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.

Rice, which supports more than half the population worldwide, is one of the most important food crops. Thus, potential yield-related quantitative trait nucleotides (QTNs) and QTN-by-environment interactions (QEIs) have been used to develop efficient rice breeding strategies. In this study, a compressed variance component mixed model, 3VmrMLM, in genome-wide association studies was used to detect QTNs for eight yield-related traits of 413 rice accessions with 44,000 single nucleotide polymorphisms. These traits include florets per panicle, panicle fertility, panicle length, panicle number per plant, plant height, primary panicle branch number, seed number per panicle, and flowering time. Meanwhile, QTNs and QEIs were identified for flowering times in three different environments and five subpopulations. In the detections, a total of 7~23 QTNs were detected for each trait, including the three single-environment flowering time traits. In the detection of QEIs for flowering time in the three environments, 21 QTNs and 13 QEIs were identified. In the five subpopulation analyses, 3~9 QTNs and 2~4 QEIs were detected for each subpopulation. Based on previous studies, we identified 87 known genes around the significant/suggested QTNs and QEIs, such as LOC_Os06g06750 (OsMADS5) and LOC_Os07g47330 (FZP). Further differential expression analysis and functional enrichment analysis identified 30 candidate genes. Of these candidate genes, 27 genes had high expression in specific tissues, and 19 of these 27 genes were homologous to known genes in Arabidopsis. Haplotype difference analysis revealed that LOC_Os04g53210 and LOC_Os07g42440 are possibly associated with yield, and LOC_Os04g53210 may be useful around a QEI for flowering time. These results provide insights for future breeding for high quality and yield in rice.

Rice (Oryza sativa) is one of the most important cereal crops in the world, and yield-related agronomic traits, including plant height (PH), panicle length (PL), and protein content (PC), are prerequisites for attaining the desired yield and quality in breeding programs. Meanwhile, the main effects and epistatic effects of quantitative trait nucleotides (QTNs) are all important genetic components for yield-related quantitative traits. In this study, we conducted genome-wide association studies (GWAS) for 413 rice germplasm resources, with 36,901 single nucleotide polymorphisms (SNPs), to identify QTNs, QTN-by-QTN interaction (QQI), and their candidate genes, using a multi-locus compressed variance component mixed model, 3VmrMLM. As a result, two significant QTNs and 56 paired QQIs were detected, amongst 5219 genes of these QTNs, and 26 genes were identified as the yield-related confirmed genes, such as LCRN1, OsSPL3, and OsVOZ1 for PH, and LOG and QsBZR1 for PL. To reveal the substantial contributions related to the variation of yield-related agronomic traits in rice, we further implemented an enrichment analysis and expression analysis. As the results showed, 114 genes, nearly all significant QQIs, were involved in 37 GO terms; for example, the macromolecule metabolic process (GO:0043170), intracellular part (GO:0044424), and binding (GO:0005488). It was revealed that most of the QQIs and the candidate genes were significantly involved in the biological process, molecular function, and cellular component of the target traits. The demonstrated genetic interactions play a critical role in yield-related agronomic traits of rice, and such epistatic interactions contributed to large portions of the missing heritability in GWAS. These results help us to understand the genetic basis underlying the inheritance of the three yield-related agronomic traits and provide implications for rice improvement.

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.

Categorical (either binary or ordinal) quantitative traits are widely observed to measure count and resistance in plants. Unlike continuous traits, categorical traits often provide less detailed insights into genetic variation and possess a more complex underlying genetic architecture, which presents additional challenges for their genome-wide association studies. Meanwhile, methods designed for binary or continuous phenotypes are commonly used to inappropriately analyze ordinal traits, which leads to the loss of original phenotype information and the detection power of quantitative trait nucleotides (QTN). To address these issues, fast multi-locus ridge regression (FastRR), which was originally designed for continuous traits, is used to directly analyze binary or ordinal traits in this study. FastRR includes three stages of continuous transformation, variable reduction, and parameter estimation, and it can computationally handle categorical phenotype data instead of link functions introduced or methods inappropriately used. A series of simulation studies demonstrate that, compared with four other continuous or binary or ordinal approaches, including logistic regression, FarmCPU, FaST-LMM, and POLMM, the FastRR method outperforms in the detection of small-effect QTN, accuracy of estimated effect, and computation speed. We applied FastRR to 14 binary or ordinal phenotypes in the Arabidopsis real dataset and identified 479 significant loci and 76 known genes, at least seven times as many as detected by other algorithms. These findings underscore the potential of FastRR as a very useful tool for genome-wide association studies and novel gene mining of binary and ordinal traits.

Although the mixed linear model (MLM) such as efficient mixed model association (EMMA), has been widely used in genome-wide association studies (GWAS), relatively little is known about fast and efficient algorithms to implement multi-locus GWAS. To address this issue, we report a fast multi-locus random-SNP-effect EMMA (FASTmrEMMA). In this method, a new matrix transformation was constructed to obtain a new genetic model that includes only quantitative trait nucleotide (QTN) variation and normal residual error; letting the number of nonzero eigenvalues be one and fixing the polygenic-to-residual variance ratio was used to increase computing speed. All the putative QTNs with the ≤0.005 P-values in the first step of the new method were included in one multi-locus model for true QTN detection. Owing to the multi-locus feature, the Bonferroni correction is replaced by a less stringent selection criterion. Results from analyses of both simulated and real data showed that FASTmrEMMA is more powerful in QTN detection, model fit and robustness, has less bias in QTN effect estimation, and requires less running time than the current single- and multi-locus methodologies for GWAS, such as E-BAYES, SUPER, EMMA, CMLM and ECMLM. Therefore, FASTmrEMMA provides an alternative for multi-locus GWAS.