在全基因组数量性状基因座(QTL)作图研究中,多个数量性状通常与标记基因型一起测量。多性状QTL(MtQTL)分析,在一个模型中包含多个数量性状,是增加QTL识别能力的有效技术。用于MtQTL映射的两种最广泛使用的经典方法是基于高斯混合模型的MtQTL(GMM-MtQTL)和基于线性回归模型的MtQTL(LRM-MtQTL)分析。存在两种类型的LRM-MtQTL方法,称为基于最小二乘的LRM-MtQTL(LS-LRM-MtQTL)和基于最大似然的LRM-MtQTL(ML-LRM-MtQTL)。这三种经典方法是QTL检测的等效替代方法,但是ML-LRM-MtQTL在计算上比GMM-MtQTL和LS-LRM-MtQTL快。然而,所有上述经典方法的一个主要限制是它们对异常值非常敏感,这导致了误导性的结果。因此,在这项研究中,我们开发了一种基于LRM的鲁棒MtQTL方法,叫做LRM-RobMtQTL,对于回交种群,基于回归参数的稳健估计,通过最大化由多元正态分布的β散度引起的β似然函数。当β=0时,提出的LRM-RobMtQTL方法简化为经典的ML-LRM-MtQTL方法。模拟研究表明,在没有异常值的情况下,ML-LRM-MtQTL和LRM-RobMtQTL方法均可识别出相同的QTL位置。然而,在存在异常值的情况下,只有提出的方法能够识别所有真实的QTL位置。实际数据分析结果表明,在存在异常值的情况下,只有我们的LRM-RobMtQTL方法可以识别所有QTL位置,因为这两种方法都没有异常值。我们得出的结论是,我们提出的LRM-RobMtQTL分析方法优于经典的MtQTL分析方法。
In genome-wide quantitative trait locus (QTL) mapping studies, multiple quantitative traits are often measured along with the marker genotypes. Multi-trait QTL (MtQTL) analysis, which includes multiple quantitative traits together in a single model, is an efficient technique to increase the power of QTL identification. The two most widely used classical approaches for MtQTL mapping are Gaussian Mixture Model-based MtQTL (GMM-MtQTL) and Linear Regression Model-based MtQTL (LRM-MtQTL) analyses. There are two types of LRM-MtQTL approach known as least squares-based LRM-MtQTL (LS-LRM-MtQTL) and maximum likelihood-based LRM-MtQTL (ML-LRM-MtQTL). These three classical approaches are equivalent alternatives for QTL detection, but ML-LRM-MtQTL is computationally faster than GMM-MtQTL and LS-LRM-MtQTL. However, one major limitation common to all the above classical approaches is that they are very sensitive to outliers, which leads to misleading results. Therefore, in this study, we developed an LRM-based robust MtQTL approach, called LRM-RobMtQTL, for the backcross population based on the robust estimation of regression parameters by maximizing the β-likelihood function induced from the β-divergence with multivariate normal distribution. When β = 0, the proposed LRM-RobMtQTL method reduces to the classical ML-LRM-MtQTL approach. Simulation studies showed that both ML-LRM-MtQTL and LRM-RobMtQTL methods identified the same QTL positions in the absence of outliers. However, in the presence of outliers, only the proposed method was able to identify all the true QTL positions. Real data analysis results revealed that in the presence of outliers only our LRM-RobMtQTL approach can identify all the QTL positions as those identified in the absence of outliers by both methods. We conclude that our proposed LRM-RobMtQTL analysis approach outperforms the classical MtQTL analysis methods.