Korean J. Math. Vol. 30 No. 1 (2022) pp.67-72
DOI: https://doi.org/10.11568/kjm.2022.30.1.67

On the adapted equations for several dyploid model in population genetics

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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 $q^2$. 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.

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Supporting Agencies

This research was supported by Incheon National University Research Grant 2021-2022.


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