Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON THE ADAPTED EQUATIONS FOR SEVERAL DYPLOID MODEL IN POPULATION GENETICS

  • Choi, Won (Department of Mathematics, Incheon National University)
  • Received : 2021.10.28
  • Accepted : 2021.11.26
  • Published : 2022.03.30
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Abstract

For a locus with two alleles (IA and IB), 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 NAA, NAB and NBB are the numbers of IAIA, IAIB and IBIB respectively and N is the total number of populations. The frequencies of the genotypes expected are calculated by using p2, 2pq and q2. 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( [1]). In this paper, let x(t, p) be the probability that IA 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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Acknowledgement

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

References

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