*4.4. Phenotyping of Bi-Parental Populations*

Individuals from the three populations were evaluated in field trials over four years (2009–2012) at two sites, Morden Research and Development Centre, Manitoba (MD) and Kernen Crop Research Farm near Saskatoon, Saskatchewan (SAS) in Canada. A type-2 modified augmented design (MAD) [76] was used for the field experiments from which phenotypic data were collected. The detailed experimental design was previously described [44,77]. All 243 individuals of the BM population were phenotyped in four years (2009–2012) and two sites (MD and SAS), while 86 individuals of the EV population and 72 individuals of the SU population were evaluated in three years (2010–2012) and two sites (MD and SAS).

Eleven common traits were evaluated in the three populations, including YLD, PLH, DTM, PRO, OIL, IOD and five fatty acid composition traits (OLE, PAL, STE, LIO, and LIN). PLH was measured from ground to the uppermost part of the plant at maturity. DTM was recorded from sowing to 95% of capsule maturity (seeds rattling in the capsules or bolls). Seed yield data were measured by harvesting two 0.5-m sections from rows located in the central part of each subplot (0.2 m<sup>2</sup> ). A total of 1 g of seed from each line at each environment was sampled for OIL measurement and fatty acid composition. Methyl esters of fatty acids were prepared according to the American Oil Chemists' Society (AOCS) Official Method Ce 2-66 [78] and fatty acid composition was measured by gas chromatography (GC) following AOCS Official Method Ce 1e-91. OIL was determined by nuclear magnetic resonance calibrated against the FOSFA extraction reference method. PRO was measured using near-infrared spectroscopy calibrated against the combustion analysis reference method and expressed on an N × 6.25 dry basis. Phenotyping of these seed quality traits has been previously described [53]. All phenotypic data from the field experiments and laboratory measurements were adjusted for soil heterogeneity as previously described based on the MAD pipeline [77]. The BLUP

values over multiple environmental phenotypes estimated using R package "lme4" [79] were used for further association study analyses. The Shapiro-Wilk normality test was performed for all traits using the R function "shapiro.test". All 11 traits followed approximately a normal or mixed normal distribution (Figure S3). Simple correlations among 11 traits were calculated using the function "rcorr" of the R package "Hmisc".
