Korean J. Math. Vol. 32 No. 2 (2024) pp.213-218
DOI: https://doi.org/10.11568/kjm.2024.32.2.213

On the adapted partial differential equation for general diploid model of selection at a single locus

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Published: Jun 30, 2024
Keywords:
adapted equation, alleles frequency, mean change, selection coefficient
Mathematics Subject Classification:
92D10, 92B05, 60G07

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

Abstract

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an $I^A I^A$ homozygote, the heterozygote $I^A I^B$ produces. W. Choi found the adapted partial differential equations for the density and operator of the frequency for one gene and applied this adapted partial differential equations to several diploid model. Also, he found adapted partial differential equations for the diploid model against recessive homozygotes and in case that the alley frequency occurs after one generation of selection when there is no dominance. (see. [1,2]).





In this paper, we find the adapted partial equations for the model of selection against heterozygotes and in case that the allele frequency changes after one generation of selection when there is overdominance. Finally, we shall find the partial differential equation of general type of selection at diploid model and it also shall apply to actual examples. This is a very meaningful result in that it can be applied in any model.






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Supporting Agencies

Incheon National University

References

[1] W.Choi, On the adapted equations in various dyploid model and Hardy-Weinburg equilibrium in a triploid model , Korean J. Mathematics 31 (1) (2023). https://doi.org/10.11568/kjm.2023.31.1.17 Google Scholar

[2] W.Choi, On the adapted equations for several dyploid model in population genetics, Korean J. Mathematics, 30 (1) (2022). https://doi.org/10.11568/kjm.2022.30.1.67 Google Scholar

[3] M.Kimura, A Stochastic model of Compensatory Neutral Evolution, Proceedings of a Workshop held in Nagoya, July 8-12. Stochastic Methods in Biology (1985). Google Scholar

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

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