Table 2. Mean prediction accuracies for the different environments of wheat data set 1, maize data set 2, and wheat data set 3 for GBLUP and GK methods, and three models including a single-environment (model (1)) and two multi-environment models (models (2) and (3)).

Environment	GBLUP			GK
	Model (1)	Model (2)	Model (3)	Model (1)	Model (2)	Model (3)
Wheat data set 1a
E1	0.500 (0.056)	0.512 (0.043)	0.543 (0.044)	0.577 (0.043)	0.575 (0.036)	0.606 (0.037)
E2	0.474 (0.048)	0.635 (0.042)	0.720 (0.031)	0.477 (0.056)	0.685 (0.030)	0.713 (0.029)
E3	0.370 (0.056)	0.592 (0.045)	0.694 (0.031)	0.422 (0.053)	0.685 (0.030)	0.699 (0.028)
E4	0.447 (0.047)	0.501 (0.040)	0.525 (0.034)	0.511 (0.044)	0.555 (0.044)	0.572 (0.040)
Maize data set 2b
E1	0.558 (0.038)	0.603 (0.043)	0.624 (0.045)	0.583 (0.042)	0.644 (0.037)	0.645 (0.037)
E2	0.507 (0.049)	0.567 (0.055)	0.575 (0.054)	0.542 (0.056)	0.581 (0.057)	0.582 (0.057)
E3	0.508 (0.051)	0.517 (0.045)	0.525 (0.046)	0.568 (0.044)	0.577 (0.044)	0.578 (0.044)
Wheat data set 3c
E1	0.529 (0.044)	0.603 (0.033)	0.617 (0.031)	0.557 (0.040)	0.625 (0.033)	0.631 (0.035)
E2	0.622 (0.045)	0.706 (0.031)	0.716 (0.029)	0.642 (0.030)	0.688 (0.033)	0.689 (0.034)
E3	0.452 (0.051)	0.506 (0.045)	0.512 (0.043)	0.523 (0.048)	0.547 (0.041)	0.551 (0.041)
E4	0.493 (0.046)	0.504 (0.041)	0.507 (0.039)	0.511 (0.042)	0.508 (0.053)	0.510 (0.052)

SDs are given in parentheses. The highest prediction accuracies for each environment in each data set are shown in boldface. GBLUP, genomic best linear unbiased predictors: GK, Gaussian kernel.

^aEmpirical 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.

^bEmpirical phenotypic correlation between environments: E1 vs. E2 = 0.388; E1 vs. E3 = 0.262; E 2 vs. E3 = 0.153.

^cEmpirical phenotypic correlation between environments: 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 = 0.22.