Table B5 Wheat data set 5
Env.Covariance Matrix Formula (Upper Triangular) and Correlation Matrix (Lower Triangular) for uCovariance Matrix Formula (Upper Triangular) and Correlation Matrix (Lower Triangular) for fVariance–Covariance Matrix Σ for ε
123451234512345
GBLUP
 E10.6260.1610.186−0.0390.0170.1410.0350.010−0.0160.0080.193
 E20.2770.538−0.0220.0920.0300.2270.1690.006−0.0040.0160.277
 E30.301−0.0380.608−0.099−0.0180.0780.0430.1160.0370.0610.140
 E4−0.0630.161−0.1630.6050.405−0.086−0.0200.2190.2470.1800.189
 E50.0290.055−0.0310.7050.5460.0380.0700.3230.6530.3080.201
GK
 E10.8490.2010.261−0.0940.0100.0830.0140.003−0.0090.0050.100
 E20.2320.8870.0140.0950.0320.1500.1050.006−0.0060.0130.136
 E30.3250.0170.759−0.0310.0600.0400.0710.0680.0120.0140.082
 E4−0.1050.104−0.0370.9490.677−0.095−0.0560.1390.1090.0310.135
 E50.0110.0350.0720.7220.9270.0470.1080.1450.2540.1370.174
  • Empirical phenotypic correlation: E1 vs. E2 = 0.166; E1 vs. E3 = 0.30; E1 vs. E4 = −0.10; E1 vs. E5 = −0.010; E2 vs. E3 = −0.033; E2 vs. E4 = 0.122; E2 vs. E5 = 0.035; E3 vs. E4 = −0.091; E3 vs. E5 = 0.023; E4 vs. E5 = 0.546. 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 five environments (E1–E5) 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.