Statistical analysis, QTL mapping, meta-analysis and interaction detection

Statistical analyses for all traits were carried out using SAS 9.2 (SAS Institute, Cary, NC, USA). Pearson’s phenotypic correlation coefficients were calculated among all traits across the three environments using the CORR procedure. The genetic correlation coefficient was calculated using the general linear model (GLM, Y_ijkl = μ + r_i + b_ij + g_k + e_ijkl, where Y_ijkl is an observation of genotype k in replication l of block j in environment i, μ is the general mean, r_i is the effect of the environment i, b_ij is the effect of block j in environment i, g_k is the effect of genotype k, and e_ijkl is the residual effect of observation, the residual variance is a combination of genotype × location interaction variance and the within location error variance.). The genetic correlation was calculated as: rG=COVGxyσGx2×σGy2, where cov_Gxy, σGx2, and σGy2 were the genetic covariance and variances of a pair-wise traits, respectively. The significance of each genetic correlation was determined using a t-test of correlation coefficients (Kong 2005). The broad-sense heritability was calculated as: h2=σg2/(σg2+σge2/n+σe2/nr), where σg2 is genotypic variance, σge2 is interaction variance of the genotype with the environment, σe2 is error variance, n is the number of environments, and r is the number of blocks in each environment. The lines with missing phenotype data were ignored in each trait.

QTLs were detected by composite interval mapping using WinQTL cartographer 2.5 (Zeng 1994). The number of control markers, window size and walk speed were set to 5, 10 and 1 cM, respectively. The LOD threshold for each trait was determined by permutation test with 1000 repetitions t. A QTL was declared when the LOD score was greater than the threshold value, LOD scores corresponding to P < 0.05 were used to identify significant QTLs. To avoid missing QTLs with small genetic effects, loci with LOD scores larger than 2.0 but smaller than the threshold in multiple environments were treated as micro-real QTLs (Long et al. 2007). These micro-real QTLs might become major QTLs in different environments or in different segregating populations (Long et al. 2007). The nomenclature of QTLs followed previous descriptions (Udall et al. 2006) with minor modifications. A QTL was named starting with the lowercase letter q; followed by an uppercase two-letter designation for the trait name (OC, SL, SS, or SW); an uppercase chromosome set letter (A or C); a chromosome number; a dot; a 1, 2, or 3 (representing 2011representing 2012, or 2013, respectively, when the QTL was detected; and a lowercase letter (a, b, c, ...) for one of the multiple QTLs detected in the same linkage group and environment (Yang et al. 2012).

To merge and compare QTLs detected in different environments and located in the same chromosome region, either for the same or different trait, meta-analysis was conducted using BioMercator 3.0 (Sosnowski et al. 2012). If QTLs for the same trait were detected in multiple environments with overlapping confidence intervals, these QTLs were firstly merged as a consensus QTL and designated with initial letters “cq” followed by trait name and linkage group (Yang et al. 2012). QTLs for different traits having overlapping confidence intervals were further integrated into unique QTL and designated with initial letters “uq” followed by the linkage group. The algorithm of BioMercator software can help to determine the position of the overlapping QTLs based on the variance of these QTLs position and the confidence interval values (Arcade et al. 2004).

Epistatic interactions were analyzed based on mixed linear model approaches using QTLNetwork 2.0 (Yang et al. 2008). The testing windows, filtration windows and walk speed were set to 10, 10 and 1 cM, respectively. Both 1D and 2D searches were analyzed with 1000 permutations. P < 0.05 was set as the significance threshold.