Korean J. Math. Vol. 28 No. 1 (2020) pp.1-7
DOI: https://doi.org/10.11568/kjm.2020.28.1.1

On the probability of genotypes in population genetics

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Published: Mar 30, 2020
Keywords:
genotype, mutation and gene conversion rate. allele.
Mathematics Subject Classification:
92D10, 60H30, 60G44

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Won Choi
Department of Mathematics, Incheon National University, Republic of Korea

Abstract

A partition X describes that there exists αi kinds of alleles occurring i loci for each i. All genes have multiple alleles, i.e., they exist in more than two allelic forms, although any one diploid organism can carry no more than two alleles. The number of possible genotypes in a multiple allel series depends on the number of alleles. We will deal with an n locus model in which mutation and gene conversion are taken into consideration. In this paper, we firstly find the probability pn(x) of genotype
pn+1(x)=pn(x)∑k=1rqkxpn(k)
with the rates of mutation and gene conversion. Also we find the probability of genotype without the rates of mutation and gene conversion and we apply this probability to two examples.



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Supporting Agencies

This research was supported by Incheon National University Research Grant 2019-2020.

References

[1] Francisco J.Ayala, Population and Evolutionary Genetics; A Primer, The Benjamin/Cummings Publishing Company, (1982). Google Scholar

[2] W.Choi, The application of stochastic analysis to population genetics model, J. App. Math. Info. 23 (2007), 455–460. Google Scholar

[3] M.Kimura and J.F.Crow, The number of alleles that can be maintained in a finite population, Genetics 49 (1964). Google Scholar

[4] T.Ohta, On the evolution of multigene families, Theor. Por. Biol. 23 (1983) 216–240. Google Scholar

[5] A.Shimizu, Stationary distribution of a diffusion process taking values in probability distributions on the partitions, Proceeding of a Workshop held in Nagoya, Japan. (1985). Google Scholar