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Seminars & Lectures

* TITLE

[JRG Seminar] Solution of the Crow-Kimura model of molecular evolution using spin-coherent states

* SPEAKERS

Name	Affiliation	E-mail
Dr. Mark Ancliff	Catholic University of Korea	Prof. Xin Zhou - xzhou(at)apctp.org

* HOST(Applicant)

Name	Affiliation	E-mail
-

* DATE / TIME

2009-03-11, 10am

* PLACE

Hogil Memorial Bldg. 512, APCTP Headquarters, POSTECH, Pohang

* ABSTRACT

\"The Crow-Kimura model[1] describes the evolution of an asexually reproducing population subject to random mutation and selection. Individuals are labelled by a DNA-like string of letters of a fixed length N, and the population is described by a distribution function on the set of possible strings. The Crow-Kimura model is a popular starting point for theoretical studies of molecular evolution, and has recently been applied to studies of virus-immune system interaction, evolution in changing environments, and extended to diploid populations[2-4].
It has been shown that the Crow-Kimura model can be mapped onto a quantum spin system similar to the one-dimensional quantum Ising model[5]. This mapping allows the application of several techniques from statistical physics. Here we present a new method for calculating equilibrium population in the Crow-Kimura model by constructing a spin coherent-state path integral representation of the evolution operator. In the large N limit a semi-classical approximation gives a description in terms of a classical Hamiltonian function on a sphere. Various extensions of the Crow-Kimura model are easily approached with our method, and results will be presented for the case when the mutation rate varies between different sites on the genome -- a phenomena observed in real populations.
\"

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