Mathematical models in genetics
- Authors: Traykov M.1, Trenchev I.1
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Affiliations:
- Cеnter for Advanced Bioinformatics Research
- Issue: Vol 52, No 9 (2016)
- Pages: 985-992
- Section: Mathematical Models and Methods
- URL: https://journals.rcsi.science/1022-7954/article/view/187894
- DOI: https://doi.org/10.1134/S1022795416080135
- ID: 187894
Cite item
Abstract
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.
About the authors
M. Traykov
Cеnter for Advanced Bioinformatics Research
Author for correspondence.
Email: metodi.gt@gmail.com
Bulgaria, Blagoevgrad, 2700
Iv. Trenchev
Cеnter for Advanced Bioinformatics Research
Email: metodi.gt@gmail.com
Bulgaria, Blagoevgrad, 2700