Korean J. Math.  Vol 29, No 1 (2021)  pp.75-80
DOI: https://doi.org/10.11568/kjm.2021.29.1.75

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

Won Choi


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.  


genotype frequencies, probability generating function. allele

Subject classification

92D10, 60H30, 60G44


Full Text:



W. Choi, On the probability of genotypes in population genetics , Korean J. Mathematics 28 (1) (2020). (Google Scholar)

R. Lewis, Human Genetics : Concepts and Applications, McGraw-Hill Education (2016). (Google Scholar)

B.A. Pierce, Genetics Essentials : Concepts and Connections, W. H. Freeman and Company (2014), 216–240. (Google Scholar)


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