Selection-mutation balance models with epistatic selection

• Дата: 2008
• Автори: Kondratiev, Yu.G., Kuna, T., Ohlerich, N.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут фізики конденсованих систем НАН України 2008
• Назва видання: Condensed Matter Physics
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/119142
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Selection-mutation balance models with epistatic selection / Yu.G. Kondratiev, T. Kuna, N. Ohlerich // Condensed Matter Physics. — 2008. — Т. 11, № 2(54). — С. 283-291. — Бібліогр.: 7 назв. — англ.

We present an application of birth-and-death 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 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.