration; D004777:Environment; D005191:Family Characteristics; D040961:Genetic Drift / Q000235:genetics*; D005828:Genetics, Population; D008432:Mathematical Computing; D008957:Models, Genetic; D010507:Periodicity; D012189:Retrospective Studies; D013997:Time Factors