Analysis of variance and estimation of variance components
The phenotypic value for genotype \(i\) when tested in replicate \(k\)in the environment \(j\) was modeled as\(y_{\text{ijk}}=u+g_{i}+t_{j}+b_{k(j)}+{(gt)}_{\text{ij}}+e_{\text{ijk}}\), where \(u\) is the population mean, \(g_{i}\) is the effect of genotype\(i\), \(t_{j}\) is the effect of environment \(j\), \(b_{k(j)}\) is the block effect associated with replicate \(k\) nested in the environment\(j\), \({(gt)}_{\text{ij}}\) is the G × E effect associated with genotype \(i\) and environment \(j\) and \(e_{\text{ijk}}\) is the error.
The analysis of variance was conducted using the R function “aov” that fits a model with the function “lm” for each stratum. The estimation of variance components was conducted with the R package “VCA” and the function “anovaVCA.”