On the adapted equations for several dyploid model in population genetics

Abstract

For a locus with two alleles ($I^A$ and $I^B$), the frequencies of the alleles are represented by
$$p=f(I^A)=\frac{2N_{AA}+N_{AB}}{2N},q=f(I^B)=\frac{2N_{BB}+N_{AB}}{2N}$$
where $N_{AA},N_{AB}$ and $N_{BB}$ are the numbers of $I^A{I}^A,I^A{I}^B$ and $I^B{I}^B$ respectively and $N$ is the total number of populations.
The frequencies of the genotypes expected are calculated by using $p^2,2pq$ and $q^2$. Choi showed the method of whether some genotypes is in these probabalities. Also he calculate the probability generating function for offspring number of genotype under a diploid model(\cite {Choi}). In this paper, let $x(t,p)$ be the probability that $I^A$ become fixed in the population by time $t$-th generation, given that its initial frequency at time $t=0$ is $p$. We find adapted equations for $x$ using the mean change of frequence of alleles and fitness of genotype. Also we apply this adapted equations to several diploid model and it also will apply to actual examples.