title: Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.
abstract: We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations.
authors.affiliation: Applied Mathematics-1, Moscow State University of Railway Engineering, Moscow 127994, Russia.
authors.forename: Yuri S
authors.initials: YS
authors.lastname: Semenov
authors.affiliation: Department of Mathematics, North Dakota State University, Fargo, ND 58108, USA. Electronic address: artem.novozhilov@ndsu.edu.
authors.forename: Artem S
authors.initials: AS
authors.lastname: Novozhilov
mesh_terms: D005075:Biological Evolution; D005787:Gene Frequency; D008954:Models, Biological; D009154:Mutation; D012641:Selection, Genetic
keywords: Crow–Kimura model; Error threshold; Quasispecies model; Selection–mutation equilibrium; Single peaked landscape