*3.2. Pleotropic QTL Associated with Seed Yield and Quality Traits*

Six genomic regions associated with more than one trait were identified. QTL for IOD, LIO, and LIN were concurrent on chromosomes 4, 7 and 12; QTL for YLD, PLH, and DTM co-located on chr4; QTL for PRO and OIL were on chr15 and QTL for PAL and OIL were on chr5 (Figures 1 and 6, Table S8).

IOD is a measure of the degree of unsaturation of the oil that is calculated from the GC-derived fatty acid composition. Thus, breeding lines with high LIN normally show high IOD [7] due to the high correlation between IOD, LIO, and LIN [44] (Table S13). QTL co-located at the same genomic regions indicate that the traits may be controlled by the same gene or tightly linked genes. The two genomic regions on chromosomes 7 and 12 harbor the two fatty acid desaturase genes, *FAD3a* and *FAD3b*. These genes are responsible for linoleic and linolenic acid composition [52,55].

PLH and DTM are complex traits that considerably impact the adaptability, biomass, and economic yield of agricultural crops [56,57]. In soybean, one QTL that strongly associated with both PLH and DTM traits was identified with an SNP at 45.0 Mb position on chromosome 19 and it harbors the candidate gene *DT1*, which is homolog to *Arabidopsis terminal flower 1* (*TFL-1*, AT5G03840) [56]. Based on in silico gene annotation, the *DT1* homolog are located on chromosomes 6 and 8 in flax

but no QTL for either PLH or DTM were identified on these two chromosomes. This could be due to the lack of functional polymorphism(s) at those loci among the parents of our three populations. However, a different genomic region on chr4 harbours five candidate genes for PLH and seven for DTM, raising the possibility that PLH and DTM are controlled by tightly linked genes in flax. The same genomic region was also associated with YLD. Because plant height and maturity affect seed yield, it is not surprising that QTL for PLH, DTM and YLD were mapped to the same locus. This pleiotropic relationship between YLD and DTM was previously validated [8] (Table 3).

Inheritance of seed oil content is complicated due to its quantitative nature. The seed oil content was directly affected by fatty acid composition traits, such as PAL, STE, OLE, LIO, and LIN, or indirectly by several major agronomic traits, such as seed yield and protein content [58]. Significant correlations of OIL were observed with PAL (−0.57; *p* = 0) and PRO (−0.70; *p* = 0) (Table S13). OIL is also usually negatively correlated with PRO in oilseed crops [59]. Of the eight QTL associated with oil content, two co-located with QTL for PAL on chr5 and for PRO on chr15, respectively.
