*3.2. Genotyping and Population Structure*

Of the 14,731 SNPs identified across the 299 genotypes, two genotypes and 70 SNPs were dropped from analysis due to minor allele frequency <0.05 and missing data of >20%. The remaining high-quality 14,661 SNPs across 297 lines were used in the analysis. These SNP markers were distributed across all 21 chromosomes with an average of 688 SNPs per chromosome (Figure 2a). Population structure, as visualized by PCA, indicated the presence of a few outliers among the genotypes in the HWWAMP (Figure 2b). A model-based clustering performed using the program STRUCTURE has previously indicated presence of four subgroups in the HWWAMP, and the plots are available in the supplementary files of Ayana et al. [45] and Sidhu et al. [65]. The STRUCTURE plots indicated presence of just a few lines with high (>80–90%) membership to each subgroup and the rest of the lines as admixed. These results of PCA and STRUCTURE suggesting a few lines with distinct backgrounds and a large number of remaining lines as admixed is expected since many of the public wheat breeding programs routinely share germplasm among each other for use as parental lines in breeding programs.

**Figure 2.** (**a**) Count of single-nucleotide polymorphisms (SNPs) on the wheat chromosomes (208 SNPs located on unanchored scaffold are not included in the plot); (**b**) principle component analysis of the 297 genotypes in the Hard Winter Wheat Association Mapping Panel (HWWAMP) using marker data.

### *3.3. Heritability Estimates for Bran Functionality Traits Using Genome-Wide SNP Markers*

The genomic and error variance estimates for bran friability were 17.64 and 20.53, and for WRC they were 473.78 and 1768.09. The marker-based heritability of friability and WRC were 0.46 and 0.21. These estimates are conservative as compared to broad-sense heritability estimates obtained using the

phenotypic data, because only the additive variance is captured with the markers. Friability had a moderately high heritability value, and this is in the range of heritability values recorded for most quality traits [56]. The relatively low heritability value of WRC suggests a slightly larger influence of nongenetic factors influencing these phenotypic measurements, and additional experiments will be needed to confirm the heritability for this trait. Nevertheless, since the marker-based heritability value was above zero WRC does appear to be influenced at least somewhat by genetics (the phenotypic values are not just noise or nongenetic factors), and thus can be further considered for marker–trait analysis.
