功能作图的混合效应模型开发

Mixed-effect model development for functional mapping

【目的】以大肠杆菌菌株丰度和功能作图模型为研究基础,通过在功能作图模型中引入群体的固定效应和个体间亲缘关系造成的随机效应,探究混合效应对功能作图模型性能的影响。【方法】本研究在功能定位框架基础上,使用大肠杆菌动态培养的生长数据作为实际案例,将亚群和SNP基因型作为固定效应的来源,将固定效应因素融入定位模型,提出了Q矩阵模型的扩展;在保留使用方差–协方差模型对随机残差建模的前提下,使用Legendre模型对随机效应建模,开展了固定效应加一般性的随机效应的混合效应模型分析(模型1);利用限制性似然估计的方法推导其方差–协方差参数、随机效应和固定效应,开展了固定效应和亲缘关系造成随机效应的混合模型(模型2)分析;利用Zwald检验法推导各标记位点p值的计算方法。【结果】(1)2种模型中,95%的标记呈现出p值与期望值相吻合的特点,p值分布在QQ图中的上翘结果满意。(2)模型2相比模型1检测到了更多的SNP位点,表明模型2对亲缘关系造成的随机效应解释性更强。(3)计算机模拟结果显示:样本量较小、遗传力较低时,模型假阳性率为4.77%;当样本量为800,遗传力为1%时,模型对QTL的发现率可超过70%;或当样本量为400,遗传力超过1.5%时,QTL发现率也可超过70%。【结论】本研究提出的在功能作图模型中引入固定效应和亲缘关系造成的随机效应的混合模型的方法较好地完善了功能定位理论,对固定效应中的协变量因素具有较好的校正功能,可有效剖分随机效应与剩余残差;为后续完善功能定位,开发固定效应加亲缘关系(Q+K)模型的软件包奠定了良好基础。

[Objective]Using the abundance of Escherichia coli strains and functional mapping model as the research foundation,this study explored the impact of mixed effects on the performance of functional mapping model by introducing fixed effects of the population and random effects caused by kinship relationship among individuals into the functional mapping model.[Method]Based on the framework of functional mapping,this study employed the growth data from dynamic cultures of Escherichia coli as a practical case.Subgroups and SNP genotypes were considered as sources of fixed effects,and these fixed effect factors were integrated into the mapping model,leading to the extension of Q-matrix model.While maintaining the use of variance-covariance model for modeling random residuals,the Legendre model was employed to model random effects.A mixed-effect model analysis combining fixed effects with general random effects(model 1)was conducted.Additionally,the restricted maximum likelihood estimation method was utilized to derive variance-covariance parameters,random effects,and fixed effects,enabling the analysis of a mixed model combining fixed effects with random effects arising from kinship relationships(model 2).Finally,the Zwald test method was utilized to derive the calculation method for p-values at each marker locus.[Result](1)In both models,95%of the markers exhibited p-values that were consistent with the expected values,resulting in satisfactory upward curvature in the QQ plot.(2)Compared with model 1,model 2 detected a greater number of SNP loci,indicating that model 2 provided a stronger explanation for the random effects caused by kinship relationship.(3)Computer simulation results revealed that when the sample size was small and the heritability was low,the false-positive rate of the model was 4.77%.However,when the sample size reached 800 and the heritability was 1%,the discovery rate of quantitative trait loci(QTL)by the model can exceed 70%.Alternatively,when the sample size was 400 and the heritability exceeded 1.5%,the QTL discovery rate can also exceed 70%.[Conclusion]The mixed model approach proposed in this study,which introduces fixed effects and random effects caused by kinship relationship into the functional mapping model,effectively improves the theory of functional localization.This approach exhibits excellent calibration capabilities for covariate factors in fixed effects and can effectively dissect random effects from remaining residuals.This lays a solid foundation for subsequent improvements in functional localization and the development of software packages for the fixed effects plus kinship(Q+K)model.