*2.3. Genome-Wide Association Analysis*

Three GWA models were tested, including GLM-Q, GLM-PCA, and MLM-K. According to the quantile-qualtile (Q–Q) plot results, the GLM-Q model showed a strong skew toward significance for every trait (Figure S4a), indicating that the Q matrix was insufficient to account for population structure and cryptic relatedness. Conversely, the MLM-K, which only used the kinship matrix, led to an overcorrection of these confounding factors, particularly for HC (Figure S4b). The GLM-PCA was tested with 5 and 10 PCA covariates for HC and MC, accounting for 30.1 and 37.1% of the variation, respectively. Both GLM-5PCA and GLM-10PCA models performed well in controlling the rate of false positives, providing suitable statistical power to identify significant marker–trait associations for MC and HC (Figure S5). Therefore, the GLM-PCA model was applied for GWA in this study.

GWA analysis identified 12 and 17 significant associations for MC in CAR2014 and HU2015, respectively (*p* < −log<sup>10</sup> (*P*) = 6.88), and markers Lu5-3808878, Lu7-13225294, and Lu11-2498303 were significant in both environments (Table 1, Figure S5). Various significant SNP markers fell into the same LD blocks. For example, five other significant markers surrounded the peak SNP Lu5-3808878 (Figure S5), thus, they were considered the same QTL. Following this criterion, seven QTL were delineated on chromosomes 2, 3, 5, 7, and 11. The peak SNPs of these QTL accounted for 11.8 to 17.3% of phenotypic variation, and the combined three consistent QTL accounted for 43.6% of the MC variation (Table 1).


**Table 1.** Genome-wide significant peak SNPs for mucilage content (MC) and hull content (HC).

<sup>1</sup> MAF: minor allele frequency; <sup>2</sup> ns: not significant at the threshold value –log<sup>10</sup> (P) = 6.88.

A total of three and four significant associations were detected for HC in CAR2014 and HU2015, respectively (*p* < −log<sup>10</sup> (*P*) = 6.88). Markers Lu7-6577527 and Lu13-2803224 were significant in both environments (Table 1). The four QTL identified on chromosomes 7, 10, 12, and 13 explained between 13.8% and 17.8% of the HC variation. The two consistent QTL Lu7-6577527 and Lu13-2803224, accounted for a combined 33% of the HC variation (Table 1).

The peak SNPs effect for MC and HC were all significant according to the non-parametric Kruskal–Wallis test (*p* < 0.05), except for Lu3-26033342 associated with MC (Figure 4a,b and Figure S6). Accessions with a thymine (T) allele at Lu2-22298066 displayed, on average, an increase of 15.3 and 9.4 mg g−<sup>1</sup> in MC, compared to accessions with a cytosine (C) allele in CAR2014 and HU2015, respectively (Figure 4a). Similarly, accessions with a "T" allele at Lu3-7398487 had, on average, 6.64 and 8.4 mg g−<sup>1</sup> higher MC compared to accessions with a "C" allele in CAR2014 and HU2015, correspondingly.

*Int. J. Mol. Sci.* **2018**, *19*, x FOR PEER REVIEW 6 of 16

**Figure 4.** Box plots illustrating the phenotypic differences between flaxseed accessions carrying different alleles of the significant SNPs, and combined phenotypic effects of favorable QTL in the association panel. (**a**) Mucilage content (MC); (**b**) Hull content (HC). CAR2014 = Vilcún location 2014, HU2015 = Huichahue location 2015. Different letters indicate significant statistical differences according to the Kruskal-Wallis non-parametric test (*p* < 0.05); (**c**) QTL effect for MC; (**d**) QTL effect for HC. Grey and white boxplots represent the CAR2014 and HU2015 locations, respectively. **Figure 4.** Box plots illustrating the phenotypic differences between flaxseed accessions carrying different alleles of the significant SNPs, and combined phenotypic effects of favorable QTL in the association panel. (**a**) Mucilage content (MC); (**b**) Hull content (HC). CAR2014 = Vilcún location 2014, HU2015 = Huichahue location 2015. Different letters indicate significant statistical differences according to the Kruskal-Wallis non-parametric test (*p* < 0.05); (**c**) QTL effect for MC; (**d**) QTL effect for HC. Grey and white boxplots represent the CAR2014 and HU2015 locations, respectively.

Accessions with a guanine (G) allele at Lu7-13225294 had, on average, 8.56 and 7.71 mg g–1 more mucilage compared to accessions carrying an adenine (A) allele in CAR2014 and HU2015, respectively (Figure 4a). The allelic effect for the other four peak SNPs is illustrated in Figure S6. The allelic effect of peak SNPs for HC revealed that accessions harboring a "C" allele at Lu7-6577527 had, on average, 1.4 and 1.3% less HC compared with "A" allele genotypes in CAR2014 and HU2015, correspondingly (Figure 4b). On average, HC was reduced by 1.4 and 1.3% (Lu7-6577527) to 2.6 and 2.7% (Lu13-2803224) in CAR2014 and HU2015, respectively (Figures 4b and S6). Accessions with a guanine (G) allele at Lu7-13225294 had, on average, 8.56 and 7.71 mg g−<sup>1</sup> more mucilage compared to accessions carrying an adenine (A) allele in CAR2014 and HU2015, respectively (Figure 4a). The allelic effect for the other four peak SNPs is illustrated in Figure S6. The allelic effect of peak SNPs for HC revealed that accessions harboring a "C" allele at Lu7-6577527 had, on average, 1.4 and 1.3% less HC compared with "A" allele genotypes in CAR2014 and HU2015, correspondingly (Figure 4b). On average, HC was reduced by 1.4 and 1.3% (Lu7-6577527) to 2.6 and 2.7% (Lu13-2803224) in CAR2014 and HU2015, respectively (Figure 4b and Figure S6).

The combined QTL effect revealed that the MC of accessions harboring none of the favorable QTL alleles averaged 44.6 and 48.9 mg g−1, compared to 72.1 and 67.6 mg g−1, for those with five favorable alleles in CAR2014 and HU2015, respectively (Figure 4c). No accession had all seven

The combined QTL effect revealed that the MC of accessions harboring none of the favorable QTL alleles averaged 44.6 and 48.9 mg g−<sup>1</sup> , compared to 72.1 and 67.6 mg g−<sup>1</sup> , for those with five favorable alleles in CAR2014 and HU2015, respectively (Figure 4c). No accession had all seven favorable QTL alleles. The combined QTL effect for HC indicated that genotypes with none of the favorable QTL alleles averaged 45.5% and 45.3% HC compared to genotypes with four favorable QTL alleles, in which HC averaged 42.7% and 42.9% in CAR2014 and HU2015, respectively (Figure 4d).
