On the representation of probability vector with special diffusion operator using the mutation and gene conversion rate

Abstract

We will deal with an $n$ locus model in which mutation and gene conversion are taken into consideration. Also random partitions of the number $n$ determined by chromosomes with $n$ loci should be investigated. The diffusion process describes the time evolution of distributions of the random partitions. In this paper, we find the probability of distribution of the diffusion process with special diffusion operator $L_1$ and we show that the average probability of genes at different loci on one chromosome can be described by the rate of gene frequency of mutation and gene conversion.