随着大数据的应用普及和测序成本的下降，全基因组关联分析（genome-wide association studies，GWAS）已在人类和动植物数量性状遗传解析方面得到广泛应用，大大推动了人类和动植物遗传学的发展。

然而，相比于传统的对数量性状核苷酸（quantitative trait nucleotide, QTN）进行全基因组扫描的方法，针对连续型数量性状上位性的全基因组关联分析方法鲜有研究。主要是因为传统的统计方法大多数是对所有上位性进行单位点扫描，使得标记数量指数级增长，会导致算法运行时间长、统计功效低、假阳性率高等问题。本研究通过对压缩方差混合模型3VmrMLM算法的应用分析，探索了高维互作组合降维的方法，同时基于加速算法SmrEMMA（Super FASTmrEMMA），提出了多位点混合线性模型上位性关联分析新算法EpiSmrEMMA。新算法分为三个阶段：

第一阶段，使用方差异质性检验方法DGLM对全基因组位点进行扫描，初筛出存在潜在互作效应的QTN，称为方差异质性数量性状核苷酸（variance-heterogeneity QTN，vQTN），随后对所有显著vQTNs标记使用Hadamard 乘积，计算得到上位性对标记。第二阶段，使用SmrEMMA算法中单位点扫描模型，对上述上位性对标记和全基因组标记分别进行独立检测，得到潜在关联标记。第三阶段，将潜在加性和上位性标记联合放入多位点模型中，最终得到显著关联的主效QTNs和QTNQTN互作（QQI）。本研究的主要结果如下：

1.新算法利用方差异质性检验实现上位性标记矩阵降维处理，同时利用多线程并行技术和C++编码进行高维矩阵运算，保证了算法高功效的同时，大大缩短了上位性检测时间。

2.模拟研究共设置了6组标记数为10,000的不同样本量、不同总遗传率的模拟数据：样本量为800、1,000时，设置了0.6、0.8两种总遗传率；样本量为2,000时，设置了0.3、0.5两种总遗传率。每组重复100次。对于QQI的检测，新算法的平均检测功效比REMMA和PLINK分别提高了24.48%和24.32%；效应估计值的均方误差分别减少了0.16和0.42；新算法的假阳性率保持在1.17E-07~2.04E-07区间，REMMA在2.25E-07~1.60E-05区间，而PLINK在8.73E-06~1.13E-03。此外，EpiSmrEMMA算法对6组实验QQI和QTN检测运行时间之和为平均105.86秒，比REMMA快了3倍以上。

3.实际数据分析了拟南芥的9个性状，样本数量在674~1,058之间，SNP数量在19,114~21,590之间。结果显示，EpiSmrEMMA算法的平均运行时间比REMMA算法快了12倍；从基因检测能力来看，新算法挖掘到的已知基因数为29，REMMA为9，且已知基因数占显著位点数的比值是REMMA的5.62倍，而PLINK由于没有考虑到群体结构和多基因背景导致检测出的显著位点数量过于庞大。这表明EpiSmrEMMA算法挖掘基因的能力更精准、更高效。

4.将方差异质性方法与3VmrMLM关联分析方法结合对拟南芥11个开花相关性状进行了应用研究。该真实数据的样本量为199，SNP数量为216,130。共挖掘出34个与开花性状相关联的已知基因，并通过差异表达、功能富集以及单倍型差异分析，挖掘出20个候选基因，其中，AT1G12990和AT1G09950可能存在相互作用。

本研究为全基因组上位性关联分析应用到大数据集上提供了新思路，同时为挖掘与数量性状相关联的上位性互作基因提供了研究方向。

With the widespread application of big data and the decline in sequencing costs, genome-wide association studies (GWAS) have been extensively applied in the genetic dissection of quantitative traits in order to promote genetic development in human, animal and plant.

However, compared to traditional methods for genome-wide scanning of quantitative trait nucleotides (QTNs), there are few studies on GWAS methods for epistasis in continuous quantitative traits. This is because traditional statistical methods involve single-locus scanning for all QQIs (QTN×QTN interactions) across the genome. This approach leads to an exponential increase in the number of markers, resulting in long algorithm running time, low statistical power, and high false - positive rates.In this study, we explored methods for dimensionality reduction of high-dimensional interaction combinations by applying the 3VmrMLM algorithm of the compressed variance mixed model. Meanwhile, based on the accelerated algorithm SmrEMMA (Super FASTmrEMMA), we proposed a new algorithm for epistatic association analysis of the multi-locus mixed linear model, named EpiSmrEMMA. The new algorithm is divided into three stages:

In the first stage, we use the variance heterogeneity test method DGLM to scan the entire genome, preliminarily screening QTNs with potential interaction effects. These QTNs are named variance-heterogeneity QTNs (vQTNs). Subsequently, perform the Hadamard product on all significant vQTNs markers to generate epistatic pair markers. In the second stage, the single-locus model in the SmrEMMA algorithm is used to independently scan the epistatic pair markers in the first stage and the genome-wide markers. In the third stage, potential additive and epistatic markers were jointly incorporated into a multi-locus model to finally identify significantly associated major-effect QTNs and QTN×QTN interactions (QQI). The main results of this study are as follows:

1.The new algorithm achieves dimensionality reduction of the epistatic marker matrix through variance heterogeneity test, and uses multi-threaded parallel processing and C++ coding to perform high-dimensional matrix operations, ensuring high statistical power while significantly reducing the time required for epistasis detection.

2. Six sets of simulated data with 10,000 markers and different sample sizes and total heritability were set up: for sample sizes of 800 and 1,000, total heritability of 0.6 and 0.8 were set; for a sample size of 2,000, total heritability of 0.3 and 0.5 were set. Each set was repeated 100 times. For QQI detection, the new algorithm had 24.48% and 24.32% higher average power than REMMA and PLINK; the average mean squared error of effect estimates was reduced by 0.16 and 0.42, respectively; the false positive rate of the new algorithm was maintained between 1.17E-07 and 2.04E-07, while REMMA was between 2.25E-07 and 1.60E-05, and PLINK was between 8.73E-06 and 1.13E-03. Moreover, the total running time of the EpiSmrEMMA algorithm for QQI and QTN detection in the six experimental sets was an average of 105.86 seconds, which is more than three times faster than REMMA.

3. In the real data analysis of nine traits in Arabidopsis, with sample sizes ranging from 674 to 1,058 and SNP numbers ranging from 19,114 to 21,590, the average running time of the EpiSmrEMMA algorithm was 12 times faster than that of the REMMA algorithm. In terms of gene detection capability, the new algorithm identified 29 known genes, compared to 9 by REMMA, and the ratio of known genes to significant loci was 5.62 times that of REMMA. PLINK, which did not account for population structure and polygenic background, resulted in an excessively large number of significant loci. This indicates that the EpiSmrEMMA algorithm is more precise and efficient in gene mining.

4.The combination of variance heterogeneity methods and 3VmrMLM was applied to 11 flowering-related traits of 199 Arabidopsis accessions with 216,130 markers. A total of 34 known genes associated with flowering-related traits were identified, and 20 candidate genes were mined through differential expression, functional enrichment, and haplotype and phenotypic difference analyses. Among these candidates, AT1G12990 and AT1G09950 may interact with each other.

This study provides a new idea for GWAS of epistasis in large datasets and offers a research direction for mining gene-by-gene interactions associated with quantitative traits.

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