广义双列杂交设计的配合力假设检验模型分析

A Generalized Approach to Analyzing Diallel Crosses of Hypothetical Test Model on Combining Ability

定义了更为广义的双列杂交第1类线性模型。根据4种双列杂交设计(Ⅰ,Ⅱ,Ⅲ,Ⅳ型)的一般配合力、反交效应、特殊配合力的定义,构造零假设H0,导出4种双列杂交的配合力的限制性方程组(Hβ=L),分别生成3种配合力的指定的假设检验模型,并合成4种双列杂交的配合力方差分析表,从而构造了广义双列杂交模型。然后,根据4种双列杂交类型配合力的限制性方程组(Hβ=L)之间的包容性关系,得到的6个"模板矩阵",双列杂交(Ⅱ、Ⅲ、Ⅳ型)的配合力的限制型矩阵可由其"模板矩阵"生成。由于双列杂交(Ⅱ、Ⅲ、Ⅳ型)可看成双列杂交Ⅰ型的"缺失型",故可推广到有少量(10%以下)的数据缺失的不完全的双列杂交假设检验。因此,对假设检验模型的结构进行修改,还可以实现广义双列杂交模型的扩充。

In this study, a linear model of a generalized diallel crosses for typeⅠis proposed. It is based on the null hypothesis （H0） with regard to the four types of diallel crosses design （TypeⅠ,Ⅱ,ⅢandⅣ）. Generally combining ability （GCA）, specific combining ability（SCA） and reciprocal cross effect. The restriction equations（Hβ=L） of the combining ability can be derived. Also the hypothetical test model of three kinds of combining ability can be carried out. A combined analysis of variance for diallel crosses of combining ability is presented in table 2, and it also constitutes the mathematical foundations for the generalized diallel crosses model（GDCM）. According to the analysis of the inclusiveness concerning the restriction equations（Hβ=L）, six types of modular matrix can be obtained. The restricted matrix for the diallel crosses of combining ability （including：TypeⅡ,ⅢandⅣ） can be derived from its modular matrix. It is generally acknowledged that the diallel crosses （TypeⅡ,ⅢandⅣ） is one of TypeⅠwith missed data. Therefore, the method to build modular matrix can be applied to hypothesis testing of incomplete diallel crosses with a small amount of data loss （less than 10%）. Finally, the modification of hypothetical test model structure will be conductive to extending GDCM.