Previous studies have reported that some important loci are missed in single-locus genome-wide association studies (GWAS), especially because of the large phenotypic error in field experiments. To solve this issue, multi-locus GWAS methods have been recommended. However, only a few software packages for multi-locus GWAS are available. Therefore, we developed an R software named mrMLM v4.0.2. This software integrates mrMLM, FASTmrMLM, FASTmrEMMA, pLARmEB, pKWmEB, and ISIS EM-BLASSO methods developed by our lab. There are four components in mrMLM v4.0.2, including dataset input, parameter setting, software running, and result output. The fread function in data.table is used to quickly read datasets, especially big datasets, and the doParallel package is used to conduct parallel computation using multiple CPUs. In addition, the graphical user interface software mrMLM.GUI v4.0.2, built upon Shiny, is also available. To confirm the correctness of the aforementioned programs, all the methods in mrMLM v4.0.2 and three widely-used methods were used to analyze real and simulated datasets. The results confirm the superior performance of mrMLM v4.0.2 to other methods currently available. False positive rates are effectively controlled, albeit with a less stringent significance threshold. mrMLM v4.0.2 is publicly available at BioCode (https://bigd.big.ac.cn/biocode/tools/BT007077) or R (https://cran.r-project.org/web/packages/mrMLM.GUI/index.html) as an open-source software.

Although nonparametric methods in genome-wide association studies (GWAS) are robust in quantitative trait nucleotide (QTN) detection, the absence of polygenic background control in single-marker association in genome-wide scans results in a high false positive rate. To overcome this issue, we proposed an integrated nonparametric method for multi-locus GWAS. First, a new model transformation was used to whiten the covariance matrix of polygenic matrix K and environmental noise. Using the transferred model, Kruskal–Wallis test along with least angle regression was then used to select all the markers that were potentially associated with the trait. Finally, all the selected markers were placed into multi-locus model, these effects were estimated by empirical Bayes, and all the nonzero effects were further identified by a likelihood ratio test for true QTN detection. This method, named pKWmEB, was validated by a series of Monte Carlo simulation studies. As a result, pKWmEB effectively controlled false positive rate, although a less stringent significance criterion was adopted. More importantly, pKWmEB retained the high power of Kruskal–Wallis test, and provided QTN effect estimates. To further validate pKWmEB, we re-analyzed four flowering time related traits in Arabidopsis thaliana, and detected some previously reported genes that were not identified by the other methods.

Many methods used in multi-locus genome-wide association studies (GWAS) have been developed to improve statistical power. However, most existing multi-locus methods are not quicker than single-locus methods. To address this concern, we proposed a fast score test integrated with Empirical Bayes (ScoreEB) for multi-locus GWAS. Firstly, a score test was conducted for each single nucleotide polymorphism (SNP) under a linear mixed model (LMM) framework, taking into account the genetic relatedness and population structure. Then, all of the potentially associated SNPs were selected with a less stringent criterion. Finally, Empirical Bayes in a multi-locus model was performed for all of the selected SNPs to identify the true quantitative trait nucleotide (QTN). Our new method ScoreEB adopts the similar strategy of multi-locus random-SNP-effect mixed linear model (mrMLM) and fast multi-locus random-SNP-effect EMMA (FASTmrEMMA), and the only difference is that we use the score test to select all the potentially associated markers. Monte Carlo simulation studies demonstrate that ScoreEB significantly improved the computational efficiency compared with the popular methods mrMLM, FASTmrEMMA, iterative modified-sure independence screening EM-Bayesian lasso (ISIS EM-BLASSO), hybrid of restricted and penalized maximum likelihood (HRePML) and genome-wide efficient mixed model association (GEMMA). In addition, ScoreEB remained accurate in QTN effect estimation and effectively controlled false positive rate. Subsequently, ScoreEB was applied to re-analyze quantitative traits in plants and animals. The results show that ScoreEB not only can detect previously reported genes, but also can mine new genes.

Previous studies reported that some important loci are missed in single-locus genome-wide association studies (GWAS), especially because of the large phenotypic error in field experiments. To solve this issue, multi-locus GWAS methods have been recommended. However, only a few software packages are available. Therefore, an R software mrMLM, which includes our six multi-locus methods, was developed. mrMLM includes three components: dataset input, parameter setting and result output. The fread function in data.table is used to quickly read datasets, especially big datasets, and the doParallel package is used to conduct parallel computation using multiple CPUs. In addition, the graphical user interface software mrMLM.GUI v4.0, built upon Shiny, is also available. To confirm the correctness of the above programs, the same simulation datasets as used in previous studies, along with three real datasets, were re-analyzed by all the methods in mrMLM v4.0 and three widely-used methods. The results confirmed the advantages of our multi-locus methods over the current methods. The conclusion is also consistent with those in a Research Topic in Frontiers in Plant Science. Although a less stringent significance threshold is adopted, the false positive rates are effectively controlled. mrMLM is publicly available at https://cran.r-project.org/web/packages/mrMLM/index.html or https://bigd.big.ac.cn/biocode/tools/BT007077 as an open-source software.

In genome-wide association studies, linear mixed models (LMMs) have been widely used to explore the molecular mechanism of complex traits. However, typical association approaches suffer from several important drawbacks: estimation of variance components in LMMs with large scale individuals is computationally slow; single-locus model is unsatisfactory to handle complex confounding and causes loss of statistical power. To address these issues, we propose an efficient two-stage method based on hybrid of restricted and penalized maximum likelihood, named HRePML. Firstly, we performed restricted maximum likelihood (REML) on single-locus LMM to remove unrelated markers, where spectral decomposition on covariance matrix was used to fast estimate variance components. Secondly, we carried out penalized maximum likelihood (PML) on multi-locus LMM for markers with reasonably large effects. To validate the effectiveness of HRePML, we conducted a series of simulation studies and real data analyses. As a result, our method always had the highest average statistical power compared with multi-locus mixed-model (MLMM), fixed and random model circulating probability unification (FarmCPU), and genome-wide efficient mixed model association (GEMMA). More importantly, HRePML can provide higher accuracy estimation of marker effects. HRePML also identifies 41 previous reported genes associated with development traits in Arabidopsis, which is more than was detected by the other methods.