*2.5. Estimating Heritability Using Genome-Wide SNP Markers*

The two traits recorded in this study, bran friability and WRC, had one phenotypic value per line. This was similar to one phenotypic measurement generally available on other quality traits in a cultivar development program [56]. A single value per line did not allow the estimation of heritability using variance components derived from a linear mixed model used for phenotypic analysis. Hence, the SNP markers were used to estimate the heritability of friability and WRC traits. The quality-filtered markers used in GWAS were imputed using mean imputations and a genomic relationship matrix (GRM) was built [57]. The details of building a GRM and fitting a genomic best linear unbiased prediction (GBLUP) model to the phenotypic measurements is described previously in our earlier study [58]. The GBLUP model was fit using the Bayesian Generalized Linear Regression (BGLR) function in the BGLR package in R and variance components for GRM (genomic variance) and residual term were estimated [57]. The heritability was estimated as the ratio of genomic variance to the sum of genomic and error variances.
