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 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

E1 | E2 | E3 | E4 | E1 | E2 | E3 | E4 | E1 | E2 | E3 | E4 | |

GBLUP | ||||||||||||

E1 | 0.534 | −0.123 | −0.121 | −0.235 | 0.302 | 0.074 | −0.095 | 0.063 | 0.238 | – | – | – |

E2 | −0.243 | 0.480 | 0.388 | 0.255 | 0.207 | 0.423 | 0.300 | 0.159 | – | 0.164 | – | – |

E3 | −0.247 | 0.834 | 0.451 | 0.283 | −0.256 | 0.682 | 0.457 | 0.114 | – | – | 0.177 | – |

E4 | −0.483 | 0.552 | 0.632 | 0.444 | 0.236 | 0.503 | 0.347 | 0.236 | – | – | – | 0.379 |

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

E1 | 0.728 | −0.159 | −0.224 | −0.219 | 0.200 | 0.118 | −0.003 | 0.094 | 0.154 | – | – | – |

E2 | −0.221 | 0.714 | 0.666 | 0.344 | 0.483 | 0.299 | 0.126 | 0.096 | – | 0.149 | – | – |

E3 | −0.287 | 0.860 | 0.839 | 0.438 | −0.015 | 0.499 | 0.213 | 0.003 | – | – | 0.163 | – |

E4 | −0.311 | 0.493 | 0.579 | 0.683 | 0.460 | 0.384 | 0.014 | 0.209 | – | – | – | 0.220 |

Empirical phenotypic correlation between environments: E1

*vs.*E2 = −0.019; E1*vs.*E3 = −0.19; E1*vs.*E4 = −0.12; E2*vs.*E3 = 0.661; E2*vs.*E4 = 0.411; E3*vs.*E4 = 0.388. 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*