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 | 0.403 | 0.368 | 0.129 | 0.169 | 0.254 | 0.086 | 0.087 | 0.017 | 0.281 | – | – | – |

E2 | 0.729 | 0.632 | 0.329 | 0.204 | 0.403 | 0.179 | 0.036 | 0.067 | – | 0.184 | – | – |

E3 | 0.273 | 0.555 | 0.556 | 0.128 | 0.362 | 0.178 | 0.228 | 0.033 | – | – | 0.322 | – |

E4 | 0.448 | 0.432 | 0.289 | 0.353 | 0.070 | 0.327 | 0.143 | 0.234 | – | – | – | 0.366 |

GK | ||||||||||||

E1 | 0.693 | 0.453 | 0.175 | 0.191 | 0.132 | −0.014 | 0.033 | −0.023 | 0.145 | – | – | – |

E2 | 0.638 | 0.727 | 0.302 | 0.248 | −0.122 | 0.099 | 0.004 | 0.012 | – | 0.123 | – | – |

E3 | 0.229 | 0.386 | 0.841 | 0.171 | 0.267 | 0.037 | 0.116 | −0.004 | – | – | 0.126 | – |

E4 | 0.269 | 0.342 | 0.219 | 0.725 | −0.168 | 0.101 | −0.031 | 0.142 | – | – | – | 0.163 |

Empirical phenotypic correlation: E1

*vs.*E2 = 0.527; E1*vs.*E3 = 0.253; E1*vs.*E4 = 0.259; E2*vs.*E3 = 0.340; E2*vs.*E4 = 0.328; E3*vs.*E4 = 0.220. Variance–covariance matrix (upper triangular) and correlation matrix (lower triangular) for random effects*u*,*f*, and variance matrix for random errorsof 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 given above. Env., environment; GBLUP, genomic best linear unbiased predictors: GK, Gaussian kernel.*ε*