*3.3. Genome-Wide Association Analysis*

Several general (GLM) and mixed (MLM) linear models have been proposed to control both population structure and cryptic relatedness [47–49]. In flax, MLM has been the preferred association model for multiple traits [24–26,42]. The "red" and "blue" clusters were weakly differentiated, and MC and HC between flax morphotypes was not statistically significant (Figure S2a,b), in contrast to a report comparing *indica* and *japonica* rice types assessed for 34 traits [39]. Hence, the genetic architecture of MC and HC seem to be only weakly correlated with population and family structures, and GLM-PCA was sufficient to control the rate of false positive associations.

The discovery of QTL for agronomic and economically important traits in crops is of great importance for marker-assisted breeding. This is the first report of QTL for MC in flax, likely because this trait has not been a breeding priority in the most important breeding programs of the world [18]. In the present study, GWAS identified seven QTL for MC, and their effects clearly suggest the promise of marker-assisted selection for modifying MC.

Chromosome 30 s multiple MC QTL harbored candidate genes orthologous to Arabidopsis *TT8* gene, which is part of a transcription factor complex that, along with *GLABRA2* (*GL2*), regulates *MUM4* gene expression [50]. *MUM4* is required to produce rhamnose, a key substrate for mucilage biosynthesis [50], and chromosome 3 Lus10009311 is its flax ortholog. In Arabidopsis, *GATL5* encodes a glycosyltransferase involved in rhamnogalacturonan I (RG I) backbone synthesis [51]. The presence of a *L. usitatissimum* ortholog Lus10009311 in a LD block, with a peak SNP for MC, corresponds to the expected role of RG I synthesis. Arabidopsis gene *SBT1.7* triggers the activation of cell wall-modifying enzymes necessary for mucilage release upon imbibition [52]. In line with the expected seed coat mucilage dynamics, we identified two orthologous copies of this gene in two independent QTL (Table 2). Arabidopsis *PECTIN METHYLESTERASE INHIBITOR 6* (*PMEI6*) mutants were defective in seed coat mucilage release [53]. An ortholog of the Arabidopsis gene, *PECTIN METHYLESTERASE 36* (*PME36*), another family member, was located at one of the MC QTL loci identified herein. While *PME36* has not been shown to be involved in mucilage release, it might participate indirectly because it exerts a similar role to that of *PMEI6* in pectin synthesis and cell wall modification [54].

Oil content is an economically important but genetically complex trait. MC is negatively correlated with oil content, therefore, reducing MC should facilitate increasing oil content. Indeed, reduced accumulation of mucilage accompanied by increased oil content was observed in Arabidopsis *MUM4* or *GL2* mutants [55]. We observed a significant negative correlation (*r* = −0.15, *p* = 0.03) between MC and oil content in the association panel (data not shown). This is perhaps due to increased carbon allocation to the embryo in reduced or no seed coat mucilage synthesis in low MC accessions as proposed in Arabidopsis [55].

Increasing seed oil content and reducing the fiber fraction of the meal have been important goals in oil crop breeding. In *B. napus* and *L. usitatissium*, seed coat thickness or HC are negatively correlated with seed oil and protein content, as well as seed color [56–58]. QTL for seed coat color to indirectly increase oil content and minimize HC have been identified in *B. napus* and soybean [37,59,60]. In flax, a pleiotropic QTL controlling yellow seed and white flower color was recently dissected at the molecular level, but its effect on HC has not been addressed [23]. Here, we identified four QTL whose effects reduced HC by 2.6%, on average. Chromosome 7 harbored Lus10035456, which resembles the *A. thaliana* transcription factor *AGL62*. *AGL62* mutants initiated embryo and endosperm formation, but failed to form a seed coat [61]. Light seed color and low HC are thought to coincide because the biochemical pathways leading to lignin and pigment synthesis share common precursors [59]. In Arabidopsis, the core components of seed coat pigments are proanthocyanidins (PAs) [62]. Chromosome 12 encompassed three candidate genes including the ortholog of Arabidopsis *O-GLYCOSYL HYDROLASES FAMILY 17* gene. *GH17* is coexpressed with *TT12*, *AHA10*, and *BAN*, that might process glycosylated flavan-3-ol monomers, leading to accumulation of PAs in the seed coat [63]. In black seed soybean, a *UDP-GLUCOSE:FLAVONOID 3-O-GLUCOSYLTRANSFERASE* (*UGT78K1*), was isolated from the seed coat, a key enzyme that catalyzes the final step in anthocyanin biosynthesis [64]. Chromosome 13 contained Lus10026926, an ortholog of the *A. thaliana UGT79B1*, a gene also involved in anthocyanin biosynthesis. Yellow seed color stems from the blocked biosynthesis of PAs that impart the brown color to the seed coat [65]. The flaxseed meal derived from brown-seeded cultivars contains PAs that negatively affect protein digestion [66], hence low PA meal is preferred in animal ration. Additional advantages of modifying the seed color and reducing MC and HC include higher limpidity of the crude oil from the removal of gum-like residues and dark pigments, higher protein content and better feeding value of flaxseed meal for livestock and poultry [7].

Few accessions combined favorable alleles for reduced MC and HC. It should be possible to combine these attributes in a single genotype through the pyramiding of the respective favorable alleles owing to the fact that the significant QTL for both traits did not co-locate in the flax genome. The development of yellow-seeded cultivars with low HC and either low or high MC for different industrial uses is an opportunity to increase market share and value.
