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

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.