*3.1. QTL Associated with Seed Yield and Seed Oil Quality Traits*

Thirty-three QTL were identified in the current study. Of which, nine QTL were identified in previous studies [7,8] for the same traits, including seed yield and seed oil quality traits. Cloutier et al. [7] detected six major QTL for LIO, LIN and IOD in SU population. These six QTL correspond to the two underlying genes, *FAD3a* and *FAD3b*. Some of these QTL were in close proximity on the same chromosome. We identified the same QTL by association mapping that were previously detected by linkage mapping [7] using the same phenotype and SNP genotype data in the SU population (Table 3). The refinement of flax pseudomolecule [45] between the linkage study and our current association study allowed reassignment of chr12 for LIO, LIN and IOD QTL which were previously assigned to LG16 [8]. In addition, the same QTL were also detected in the EV population as well as the merged population. Our association study also validated three QTL for YLD, DTM and PAL which were previously identified using linkage mapping using SSRs and SNPs [8,9] and from the association mapping using a flax core collection population with SSR markers [53] (Table 3). These verified QTL for fatty acid composition, seed yield and maturity demonstrate the feasibility of the association mapping method to detect QTL in a bi-parental population as well as a multi-parent population.

An additional 24 novel QTL were detected in our current study which were not discovered in previous studies using individual BM or SU populations. These new QTL were detected using the merged population which greatly increased the population size, thereby enhancing the association power and resolution for QTL detection. We noted that only two QTL were discovered from the BM population alone. This is likely the result of significantly reduced representation of lines re-sequenced from BM population [8]. The discovery of new QTL demonstrates that GWAS using multiple bi-parental populations is equally or more efficient for QTL detection than QTL mapping using single bi-parental populations alone.

We tested the statistical significance of QTL effects for all 33 QTL identified for the 11 traits and found that all effect differences were significant. We also observed significant positive correlation between the number of positive-effect QTL and corresponding trait phenotypes in individuals for eight traits from which had two or more QTL were identified (Figures 4 and 5, Table S7). These results not only corroborate the significance of the QTL but also demonstrate that effects of QTL in an individual performed additively, suggesting that marker-assisted selection (MAS) for these QTL would be effective in breeding. Thus, we listed the flanking sequences of these QTL in Table S12 for MAS purpose.
