Title: Selection-mutation balance models with epistatic selection
Author(s):

	Yu.G.Kondratiev (Universität Bielefeld, Postfach 10 01 31, D-33501 Bielefeld, Germany; BiBoS, Univ. Bielefeld, Germany) ,
	T.Kuna (Universität Bielefeld, Postfach 10 01 31, D-33501 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, D-33501 Bielefeld, Germany; BiBoS, Univ. Bielefeld, Germany)

We present an application of birth-and-death processes on configuration spaces to a generalized mutation-selection 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 infinite-population, infinite-sites model in continuum. The dynamical equation which describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 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: birth-and-death processes, Poisson measure
PACS: 02.50.Ga