title: An introduction to the mathematical structure of the Wright-Fisher model of population genetics.
abstract: In this paper, we develop the mathematical structure of the Wright-Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection. We establish a new concept of a global solution for the diffusion approximation (Fokker-Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution. Thus, our solution turns out to be superior to the local solution constructed by Kimura.
authors.affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany. trandat@mis.mpg.de
authors.forename: Tat Dat
authors.initials: TD
authors.lastname: Tran
authors.forename: Julian
authors.initials: J
authors.lastname: Hofrichter
authors.forename: Jürgen
authors.initials: J
authors.lastname: Jost
mesh_terms: D000465:Algorithms; D000483:Alleles; D005075:Biological Evolution; D040961:Genetic Drift; D005828:Genetics, Population; D008957:Models, Genetic; D011336:Probability