Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON THE ADAPTED PARTIAL DIFFERENTIAL EQUATION FOR GENERAL DIPLOID MODEL OF SELECTION AT A SINGLE LOCUS

  • Won Choi (Department of Mathematics, Incheon National University)
  • Received : 2023.09.24
  • Accepted : 2024.04.26
  • Published : 2024.06.30
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Abstract

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an IAIA homozygote, the heterozygote IAIB 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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Acknowledgement

This research was supported by Incheon National University Research Grant, 2023-2024.

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
  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
  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).
  4. R. Lewis, Human Genetics : Concepts and Applications, McGraw-Hill Education (2016).
  5. B.A. Pierce, Genetics Essentials : Concepts and Connections, W.H.Freeman and Company (2014), 216-240.