@inproceedings{1587193,
abstract = {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.},
author = {Kondratiev, Yuri and Kuna, T. and Ohlerich, N.},
issn = {1607-324X},
keyword = {birth-and-death processes, Poisson measure},
number = {2},
pages = {283--291},
publisher = {INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE},
title = {{Selection-mutation balance models with epistatic selection}},
doi = {10.5488/CMP.11.2.283},
volume = {11},
year = {2008},
}