Condensed Matter Physics, 2008, vol. 11, No. 2(54), p. 283, English
DOI:10.5488/CMP.11.2.283
Title:
Selectionmutation balance models with epistatic selection
Author(s):

Yu.G.Kondratiev
(Universität Bielefeld, Postfach 10 01 31, D33501 Bielefeld, Germany; BiBoS, Univ. Bielefeld, Germany)
,


T.Kuna
(Universität Bielefeld, Postfach 10 01 31, D33501 Bielefeld, Germany; BiBoS, Univ. Bielefeld, Germany; University of Reading, Department of Mathematics, Whiteknights, PO Box 220, Reading RG6 6AX, UK)
,


N.Ohlerich
(Universität Bielefeld, Postfach 10 01 31, D33501 Bielefeld, Germany; BiBoS, Univ. Bielefeld, Germany)

We present an application of birthanddeath processes on configuration spaces to a generalized mutationselection balance model. The model describes the aging of population as a process of accumulation of mutations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. Our model describes an infinitepopulation, infinitesites model in continuum. The dynamical equation which describes the system, is of KimuraMaruyama type. The problem can be posed in terms of evolution of states (differential equation) or, equivalently, represented in terms of FeynmanKac formula. The questions of interest are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the nonepistatic case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of an epistatic potential on these mutations.
Key words:
birthanddeath processes, Poisson measure
PACS:
02.50.Ga
