摘要

用与生产关系密切且广泛存在的孟德尔群体，讨论数量遗传理论。首先，对NilssonEhle小麦粒色实验的原始资料进行分析，得知小麦种皮的深红色受3对基因控制，进而作X²检验，说明数量性状受多基因控制。用Lyapunov中心极限定理证明，基因型值G呈正态分布，小生境环境效应E呈正态分布。从概率角度，阐述G与E的独立，用正态分布的可加性合成G与E，使P=G+E呈正态分布，并且绘制出三正态曲线图。这说明在随机交配下，不论是否连锁，不论基因效应是否相等，不论等位基因是否存在显性和什么样的显性，表现型值P均服从正态分布。吸收微效多基因假说的合理内核，引入环境效应，其应用范围突破微效多基因假说，更加全面和科学。

关键词 数量性状遗传;孟德尔群体;中心极限定理;基因型值G;环境效应E;表现型值P;正态分布

中图分类号 S188+.1;Q348  文献标识码 A  文章编号 0517-6611（2015）03-004-03

Three Normal Distributions—A New Solution for Theory on Quantitative Inheritance

ZHANG Tingzhen

（College of Forestry， Northwest A & F University， Yangling， Shaanxi  712100）

Abstract The theory on quantitative inheritance was discussed in Mendelian group which had a close relation with production. At first the original data of NilssonEhle wheat experiment was analyzed with known genetic knowledge. It was found that red color in the seed coat of a very old red variety was determined by three independent allelomorphic pairs and then a X² test was made indicating quantitative characters were determined by multiple genes. By means of Lyapunov central limit theorem it was certificated that both genotypic value G and the environmental effect in a niche E would be subordinated to the normal distribution and respectively. The independence between G and E was illustrated in the light of probability theory. According to the additivity of independent normal distribution P was composed of G and E making the phenotype value P=G +E would be submitted to the normal distribution N （μG+μE， σ²G+σ²E ）， whether or not the linkage was present， whether or not every gene effect was equal， whether or not there was dominance and what kind of dominance between alleles.

Key words  Inheritance of quantitative character; Mendelian population; Central limit theorem;

Genotypic value G; Environmental effect E; Phenotypic value P; Normal distribution

作者簡介

张廷桢（1939-），男，陕西户县人，教授，从事林木遗传育种方面的研究。

收稿日期 20141205

数量性状遗传是遗传学的重要内容之一。自1909年NilssonEhle发表小麦杂交实验100年以来，国内外在数量遗传理论上都延用着他的研究，但许多人将F₂（种子）的表现型隐去真像，指出由白粒到深红粒有多种级别。实际上，小麦F₂胚外包被的是母体F₁₂n组织，种子应是同一红色。这里所谈的是一种假象。这是其一。第二，没有引入组成数量遗传的另一重要组分——环境效应。NilssonEhle认为没有环境影响。Ayala等认为，环境对小麦粒色变异的影响极小。在NilssonEhle实验中，环境的影响可忽略不计。……