孟德尔群体数量性状遗传的概率论分析

以随机交配的孟德尔群体为对象，用Lyapunov和De Moivre-Laplace中心极限定理证明，当基因位点数n充分大时，在一般孟德尔群体和p=q=1/2的Hardy-Weinberg平衡群体中，基因型值（G）均呈正态分布；用Lyapunov中心极限定理证明，当环境因子n充分大时, 以个体数众多为特点的孟德尔群体的小生境环境效应（E）呈正态分布。从概率论角度阐述G、E之间的独立性。 由相互独立正态分布的可加性得出了P=G+E呈正态分布，即孟德尔群体的数量性状呈正态分布。从基因型和环境两方面讨论了数量性状的遗传问题。

Analysis on the Inheritance of Quantitative Characters in Mendelian Population By Means of Probability Theory

A random mating Mendelian population was used as the research object to discuss quantitative character inheritance. In a general Mendelian population and Hardy-Weinberg equilibrium population with p=q=1/2, with the help of Lyapunov central limit theorem and De Moivre-Laplace central limit theorem, it was proved respectively that both genotypic value G would be submitted to the normal distributionN(μ_G,σ₂G), when the number of gene locus n is sufficiently large. By means of Lyapunov central limit theorem it was certificated that the environmental effect in a niche E would be subordinated to the normal distributionN(μ_E,σ₂E), when the number of the environmental factor n is sufficiently large. The independence between A and E was illustrated in the light of probability theory. According to the additivity of the independent normal distribution it was concluded that the phenotype value P=G+E would be submitted to the normal distribution N(μ_G+μ_E,σ₂G+σ₂E), namely, the quantitative character in the Mendelian population would obey the normal distribution. Thus, the inheretance of quantitative character were elaborated in both genotypic and environmental aspects.