A random evolution related to a Fisher-Wright-Moran model with mutation, recombination and drift. (English) Zbl 1032.92025
Summary: The paper deals with a model of the genetic process of recombination, one of the basic mechanisms of generating genetic variability. Mathematically, the model can be represented by the so-called random evolution of R. J. Griego and R. Hersh [Trans. Am. Math. Soc. 156, 405-418 (1971; Zbl 0223.35082); Proc. Natl. Acad. Sci. USA 62, 305-308 (1969; Zbl 0174.15401)], in which a random switching process selects from among several possible modes of operation of a dynamical system. The model, introduced by J. Polańska and M. A. Kimmel [Arch. Control Sci. 9 (XVL) (1-2), 143-157 (1999)], involves mutations in the form of a time-continuous Markov chain and genetic drift. We demonstrate asymptotic properties of the model under different demographic scenarios for the population in which the process evolves.
MSC:
| 92D15 | Problems related to evolution |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
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