*4.9. Genome-Wide Selective Sweep Scan*

A WG3S was performed along chromosomes across two populations using the program XP-CLR [34]. Comparisons between BM and EV using XP-CLR were conducted. The genetic distances (cM) between SNPs were estimated using the integrated flax consensus genetic map [43], assuming uniform recombination between SNPs. For each chromosome, XP-CLR was executed with the parameters "-w1 0.005 100 100 1 -p1 0.7" to estimate XP-CLR scores for 100-bp windows. Each chromosome was then divided into 10-kb segments and the highest XP-CLR score from windows with at least one SNP were assigned to each 10-kb segment (*xmax*,*<sup>i</sup>* ). If the XP-CLR scores (*xmax*, *<sup>i</sup>* and *xmax*, *<sup>i</sup>*+<sup>1</sup> ) of two adjacent 10-kb segments were greater than the 80th percentile (*xmax*,80*th*) of the genome-wide scores of all 10-kb fragments, then they were grouped as a single putative selective sweep. In addition, putative selective sweeps were also merged if they were separated by no more than one low score (<*xmax*,80*th*) segment. Merged selective sweeps were assigned the highest score from their merged 10-kb segments. These merged segments were further combined into a larger region if these segments belonged to the same peak in the genome-wide selective sweep plot (Figure 5a). Finally, the combined regions falling in the highest 10th percentile of all putative selective sweeps were considered differentially selected regions or selection signatures.

The selection signatures were compared to both our detected QTL and previously reported QTL on the genetic loci to find associations between them. Positions where the QTL corresponding markers were located were extended by 100 kb on both sides and then compared with the position of the selection signatures. The QTL and selection signatures were considered associated when they overlapped.

**Supplementary Materials:** Supplementary materials can be found at http://www.mdpi.com/1422-0067/19/8/ 2303/s1.

**Author Contributions:** S.C., F.M.Y., S.D.D., H.M.B. and K.Y.R. conceived and designed the study. S.C. performed sequencing. S.D.D., H.M.B. and K.Y.R. performed the phenotyping. F.M.Y., J.X., P.L., Z.Y., G.J., L.H., S.K. and B.S.-C. analyzed the data. F.M.Y., J.X., S.K. and S.C. wrote the manuscript. All authors reviewed and edited the manuscript.

**Funding:** This research was funded by Genome Canada and other industrial stakeholders for the Total Utilization Flax GENomics (TUFGEN) project, by Agriculture and Agri-Food Canada for an A-base project, and by Western Grain Research Foundation (WGRF) and the Saskatchewan Flax Development Commission (SFDC) for the flax breeding database project.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
