PAL. *2.8. Phenotypic Variation Explained by QTL*

*2.8. Phenotypic Variation Explained by QTL*  Phenotypic variations explained by individual QTL (ℎொ் <sup>ଶ</sup> ) were estimated (Table S4). Overall, the QTL explained 4 to 66% of the total phenotypic variation, with an average of 32.5% which is more than half of the average ℎௌே <sup>ଶ</sup> (51%). For five traits (IOD, LIO, LIN, PAL and OIL), QTL explained an average of 61% of the variation (Tables 2 and S4). We also estimated the phenotypic variation explained by all QTL for a trait (ℎீௐௌ <sup>ଶ</sup> ) (Table 2). In the merged population, the QTL explained 48– 73% of the phenotypic variation for OIL, IOD, PAL, LIO and LIN but only 8–14% for PLH, DTM and Phenotypic variations explained by individual QTL (*h* 2 *QTL*) were estimated (Table S4). Overall, the QTL explained 4 to 66% of the total phenotypic variation, with an average of 32.5% which is more than half of the average *h* 2 *SNP* (51%). For five traits (IOD, LIO, LIN, PAL and OIL), QTL explained an average of 61% of the variation (Table 2 and Table S4). We also estimated the phenotypic variation explained by all QTL for a trait (*h* 2 *GWAS*) (Table 2). In the merged population, the QTL explained 48–73% of the phenotypic variation for OIL, IOD, PAL, LIO and LIN but only 8–14% for PLH, DTM and YLD.

#### YLD. *2.9. Candidate Genes Underlying QTL*

*2.9. Candidate Genes Underlying QTL*  Based on the GWAS results, we investigated the genes annotated in the flax genome [54] in an attempt to predict candidate genes from loci significantly associated with each trait. The genomic locations of SNP markers at the peaks of the QTL were scanned within a 500 Kb window in either direction to constitute a subset of genes from which we deduced a candidate gene list based on *a priori* knowledge of their function(s). Candidate genes were identified for every QTL except for the YLD QTL (Table 3). We discovered seven candidate genes underlying QTL for DTM on chr4. The QTL for PLH harbors five candidate genes of completely different function. The genes underlying QTL for fatty acid composition include *KCS14-2*, *FAD3a*, and *FAD3b* for IOD/LIN/LIO, *KCS12-3* and Based on the GWAS results, we investigated the genes annotated in the flax genome [54] in an attempt to predict candidate genes from loci significantly associated with each trait. The genomic locations of SNP markers at the peaks of the QTL were scanned within a 500 Kb window in either direction to constitute a subset of genes from which we deduced a candidate gene list based on *a priori* knowledge of their function(s). Candidate genes were identified for every QTL except for the YLD QTL (Table 3). We discovered seven candidate genes underlying QTL for DTM on chr4. The QTL for PLH harbors five candidate genes of completely different function. The genes underlying QTL for fatty acid composition include *KCS14-2*, *FAD3a*, and *FAD3b* for IOD/LIN/LIO, *KCS12-3* and *KAS Ic-1* for PAL, *KCS9-1* and *KCS1-1* for OLE, and *KCS18-2* and *SAD1* for STE.

*KAS Ic-1* for PAL, *KCS9-1* and *KCS1-1* for OLE, and *KCS18-2* and *SAD1* for STE.

*Int. J. Mol. Sci.* **2018**, *19*, x 12 of 24

**Figure 6.** Relations of −log10(*P*) values of SNP markers between two traits showing pleiotropy or linkage relationship of SNP markers in different pairs of traits. (**a**) IOD vs. LIN; (**b**) IOD vs. LIO; (**c**) LIN vs. LIO; (**d**) OIL vs. PRO; (**e**) PLH vs. DTM; (**f**) DTM vs. YLD. Results of the GWAS using a GLM and data from the BM + EV + SU population for IOD, LIO, and LIN (**a**–**c**), the EV population for OIL and PRO (**d**), the BM population for PLH and DTM (**e**) and the BM + EV + SU population for DTM and YLD (**f**) are shown. The vertical and horizontal dashed lines show the cut-off value of significant SNP markers associated with a trait. YLD: seed yield (t ha<sup>−</sup>1); DTM: days to maturity; OIL: oil content (%); PRO: protein content (%); IOD: iodine value; LIO: linoleic acid content (%); LIN: linolenic acid content (%). **Figure 6.** Relations of −log10(*P*) values of SNP markers between two traits showing pleiotropy or linkage relationship of SNP markers in different pairs of traits. (**a**) IOD vs. LIN; (**b**) IOD vs. LIO; (**c**) LIN vs. LIO; (**d**) OIL vs. PRO; (**e**) PLH vs. DTM; (**f**) DTM vs. YLD. Results of the GWAS using a GLM and data from the BM + EV + SU population for IOD, LIO, and LIN (**a**–**c**), the EV population for OIL and PRO (**d**), the BM population for PLH and DTM (**e**) and the BM + EV + SU population for DTM and YLD (**f**) are shown. The vertical and horizontal dashed lines show the cut-off value of significant SNP markers associated with a trait. YLD: seed yield (t ha−<sup>1</sup> ); DTM: days to maturity; OIL: oil content (%); PRO: protein content (%); IOD: iodine value; LIO: linoleic acid content (%); LIN: linolenic acid content (%).

