*3.4. GWAS for Bran Friability*

Among models tested, the MLM with kinship and bran yield as a covariate provided the best fit to the data and was used in further analysis (Figure 3). GWAS analysis identified two SNPs located on the 5D chromosome: BS00000020\_51 (3,609,894 bp) and Excalibur\_c49805\_63 (1,614,602 bp), that were significantly associated with bran friability (Bonferroni corrected *p*-value < 0.05; Figure 4). Of the 297 genotypes, 46 carried the GG genotype (BS00000020\_51 marker) and 43 carried the AA genotype (Excalibur\_c49805\_63 marker), which were associated with increased bran friability (Table 1; Supplementary Table S1). These genotypes were randomly distributed on a PCA biplot generated using the marker data, suggesting the absence of groupings among lines carrying the favorable alleles (Supplementary Figure S1).

**Figure 3.** Quantile-quantile plots for bran friability trait: (**a**) General linear model (GLM) with no covariates; (**b**) GLM with bran yield (BY) as covariate; (**c**) GLM with water retention capacity (WRC) as covariate; (**d**) GLM with BY and WRC as covariates; (**e**) mixed linear model (MLM) with kinship and no covariates; (**f**) MLM with kinship and BY as covariates; (**g**) MLM with kinship and WRC as covariates; (**h**) MLM with kinship and BY and WRC as covariates. red line: X = Y; blue diamonds: actual values.

**Figure 4.** Manhattan plot showing trait associated SNPs for friability; Un, unanchored scaffold; red line, Bonferroni correction (adjusted *p* < 0.05) cuto ff.


**Table 1.** Trait-associated SNPs and their annotations.a

165

Low bran friability is desirable for refined flour production because bran particles remain large and intact and are thus easier to separate from the endosperm flour. As refined flour represents the majority of wheat flour production [3], this may be why so few lines carried the high bran friability alleles. However, for whole wheat flour milling, the high bran friability trait would be beneficial because smaller bran particle sizes have been shown to result in bread with higher volume [6]. As demand for whole wheat flour increases [3], wheat genotypes that carry the high bran friability trait may become more sought after. The markers associated with bran friability in this study, after validation in independent population, will be a useful resource for developing lines with increased bran friability. The 43 to 46 genotypes carrying increased bran friability favorable alleles can be used as parental lines while making crosses to develop lines with increased bran friability (Supplementary Table S1).
