On the relations for limiting case of selection with equilibrium and mutation of diploid model

Abstract

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an $I^A I^A$ homozygote, the heterozygote $I^A I^B$ produces. Choi find the adapted partial equations for the model of selection against heterozygotes and in case that the allele frequency changes after one generation of selection when there is overdominance. Also he find the partial differential equation of general type of selection at diploid model and it also shall apply to actual examples. This is a very meaningful result in that it can be applied in any model ([1], [2]). In this paper, we start with the limiting case of selection against recessive alleles. For the time being, assume that the trajectories of $p_t$ and $q_t$ at time $t$ can be approximated by paths which are continuous and therefore we have a diffusion process. We shall find the relations for time $t$, $p_t$ and $q_t$ and apply to equilibrium state and mutation.