Analysis of Difference Equations for Population Genetics

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Puntani Pongsumpun*

Abstract

The genetics of populations with discrete generations were studied in this paper. We explored the change of the relative frequencies of genes based on the Hardy-Weinberg law. The difference equations were formulated for describing their changes. The stability theorem was used for analysis. The numerical simulations were found with the different situations.


Keywords: difference equations, genetics, Hardy-Weinberg law, stability theorem


*Corresponding author:


E-mail: [email protected]

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Original Research Articles

References

[1] Crow, J.F. and Kimura, M., 1970. An Introduction to population genetics theory. Harper and Row, New York.
[2] Mathematical Genetics, [online] Avaiable at: https://www.genetics.ucla.edu/courses/ hg236b/Lange_Chapter_PopGenetics.pdf.
[3] Population genetics, [online] Avaiable at: https://www2.le.ac.uk/departments/genetics/vgec/ schoolscolleges/topics/population-genetics.
[4] Chen, T., He, H.L. and Church, G.M., 1999. Modeling gene expression with differential equations, Pacific Symposium on Biocomputing, 4, 2940.
[5] Sargolzaie, N. and Miri-Moghaddam, E., 2014. A local equation for differential diagnosis of β-thalassemia trait and iron deficiency anemia by logistic regression analysis in Southeast Iran. Hemoglobin, 38(5), 355358.
[6] Sirachainan, N., Iamsirirak, P., Charoenkwan, P., Kadegasem, P., Wongwerawattanakoon, P., Sasanakul, W., Chansatitporn, N. and Chuansumrit, A., 2014. New Mathematical Formula for Differentiating Thalassemia Trait and Iron Deficiency Anemia in Thalassemia Prevalent Area: A study in Healthy School-Age Children, The Southeast Asian Journal of Tropical Medicine and Public Health, 45(1), 174182.
[7] Keshet, E.L., 1989. Mathematical models in biology. 1st ed. New York: Random House.
[8] Ewens, W.J., 1979. Mathematical Population Genetics. SpringerVerlag,New York.
[9] Li, C.C., 1976. A First Course in Population Genetics. Boxwood Press, Pacific Grove, Calif.
[10] Roughgarden, J., 1979. Theory of Population Genetics and Evolution Ecology: An Introduction. Macmillan, New York.
[11] Segel, L.A., 1984. Modeling Dynamic Phenomena in Molecular and Cellular Biology. Cambridge University Press, Cambridge.
[12] Smith, J.M., 1968. Mathematical Ideas in Biology. Cambridge University Press, Cambridge.
[13] Allman, E.S. and Rhodes, J.A., 2004. Mathematical models in Biology: An Introduction, Cambridge University Press.
[14] Etheridge, A., 2009. Some Mathematical Models from Population Genetics, [online] Avaiable at: https://www.stats.ox.ac.uk/~etheridg/orsay/notes1.pdf.