孟德尔群体数量性状遗传的概率论分析

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

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。

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 Gwould be submitted to the normal distributionN（μG,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（μE,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＋Ewould be submitted to the normal distribution N（μG＋μE,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.