Mathematical models in genetics

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• 作者：M. Traykov ; Iv. Trenchev
• 关键词：genetics ; mathematical models ; mathematical genetics ; bioinformatics
• 刊名：Russian Journal of Genetics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：52
• 期：9
• 页码：985-992
• 全文大小：194 KB
• 刊物类别：Biomedical and Life Sciences
• 刊物主题：Biomedicine
  Human Genetics
  Animal Genetics and Genomics
  Microbial Genetics and Genomics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1608-3369
• 卷排序：52

文摘

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.