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Selection-mutation balance models with epistatic selection

Kondratiev, Y. G., Kuna, T. and Ohlerich, N. (2008) Selection-mutation balance models with epistatic selection. Condensed Matter Physics, 11 (2). pp. 283-291. ISSN 1607-324X

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Official URL: http://www.icmp.lviv.ua/journal/zbirnyk.54/index.h...

Abstract/Summary

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:1397
Additional Information:Conference on Infinite Particle Systems - Complex Systems III JUN, 2007 Kazimierz Dolny, POLAND
Publisher:Institute for Condensed Matter Physics

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