数量性状基因（quantitative trait locus, QTL）定位以及数量性状遗传规律研究，对于基础作物生物学和农业育种具有十分重要的理论意义和应用价值。基于双亲群体的连锁分析（linkage analysis）能检测到的QTL个数有限，作图精度低；基于自然群体的全基因组关联分析（genome-wide association analysis, GWAS）受群体结构影响大，假阳性率（false discovery rate, FDR）高。不少研究表明，上位性QTL在生物性状的遗传结构和解释性状的遗传变异中起着不可忽视的作用。但是，在人类遗传学中提出的上位型检测方法不适用于作物遗传学研究，在作物中适用于分离群体的上位型检测方法不适用于自然群体，如何从统计模型上整合连锁和关联分析提高上位性QTL的检测功效也鲜有报道。 针对以上问题，本研究提出了QTL以及上位性QTL定位的新方法—SVDReg。SVDReg首先利用矩阵论中的奇异值分解（singular value decomposition, SVD）选取主要的成分。然后经过最小二乘回归和线性变换得到分子标记的效应估计值，再通过构造检验统计量筛选重要标记，定位出控制性状的QTL。最后借助LASSO（least absolute shrinkage and selection operator）回归筛选出与性状显著关联的上位性QTL。为验证SVDReg的有效性，通过蒙特卡洛计算机模拟试验和五套真实群体对动植物复杂性状进行了遗传研究。在模拟试验中，分别对双亲群体和自然群体模拟三种不同的遗传模型，将SVDReg与双亲QTL定位主流统计方法完备区间作图（inclusive composite interval mapping, ICIM）、关联分析QTL定位主流方法FarmCPU（fixed and random model circulating probability unification）和混合线性模型（mixed linear model, MLM）做比较。 结果表明在自然群体中SVDReg的QTL和互作QTL的检测功效都高于90%，FDR都低于10%。在真实的大麦加倍单倍体（doubled haploid, DH）群体中，SVDReg定位出控制三个环境下粒重性状的基因个数分别为9、11和6；由于缺乏有效的自然群体中上位性QTL定位方法，在真实大豆自然群体中，Fang等在2017年通过实验发现并验证了两个大豆株高基因Dt1和Dt2间的互作，SVDReg也利用这套数据定位出Dt1和Dt2间的互作，除此之外还检测出34个加性QTL和4对上位性QTL，解释株高表型变异的71.91%。在玉米自然群体中，SVDReg定位的QTL和上位性QTL解释油份浓度表型变异的87.17%，解释生长度日（growing degree days, GDD）表型变异的82.08%；在猪群体中，SVDReg定位的QTL和上位性QTL分别解释7.36%和21.11%的体重表型变异。 模拟试验和实际数据应用结果均表明，SVDReg在统计模型上整合了连锁和关联分析，既能对双亲群体进行有效分析，又能对自然群体进行精准研究；不仅能检测QTL自身的效应，而且能在短时间内检测到QTL间的互作效应。SVDReg为应用测序时代高通量分子标记进行数量性状遗传分析提供了高效的工具，为遗传网络的检测奠定了方法基础。

Detecting QTL (quantitative trait locus) and studying the genetic architecture of the quantitative traits are of great theoretical significance and application value for basic crop biology and agricultural breeding. It is well-known that based on bi-parental population the number of QTL detected by linkage analysis was limited and mapping accuracy was low; while based on natural population QTL detected by GWAS (genome-wide association analysis) was strongly influenced by population structure thus had a high FDR (false discovery rate). Previous studies showed that epistasis was important in determining the genetic architecture of quantitative traits and explaining their genetic variation. But epistasis mapping methods proposed in human genetics were not suitable for crop genetics, methods of epistatic mapping for bi-parental population in crops were not suitable for natural population, and how to integrate linkage and association analysis in one statistical model to further improve the detection efficiency of epistasis was rarely reported. To solve the above problems, we proposed a new method called SVDReg to detect QTL and epistasis. Firstly, SVD (singular value decomposition) was applied to choose important principal components. Secondly, least square regression and linear transformation were used to estimate the effects of markers, then molecular markers were scanned by test statistics as major-effect QTL associated with the trait of interest. Finally, LASSO (least absolute shrinkage and selection operator) was utilized to detect the epistatic QTL. To validate the effectiveness and efficiency of SVDReg, we used Monte Carlo simulation experiments and five real populations to study the inheritance of complex traits on animals and plants. In simulation experiments, we considered three genetic models in both bi-parental and natural populations, and compared SVDReg with ICIM (inclusive composite interval mapping) as the mainstream statistical method for detecting QTL in bi-parental population, and FarmCPU (fixed and random model circulating probability unification) and MLM (mixed linear model) as the mainstream association analysis for detecting QTL. Results showed that power of QTL and epistatic QTL from SVDReg was higher than 90%, and FDR was lower than 10% in natural population. In real barley DH (doubled haploid) population, the number of QTL detected by SVDReg were 9, 11 and 6 for kernel weight in three different environments, respectively. Due to the lack of approporiate method for detecting epistatic QTL in natural population, Fang et al. found and verified the interaction between gene Dt1 and Dt2 controlling plant height through experiment in 2017 in a real soybean natural population. SVDReg also found the interaction between Dt1 and Dt2. In addition, 34 additive QTL and 4 pairs of epistatic QTL detected by SVDReg explained 71.91% of the phenotypic variation of plant height. In maize population, markers and interactions detected by SVDReg explained 87.17% of the phenotypic variance of oil concentration, and explained 82.08% of the phenotypic variance of GDD (growing degree days). In pig population with body weight, QTL detected by SVDReg explained 7.36% of the phenotypic variance, and epistatic QTL detected by SVDReg explained 21.11% of the phenotypic variance. The results obtained in this study showed that SVDReg integrated linkage and association analysis in one statistical model. SVDReg not only can effectively analyze bi-parental population, but also precisely study natural population. SVDReg can detect the effect of QTL and interaction between QTL in a short time. SVDReg provided an efficient tool for genetic analysis of quantitative trait by using high-throughput molecular markers in sequencing era, and laid the foundation for the detection of genetic network.