#### *2.10. Selection Signatures in Bi-Parental Populations 2.10. Selection Signatures in Bi-Parental Populations*

A GW3S was performed to identify potential selection signatures during breeding improvement using XP-CLR [34]. Due to the high genetic diversity in BM and EV (Table 1) and large phenotypic differences between them (Table S9), GW3S between BM and EV was conducted. A total of 114 selection signatures with an average size of 226.3 kb were identified (Figures 1 and 7, Table S10), accounting for 7.82% of the flax pseudomolecules (~316 Mb). These putative selection signatures overlapped with 11 GWAS-detected genomic regions associated with 18 QTL (Figures 1 and 7). A GW3S was performed to identify potential selection signatures during breeding improvement using XP-CLR [34]. Due to the high genetic diversity in BM and EV (Table 1) and large phenotypic differences between them (Table S9), GW3S between BM and EV was conducted. A total of 114 selection signatures with an average size of 226.3 kb were identified (Figures 1 and 7, Table S10), accounting for 7.82% of the flax pseudomolecules (~316 Mb). These putative selection signatures overlapped with 11 GWAS-detected genomic regions associated with 18 QTL (Figures 1 and 7).

Some selection signatures were also associated with previously identified QTL (Table S11). For example, the selection signatures were associated with 10 previously reported QTL (Figure 7). The signatures at position 2.45–2.46 Mb on chr1 overlapped with SNP marker *Lu1\_2670961* linked to QTL *QSte.BM.crc-LG1* for STE; the ones at 4.74–4.77 Mb on chr3 overlapped with *Lu3\_5950394*, a SNP linked to QTL *QOle.BM.crc-LG3-1*/*QLio.BM.crc-LG3* for OLE and LIO; signatures at 7.24–7.25 Mb on chr3 overlapped with SNP *Lu3\_8415336* linked to QTL *QSte.BM.crc-LG3* for STE [8]; position 16.80– 16.81 Mb on chr10 harbors signatures that overlap with SSR *Lu2262* linked to an unnamed QTL for

**Figure 7.** Genome-wide selective sweep scan using XP-CLR between BM and EV (**a**), and Manhattan plots of QTL overlapping with selective sweeps for (**b**) seed yield (YLD), (**c**) linoleic acid content (LIO), (**d**) steric acid content (STE), (**e**) oil content (OIL), (**f**) palmitic acid content (PAL), (**g**) oleic acid content (OLE), (**h**) linolenic acid content (LIN), and (**i**) protein content (PRO). QTL associated with selective sweeps are also labeled on peaks of selective sweeps. The numbers represent the QTL numbers listed in Table 3. Multiple numbers on the same peak represent genomic regions co-located with more than one trait. The labels 'm-#' represent the genomic regions associated with QTL previously identified and listed in Table S11. The green dots on Manhattan plots represent significant SNPs. **Figure 7.** Genome-wide selective sweep scan using XP-CLR between BM and EV (**a**), and Manhattan plots of QTL overlapping with selective sweeps for (**b**) seed yield (YLD), (**c**) linoleic acid content (LIO), (**d**) steric acid content (STE), (**e**) oil content (OIL), (**f**) palmitic acid content (PAL), (**g**) oleic acid content (OLE), (**h**) linolenic acid content (LIN), and (**i**) protein content (PRO). QTL associated with selective sweeps are also labeled on peaks of selective sweeps. The numbers represent the QTL numbers listed in Table 3. Multiple numbers on the same peak represent genomic regions co-located with more than one trait. The labels 'm-#' represent the genomic regions associated with QTL previously identified and listed in Table S11. The green dots on Manhattan plots represent significant SNPs.

**3. Discussion**  *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 Some selection signatures were also associated with previously identified QTL (Table S11). For example, the selection signatures were associated with 10 previously reported QTL (Figure 7). The signatures at position 2.45–2.46 Mb on chr1 overlapped with SNP marker *Lu1\_2670961* linked to QTL *QSte.BM.crc-LG1* for STE; the ones at 4.74–4.77 Mb on chr3 overlapped with *Lu3\_5950394*, a SNP linked to QTL *QOle.BM.crc-LG3-1*/*QLio.BM.crc-LG3* for OLE and LIO; signatures at 7.24–7.25 Mb on chr3 overlapped with SNP *Lu3\_8415336* linked to QTL *QSte.BM.crc-LG3* for STE [8]; position 16.80–16.81 Mb on chr10 harbors signatures that overlap with SSR *Lu2262* linked to an unnamed QTL for OIL; finally, position 17.52–17.53 Mb on chr10 has selection signatures that coincide with SSR *Lu2746* linked to an unnamed QTL for LIN/IOD [53].
