The integration of quantile regression with 3VmrMLM identifies more QTNs and QTNs-by-environment interactions using SNP and haplotype-based markers.

Current methods used in genome-wide association studies frequently lack power due to their inability to detect heterogeneous associations and rare and multiallelic variants. To address these issues, quantile regression was integrated for the first time with a compressed variance component multi-locus random-SNP-effect mixed linear model (3VmrMLM) to propose q3VmrMLM for detecting heterogeneous quantitative trait nucleotides (QTNs) and QTN-by-environment interactions (QEIs), while q3VmrMLM-Hap was designed to identify multiallelic haplotypes and rare variants. In Monte Carlo simulation studies, q3VmrMLM had higher power than 3VmrMLM, SKAT, and iQRAT. In the re-analysis of 10 traits in 1439 rice hybrids, 261 known genes were identified only by q3VmrMLM and q3VmrMLM-Hap, while 175 known genes were detected commonly by the new and existing methods. Of all the significant QTNs with known genes, q3VmrMLM (179: 140 variance heterogeneity and 157 quantile effect heterogeneity) found more heterogeneous QTNs than 3VmrMLM (123), SKAT (27) and iQRAT (29), q3VmrMLM-Hap (121) mapped more low-frequency (<0.05) QTNs than q3VmrMLM (51), 3VmrMLM (43), SKAT (11) and iQRAT (12), and q3VmrMLM-Hap (12), q3VmrMLM (16) and 3VmrMLM (12) had similar power in identifying gene-by-environment interactions. All significant and suggested QTNs achieved the highest predictive accuracy (r=0.9045). In conclusion, this study provides a new and complementary approach to mining genes and unrevealing the genetic architecture of complex traits in crops.