遗传学中的数学模型。

Genetika Pub Date : 2016-09-01 DOI:10.7868/s0016675816080130
M Traykov, Iv Trenchev
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引用次数: 0

摘要

在本研究中,我们提出了一些群体遗传学的基本思想。群体遗传学的创始人是R.A. Fisher, S. Wright和J. B.S. Haldane。他们不仅发展了几乎所有与遗传学相关的基本理论,而且还发起了多项实验来支持他们的理论。哈代-温伯格定律产生的最早的重要见解之一是,孟德尔遗传保留了自然选择作用的基因变异。我们将限于用微分方程表示的简单模型。其中一些微分方程是非线性的,因此强调诸如不动点的稳定性和这些方程运行的时间尺度等问题。首先,我们考虑了选择作用于二倍体位点的经典情况,在二倍体位点上可以获得任意数量的等位基因。然后,我们考虑包含多位点重组和选择的摘要。此外,我们还讨论了数量性状的演化。在这种情况下,理论是根据直接可测量的量制定的。几十年来,这一理论的特殊情况已成功地应用于植物和动物育种。
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Mathematical models in genetics.

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.

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