*3.1. Bran Functionality Traits*

With the emphasis on consumption of whole grain foods by governmental agencies [63], it is relevant to identify and develop wheat lines with specialized traits for whole grain products. Bran particle size and bran WRC have been identified as important determinants of whole grain breadmaking quality [5,8,9]. Therefore, we examined bran friability and WRC in a diverse set of 299 hard winter wheat genotypes to identify genomic regions that may be associated with whole grain end-use quality.

Bran friability was normally distributed from 34.5% to 65.9% with a median of 51.1% (Figure 1a; Shapiro–Wilk, W = 0.99, *p* = 0.83). The wide range in this trait suggested a significant variation in milling performance among wheat genotypes in the HWWAMP.

The WRC ranged from 159–458% with a median of 331% (Figure 1b). The WRC data distribution was close to normal, but had a significant Shapiro–Wilk test (W = 0.97; *p* < 0.001). The broad range in WRC data suggested a significant genetic e ffect on this trait. However, unlike friability, the distribution departed slightly from normal.

Correlations among bran yield, friability, and water retention were calculated in order to determine their application as a covariates in the GWAS models. Only bran yield and WRC were significantly correlated (r = 0.21; *p* = 0.0002).

**Figure 1.** Data distribution of the selected traits: (**a**) bran friability and (**b**) water retention capacity; normal distribution curve shown in red.
