四向杂交（four-way cross）设计是指4个纯系亲本参与杂交衍生分离群体的一种交配设计。尽管国际上已经提出基于四向杂交设计的迭代重新加权最小平方（iteratively reweighed least squares，IRWLS）QTL作图方法，但该方法忽略了双侧标记基因型内QTL基因型的混合分布特性，当QTL位置和标记的位置不重合时作图精度较低。本文根据四向杂交设计的数量遗传模型，发展出基于四向杂交设计和混合分布理论的QTL作图的极大似然估计方法。首先利用染色体上所有标记基因型联合计算该染色体上任一假定位置QTL的条件概率，然后根据混合分布理论建立基于EM算法实现的QTL作图的极大似然估计方法。以计算机模拟数据研究了QTL遗传力、样本容量和分子标记信息含量3个因素对方法的影响，结果表明,（1）在QTL的被发现能力上，标记信息不完全的四向杂交设计仅略低于信息完全时的四向杂交设计；（2）随着QTL遗传力、样本容量和标记信息含量的增大，QTL位置以及效应估计值的准确度和精确度逐步提高。
In recent years, there has been a great deal of interests in the development of methodology to map quantitative trait loci (QTLs) relative to known marker map in population derived from inbred line crosses. However, mapping populations that can be handled by most of developed methods must be derived from the cross of two inbred lines. The drawback of these designs is that the statistical inference space is quite narrow and thus results from one cross cannot be generalized to other crosses derived from different inbred lines. Xu first proposed the four-way cross design of QTL mapping intended to increase the statistical inference space and the opportunity for detecting more QTL. Four-way cross design is a mating design that is derived from the cross of four inbred lines. Although iteratively reweighted least squares (IRWLS) method for mapping QTL in four-way cross design has been proposed, low efficiency of this method was predicted due to neglecting the mixture distribution of QTL genotypes within flanking marker genotypes. In this paper, based on the quantitative genetic model of four-way cross design and the mixture distribution theory, a new method of QTL mapping for four-way cross design was proposed. At first, the conditional probability of QTL genotype at a putative QTL position on chromosome was calculated jointly by using all of marker genotypes on this chromosome; and then a maximum likelihood method implemented via EM algorithm was proposed. The effects of the power of detection, accuracy and precision of QTL mapping in different QTL heritabilities, sample size and molecular marker polymorphism information contents on the proposed method were studied based on simulated data. The results showed: (1) In the power of QTL detection, four-way cross with incomplete genotypic information of DNA molecular markers is slightly lower than that complete marker information. (2) The accuracy and precision of estimates of QTL position and effects will be enhanced as the increasing of QTL heritability, sample size and polymorphism information content of molecular marker.
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