title: Genealogical histories in structured populations.
abstract: In genealogies of genes sampled from structured populations, lineages coalesce at rates dependent on the states of the lineages. For migration and coalescence events occurring on comparable time scales, for example, only lineages residing in the same deme of a geographically subdivided population can have descended from a common ancestor in the immediately preceding generation. Here, we explore aspects of genealogical structure in a population comprising two demes, between which migration may occur. We use generating functions to obtain exact densities and moments of coalescence time, number of mutations, total tree length, and age of the most recent common ancestor of the sample. We describe qualitative features of the distribution of gene genealogies, including factors that influence the geographical location of the most recent common ancestor and departures of the distribution of internode lengths from exponential.
authors.affiliation: Department of Biology, Box 90338, Duke University, Durham, NC 27708-0338, USA.
authors.forename: Seiji
authors.initials: S
authors.lastname: Kumagai
authors.affiliation: Department of Biology, Box 90338, Duke University, Durham, NC 27708-0338, USA. Electronic address: marcy@duke.edu.
authors.forename: Marcy K
authors.initials: MK
authors.lastname: Uyenoyama
mesh_terms: D005789:Genealogy and Heraldry; D005828:Genetics, Population; D063426:Human Migration; D006801:Humans; D008957:Models, Genetic; D010375:Pedigree
keywords: Coalescence time; Generating functions; MRCA age; Migration; Population structure