Mathematical models in genetics
- 80 Downloads
In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.
Keywordsgenetics mathematical models mathematical genetics bioinformatics
Unable to display preview. Download preview PDF.
- 2.Lange, K., Applied Probability, New York: Springer-Verlag, 2003.Google Scholar
- 5.Cavalli-Sforza, L.L. and Bodmer, W.F., The Genetics of Human Populations, San Francisco: Freeman, 1971.Google Scholar
- 6.Crow, J.F. and Kimura, M., An Introduction to Population Genetics Theory, New York: Harper and Row, 1970.Google Scholar
- 7.Elandt-Johnson, R.C., Probability Models and Statistical Methods in Genetics, New York: Wiley, 1971.Google Scholar
- 8.Hartl, D.L. and Clark, A.G., Principles of Population Genetics, Sunderland: Sinauer Assoc., 1989.Google Scholar
- 12.Li, C.C., First Course in Population Genetics, Pacific Grove: Boxwood Press, 1976.Google Scholar
- 13.Nesse, R.M., When Bad Genes Happen to Good People, Technology Review, 1995.Google Scholar
- 20.Bürger, R., Some Mathematical Models in Evolutionary Genetics, Basel: Springer-Verlag, 2011, pp. 67–89.Google Scholar
- 27.Shahshahani, S., A New Mathematical Framework for the Study of Linkage and Selection, Providence: Amer. Math. Soc., 1979.Google Scholar
- 28.Svirezhev, Yu.M., Optimality principles in population genetics, in Studies in Theoretical Genetics, Novosibirsk: Inst. Tsitol. Genet., 1972, pp. 86–102.Google Scholar
- 29.Bürger, R., The Mathematical Theory of Selection, Recombination, and Mutation, Chichester: Wiley, 2000.Google Scholar