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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| Datum: | 2008 |
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Інститут фізики конденсованих систем НАН України
2008
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| Schriftenreihe: | Condensed Matter Physics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/119142 |
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| Zitieren: | 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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irk-123456789-1191422017-06-05T03:03:55Z Selection-mutation balance models with epistatic selection Kondratiev, Yu.G. Kuna, T. Ohlerich, N. 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. Ми представляємо застосування процесiв народження-знищення на конфiгурацiйних просторах до узагальненої моделi селекцiйно-мутацiйного балансу. Модель описує старiння популяцiї як процес накопичення мутацiй в генотипi. В математично строгому пiдходi мутацiї вiдповiдають точкам у абстрактному просторi. Наша модель описує нескiнчено-популяцiйну модель з безмежною кiлькiстю точок у континуумi. Динамiчне рiвняння, що описує систему, є типу Кiмури-Маруями. Проблема може бути поставлена в термiнах еволюцiї станiв (диференцiальнi рiвняння) або, що є еквiвалентно, за допомогою формули Фейнмана-Каца. Дослiджується питання iснування розв’язку, його асимптотичної поведiнки, властивостi граничного стану. У неепiстатичному випадку проблема була поставлена i розв’язана у [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 35(1)]. В нашiй моделi ми розглядаємо топологiчний простiр X як простiр позицiй мутацiй та вплив на епiстатичний потенцiал. 2008 Article 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. 1607-324X PACS: 02.50.Ga DOI:10.5488/CMP.11.2.283 http://dspace.nbuv.gov.ua/handle/123456789/119142 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Kondratiev, Yu.G. Kuna, T. Ohlerich, N. |
| spellingShingle |
Kondratiev, Yu.G. Kuna, T. Ohlerich, N. Selection-mutation balance models with epistatic selection Condensed Matter Physics |
| author_facet |
Kondratiev, Yu.G. Kuna, T. Ohlerich, N. |
| author_sort |
Kondratiev, Yu.G. |
| title |
Selection-mutation balance models with epistatic selection |
| title_short |
Selection-mutation balance models with epistatic selection |
| title_full |
Selection-mutation balance models with epistatic selection |
| title_fullStr |
Selection-mutation balance models with epistatic selection |
| title_full_unstemmed |
Selection-mutation balance models with epistatic selection |
| title_sort |
selection-mutation balance models with epistatic selection |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119142 |
| citation_txt |
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. |
| series |
Condensed Matter Physics |
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2025-07-08T15:18:47Z |
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2025-07-08T15:18:47Z |
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