Abstract

STEPHENS, C.R.; CHRYSSOMALAKOS, C.  and  ZAMORA, Adolfo. Coarse graining in genetic dynamics: A renormalization group analysis of a simple genetic system. Rev. mex. fis. [online]. 2004, vol.50, n.4, pp.388-396. ISSN 0035-001X.

We show how the idea of coarse graining can be applied fruitfully to the area of genetic dynamics, both in the context of "effective" theories -leading to more appropriate effective degrees of freedom with which to describe the dynamics - as well as in terms of integrating out degrees of freedom, using the Renormalization Group as a systematic calculational scheme. Specializing to dynamics in the presence of selection and mutation we show how the Renormalization Group can be implemented at the level of a transfer matrix-type description. Further, we present an explicit exact RG transformation for the simple case of a one gene-two allele system, solving for its fixed points and the asymptotic behaviour of the system in the vicinity of these fixed points.

Keywords : Renormalization Group; Genetic Dynamics; Coarse graining; Selection; Mutation; Evolution.