Selection-mutation balance models with epistatic selection
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...
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| Date: | 2008 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2008
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| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/119142 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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