根据三倍体胚乳性状的数量遗传模型，发展出一种新的专用于胚乳性状数量基因座位（QTL）区间作图的统计方法。该方法以分离群体中各植株的分子标记基因型以及植株上若干粒种子胚乳性状的平均值为数据模式，采用基于平均值混合分布理论的极大似然方法进行QTL分析。QTL效应估计通过EM算法实现。由于该方法利用标记基因型内QTL基因型的混合分布特性，因此，它比同样基于株平均值的最小平方QTL分析方法以及迭代重新加权最小平方QTL分析方法具有更高的统计功效和精确度。方法的可行性和有效性通过计算机模拟数据分析得到了进一步验证。
Endosperm traits are important in determining grain quality in cereals. Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue whose genetic constitution is more complex than common diploid tissue. Current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. Based on the quantitative genetic models for triploid endosperm traits and mixture distribution theory, a new maximum likelihood method implemented via expectation-maximization algorithm which included the exact and approximate EM algorithms for mapping of quantitative trait loci (QTL) underlying endosperm traits was proposed in this paper. The method used the DNA molecular marker genotypes of each plant in segregation population such as F2, backcross etc. and the plant average of several endosperms of each plant as data set to map QTL. Because the method considered the mixture distribution property of QTL genotypes within flanking marker genotypes, it was expected that the proposed method not only increase the statistical power of QTL mapping but also improved the accuracy and precision of QTL effect estimates. Efficiency and feasibility of the methods have been verified through Monte Carlo simulation studies. The means and standard deviations of the estimated QTL effects and locations as well as the empirical powers under different QTL heritabilities and sampling strategies were listed in Table 1. Results of simulation showed that: (1) Whether the exact EM algorithm or the approximate EM algorithm, the method may provide accurate estimates of both the QTL effects and locations with very high statistical power; (2) Though the exact EM algorithm can’t significantly increase the statistical power of QTL detecting and the accuracy of QTL locations compared with the approximate EM algorithm, it may apparently increase the precision of QTL locations. The exact EM algorithm had less standard deviation of the estimated QTL locations than the approximate EM algorithm under the investigated treatments. The next step of endosperm QTL mapping is to consider both the maternal diploid genotype and the triploid endosperm genotypes jointly.
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