Coarse graining in genetic dynamics: A renormalization group analysis of a simple genetic system

Abstract

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.