## 3 Results
### Comparison of the Stable SNPs  
Appropriately reducing plant height can not only improve lodging tolerance but also increase harvest index. For PH, four SNPs, namely A02_random_355708, A03_25488780, C09_36899682, and C04_47349279, were co-detected by three environments with PVE 5.2-35.6%. These were stable SNPs for controlling plant PH. Since multi-environmental phenotypic data were used in GWAS, we examined the association of the SNPs with BLUP values. As expected, all of them showed extremely significant associations with PH(Figure 3A). Interestingly, the majority of them showed a significant correlation with SYP, such as A01_1783685 and A03_25488780, while the A allele of SNP C09_36899682 was also associated with low BYP. Moreover, C09_36899682 explained for over 27.4% of the phenotypic variation of PH, and others only explained for 5.5-18.1% (Table S2). C09_36899682 could be an effective locus to control PH to decrease BYP without reducing SYP. Figure 1: Phenotypic analysis for HI and HI-related traits. Upper parts of (**A–N**) are statistical analyses of the respective test traits. The violin plots display the distribution patterns of phenotypic values. The width of the violin plot represents the density of the distribution. The black horizontal line in the box plot shows the median value, and the upper and lower boxes in the box represent the upper and lower quartiles of the data set. Statistical significance is determined by the Wilcoxon test. *, **, ***, and **** represent significant at 0.05, 0.01, 0.001, and 0.0001, and ns is short for no significance. Lower parts of (**A–N**) show the relationships among the respective environments. The redder the color, the stronger the correlation. BN, numbers of primary valid branch; BAI, branch angle index; BYP, biomass yield per plant; HI, harvest index; MIL, main inflorescence length; MINS, number of effective siliques on main inflorescence; MSD, silique density of the main inflorescence; NSP, number of siliques per plant; NSS, number of seeds per silique; PH, plant height; SL, silique length; SW, silique width; SYP, seed yield per plant; TSW, thousand-seed weight. Silique and seed characteristics are important factors of seed yield. For NSS (Figure 3B), C06_22559430 and A07_random_1623623 were co-detected by at least three environments explaining the phenotypic variation from 4.5 to 21.2%. The T allele of C06_22559430 was associated with high NSS, but the A allele of A07_random_1623623 did not show significant association with NSS distribution. For TSW, A03_22103527 was detected by TSW across four environments, and the G allele showed higher TSW than the A allele (Figure 3C). For pleiotropic SNPs, A01_1783685 was identified by PH_2018 and SYP_2018, and C06_26638717 was detected by PH_2019, PH_2021, NSS_2021, and NSS_BLUP (Figure 4 and Table S2). Notably, A01_1783685 and C06_26638717 were located in the interval  
Figure 3: Trait distribution for the alleles of significant SNPs. (**A**) BYP, PH, and SYP distribution for the significant SNPs detected by PH. The horizontal line in the box plot shows the median value, and the upper and lower boxes represent the upper and lower quartiles of the data set. Statistical significance is determined by the Wilcoxon test. (**B–I**) show distributions for the alleles of stable significant SNPs detected by NSS, TSW, HI, BAI, BN, BYP, MINS, and SL, respectively. Figure 2: Distribution of SNPs identified in different environments and algorithms. (**A**) Veen of significant SNPs detected by different algorithms. Here, the SNPs detected for a certain trait (without distinguishing the environments) by different algorithms are regarded as one SNP. Upper right displays distribution of SNPs identified by different algorithms. (**B**) Veen of significant SNPs detected by different environments. The SNPs detected for a certain trait in different environments (without distinguishing the algorithms) are regarded as one SNP.