Statistical analysis

Plot data of leaf-to-stem ratio, protein and fiber concentrations, and NDFD were subjected to an analysis of variance (ANOVA), testing the variation among progenies (P), among conditions (C), and P×C interactions. Genetic coefficients of variation were computed for each environment as:

where σ²_g is the variance component of genotype and X´ is the trait mean.

Broad-sense heritability (hB2) on a progeny mean basis was estimated across conditions as:

where c is the number of conditions, k is the number of replications within conditions, and σ²_g, σ²_ge and σ² are the estimated variance components for progeny, progeny × condition interaction and experiment error, respectively.

Genetic coefficient of correlation (r_g) for progeny response across a pair of conditions i, j was estimated for each pair of conditions (C1 vs C2; C2 vs C3; C1 vs C3) as [37]:

where r_p is the phenotypic coefficient of correlation, and hB2Ci and hB2Cj is the broad-sense heritability of the relevant pair of conditions.

Phenotypic correlation coefficients for progeny values averaged over conditions were estimated between quality traits within leaf and stem samples, as well as between leaf and stem values of each quality trait.

Phenotypic trait values for genomic selection and GWAS studies were adjusted using BLUP (best linear unbiased predictors) computed from half-sib progeny mean values, as described in [38]. Statistical analyses were carried out using the softwares SAS and PBTools (PBTools, version 1.4., International Rice Research Institute, Los Baños, The Philippines; http://bbi.irri.org/products).