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 | 1 | 2 | 3 | 1 | 2 | 3 | |

GBLUP | |||||||||

E1 | 0.442 | 0.275 | 0.117 | 0.268 | 0.101 | 0.094 | 0.221 | – | – |

E2 | 0.524 | 0.622 | −0.001 | 0.415 | 0.221 | 0.025 | – | 0.226 | 0.000 |

E3 | 0.255 | −0.002 | 0.475 | 0.369 | 0.108 | 0.242 | – | – | 0.288 |

GK | |||||||||

E1 | 0.620 | 0.319 | 0.204 | 0.140 | 0.022 | 0.016 | 0.161 | – | – |

E2 | 0.468 | 0.748 | 0.030 | 0.167 | 0.124 | 0.015 | – | 0.147 | 0.000 |

E3 | 0.318 | 0.043 | 0.663 | 0.116 | 0.116 | 0.136 | — | — | 0.171 |

Empirical phenotypic correlation: Sample phenotypic correlations: E1vsE2 = 0.388; E1

*vs.*E3 = 0.262; E2*vs.*E3 = 0.153. 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 three environments (E1–E3) 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*