Analysis of Difference Equations for Population Genetics
Main Article Content
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: kppuntan@kmitl.ac.th
Article Details
Copyright Transfer Statement
The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.
The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
Here is the link for download: Copyright transfer form.pdf
References
[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, 2940.
[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), 355358.
[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), 174182.
[7] Keshet, E.L., 1989. Mathematical models in biology. 1st ed. New York: Random House.
[8] Ewens, W.J., 1979. Mathematical Population Genetics. SpringerVerlag,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.