Table B4. Wheat data set 4.
| Env. | Covariance Matrix (Upper Triangular) and Correlation Matrix (Lower Triangular) for u | Covariance Matrix (Upper Triangular) and Correlation Matrix (Lower Triangular) for f | Variance–Covariance Matrix Σ for ε | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | |
| GBLUP | ||||||||||||
| E1 | 0.483 | 0.111 | 0.004 | 0.133 | 0.409 | 0.230 | −0.055 | 0.215 | 0.175 | – | – | – |
| E2 | 0.234 | 0.467 | 0.291 | 0.246 | 0.585 | 0.378 | 0.091 | 0.199 | – | 0.242 | – | – |
| E3 | 0.008 | 0.560 | 0.578 | 0.292 | −0.163 | 0.280 | 0.279 | 0.105 | – | – | 0.230 | – |
| E4 | 0.304 | 0.572 | 0.610 | 0.396 | 0.541 | 0.521 | 0.320 | 0.386 | – | – | – | 0.243 |
| GK | ||||||||||||
| E1 | 0.968 | 0.353 | −0.042 | 0.378 | 0.142 | 0.084 | −0.021 | 0.059 | 0.111 | – | – | – |
| E2 | 0.395 | 0.826 | 0.417 | 0.476 | 0.502 | 0.197 | −0.007 | 0.045 | – | 0.176 | – | – |
| E3 | −0.044 | 0.470 | 0.952 | 0.439 | −0.170 | −0.048 | 0.107 | 0.009 | – | – | 0.129 | – |
| E4 | 0.429 | 0.584 | 0.502 | 0.803 | 0.383 | 0.248 | 0.067 | 0.167 | – | – | – | 0.192 |
Empirical phenotypic correlation: E1 vs. E2 = 0.342; E1 vs. E3 = −0.054; E1 vs. E4 = 0.311; E2 vs. E3 = 0.328; E2 vs. E4 = 0.414; E3 vs. E4 = 0.223. Variance–covariance matrix (upper triangular) and correlation matrix (lower triangular) for random effects u, f, and variance matrix for random errors ε of multi-environment model (3) including four environments (E1–E4) for linear kernel GBLUP and nonlinear Gaussian kernel (GK). Pair-wise sample phenotypic correlations between environments are above. Env., environment; GBLUP, genomic best linear unbiased predictors: GK, Gaussian kernel.