Average time until fixation of a mutant allele in a given population

Abstract

One of the important problems in population genetics is how long it takes for a gene to go to fixation (become established). A mutant gene in a given population will eventually be lost or established. The particular interest of this research is to know the mean time for a mutant gene to become fixed in a population, and we will exclude the case when this gene is lost. A diploid population of N individuals will be considered with a forward and backward mutation of u and v respectively per basis. Using a set of nonlinear equations, we will first calculate the genotype frequencies which will allow us to find the equilibrium points for the infinite population. With the diffusion theory, we will approximate the time to fixation for finite populations. We will then proceed with a numerical approximation using C++ to see a close result for the problem.