Selection-mutation balance models with epistatic selection

Kondratiev Y, Kuna T, Ohlerich N (2008)
In: Condensed Matter Physics. CONDENSED MATTER PHYSICS, 11(2). INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE: 283-291.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Kuna, T.; Ohlerich, N.
Abstract / Bemerkung
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.
Stichworte
birth-and-death processes; Poisson measure
Erscheinungsjahr
2008
Titel des Konferenzbandes
Condensed Matter Physics
Band
11
Ausgabe
2
Seite(n)
283-291
ISSN
1607-324X
Page URI
https://pub.uni-bielefeld.de/record/1587193

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Kondratiev Y, Kuna T, Ohlerich N. Selection-mutation balance models with epistatic selection. In: Condensed Matter Physics. CONDENSED MATTER PHYSICS. Vol 11. INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE; 2008: 283-291.
Kondratiev, Y., Kuna, T., & Ohlerich, N. (2008). Selection-mutation balance models with epistatic selection. Condensed Matter Physics, CONDENSED MATTER PHYSICS, 11, 283-291. INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE. doi:10.5488/CMP.11.2.283
Kondratiev, Y., Kuna, T., and Ohlerich, N. (2008). “Selection-mutation balance models with epistatic selection” in Condensed Matter Physics CONDENSED MATTER PHYSICS, vol. 11, (INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE), 283-291.
Kondratiev, Y., Kuna, T., & Ohlerich, N., 2008. Selection-mutation balance models with epistatic selection. In Condensed Matter Physics. CONDENSED MATTER PHYSICS. no.11 INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE, pp. 283-291.
Y. Kondratiev, T. Kuna, and N. Ohlerich, “Selection-mutation balance models with epistatic selection”, Condensed Matter Physics, CONDENSED MATTER PHYSICS, vol. 11, INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE, 2008, pp.283-291.
Kondratiev, Y., Kuna, T., Ohlerich, N.: Selection-mutation balance models with epistatic selection. Condensed Matter Physics. CONDENSED MATTER PHYSICS. 11, p. 283-291. INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE (2008).
Kondratiev, Yuri, Kuna, T., and Ohlerich, N. “Selection-mutation balance models with epistatic selection”. Condensed Matter Physics. INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE, 2008.Vol. 11. CONDENSED MATTER PHYSICS. 283-291.