On the genotype frequencies and generating function for frequencies in a dyploid model

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 $q^2$. So in this paper, we consider the method of whether some genotypes is in Hardy-Weinburg equilibrium. Also we calculate the probability generating function for the offspring number of genotype produced by a mating of the $i$th male and $j$th female under a diploid model of $N$ population with $N_1$ males and $N_2$ females. Finally, we have conditional joint probability generating function of genotype frequencies.