The mixed linear model (MLM) has been widely used in genome-wide association study (GWAS) to dissect quantitative traits in human, animal, and plant genetics. Most methodologies consider all single nucleotide polymorphism (SNP) effects as random effects under the MLM framework, which fail to detect the joint minor effect of multiple genetic markers on a trait. Therefore, polygenes with minor effects remain largely unexplored in today’s big data era. In this study, we developed a new algorithm under the MLM framework, which is called the fast multi-locus ridge regression (FastRR) algorithm. The FastRR algorithm first whitens the covariance matrix of the polygenic matrix K and environmental noise, then selects potentially related SNPs among large scale markers, which have a high correlation with the target trait, and finally analyzes the subset variables using a multi-locus deshrinking ridge regression for true quantitative trait nucleotide (QTN) detection. Results from the analyses of both simulated and real data show that the FastRR algorithm is more powerful for both large and small QTN detection, more accurate in QTN effect estimation, and has more stable results under various polygenic backgrounds. Moreover, compared with existing methods, the FastRR algorithm has the advantage of high computing speed. In conclusion, the FastRR algorithm provides an alternative algorithm for multi-locus GWAS in high dimensional genomic datasets.

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.

Currently a hot topic, genomic selection (GS) has consistently provided powerful support for breeding studies and achieved more comprehensive and reliable selection in animal and plant breeding. GS estimates the effects of all single nucleotide polymorphisms (SNPs) and thereby predicts the genomic estimation of breeding value (GEBV), accelerating breeding progress and overcoming the limitations of conventional breeding. The successful application of GS primarily depends on the accuracy of the GEBV. Adopting appropriate advanced algorithms to improve the accuracy of the GEBV is time-saving and efficient for breeders, and the available algorithms can be further improved in the big data era. In this study, we develop a new algorithm under the Bayesian Shrinkage Regression (BSR, which is called BayesA) framework, an improved expectation-maximization algorithm for BayesA (emBAI). The emBAI algorithm first corrects the polygenic and environmental noise and then calculates the GEBV by emBayesA. We conduct two simulation experiments and a real dataset analysis for flowering time-related Arabidopsis phenotypes to validate the new algorithm. Compared to established methods, emBAI is more powerful in terms of prediction accuracy, mean square error (MSE), mean absolute error (MAE), the area under the receiver operating characteristic curve (AUC) and correlation of prediction in simulation studies. In addition, emBAI performs well under the increasing genetic background. The analysis of the Arabidopsis real dataset further illustrates the benefits of emBAI for genomic prediction according to prediction accuracy, MSE, MAE and correlation of prediction. Furthermore, the new method shows the advantages of significant loci detection and effect coefficient estimation, which are confirmed by The Arabidopsis Information Resource (TAIR) gene bank. In conclusion, the emBAI algorithm provides powerful support for GS in high-dimensional genomic datasets.

Yield-related traits of rice (Oryza sativa L.) are pivotal to safeguarding global food security. As a powerful and efficient strategy, genome-wide association study (GWAS) has identified numerous genes for yield-related traits in rice over recent decades, providing critical resources for germplasm improvement. Most yield-related traits are complex quantitative traits controlled by multiple genes with diverse effect sizes, and traditional GWAS approaches have limited power to detect small-effect loci. In this study, we employed Fast3VmrMLM, a compressed mixed linear model integrating genome-wide scanning and machine learning, to perform GWAS for 10 key yield-related traits using a panel of 529 rice accessions and 4,945,006 single-nucleotide polymorphisms (SNPs). The traits included heading date, plant height, panicle number, effective panicle number, yield per plant, spikelet length, grain length, grain width, grain weight, and grain thickness. We detected 141 significant quantitative trait nucleotides (QTNs) associated with target traits and identified 92 previously validated genes located near these QTNs. As a key environmental regulator, photoperiod directly controls flowering and indirectly modulates yield-related traits, and we further identified 182 photoperiod-responsive candidate genes via differential expression and Gene Ontology (GO) enrichment analysis. Through tissue-specific expression analysis, homology analysis with Arabidopsis genes, and haplotype-phenotype differential analysis, six pleiotropic candidate genes were confirmed; notably, LOC_Os02g02210 appears to contribute substantially to grain width and yield-related traits. In conclusion, Fast3VmrMLM proved effective for dissecting the genetic basis of yield-related traits, especially in detecting small-effect loci. These results not only establish a potential genetic link between photoperiod regulation and rice yield formation but also provide high-confidence candidate genes and loci that will accelerate functional genomic studies and precision molecular breeding for high-yield rice.

Genome-wide association studies (GWASs) are powerful and flexible tools for identifying single nucleotide polymorphisms (SNPs) associated with quantitative traits (yield, stress resistance) in plants. Variable selection and machine learning are two effective approaches in GWAS. However, both face limitations in complex, noisy data analysis in the big-data era. In this study, we integrated variable selection and machine learning under the mixed linear model framework, proposing a novel method, the improved LASSO screening and sparse Bayesian learning algorithm (ILSBL). The ILSBL first corrects the polygenic and environmental noise, then reduces genotypic dimensionality by LASSO-based variable selection, and finally performs parameter estimation using sparse Bayesian learning. Two simulation experiments and association analyses of three flowering-time-related traits in Arabidopsis thaliana were conducted to validate the new algorithm. The results showed that, compared to established methods, the ILSBL exhibited flexibility in simulation studies and maintained robust performance under complex genetic backgrounds, achieving a favorable balance among statistical power, parameter estimation accuracy, runtime efficiency, and false-positive rate. The analysis of the real Arabidopsis datasets further confirmed the advantages of ILSBL for GWASs, with 30 candidate genes adjacent to significant quantitative trait nucleotides (QTNs) associated with flowering-related traits. These results provide valuable insights for a better understanding of the genetic basis underlying flowering-related traits in Arabidopsis.