Table 5 Maize USP data set. Mean Pearson’s correlation (50 partitions) of each environment for random cross-validation CV2, for the multi-environment models, main genotypic effect model (MM), single variance G×E deviation model (MDs), environment-specific variance G×E deviation model (MDe), multi-environment unstructured covariance models (MUC and MUCf) with two kernels, GBLUP (GB) and Gaussian kernel (GK) for grain yield with the proposed random effect l and without the random effect l (standard deviation in parentheses)
Proposed models with random effects l and f
Environment*MMl-GKMMl-GBMDsl-GKMDsl-GBMDel-GKMDel-GBMUCf-GK MUCf-GB
P-LN0.525 (0.07)0.521 (0.06)0.545 (0.07)0.546 (0.07)0.549 (0.05)0.544 (0.08)0.563 (0.06)0.564 (0.06)
P-IN0.575 (0.05)0.566 (0.06)0.593 (0.05)0.591 (0.06)0.594 (0.05)0.595 (0.04)0.592 (0.06)0.597 (0.05)
A-LN0.493 (0.06)0.493 (0.07)0.508 (0.06)0.515 (0.06)0.509 (0.05)0.503 (0.05)0.526 (0.05)0.515 (0.06)
A-IN0.603 (0.05)0.599 (0.06)0.627 (0.05)0.629 (0.06)0.631 (0.05)0.627 (0.06)0.630 (0.05)0.618 (0.06)
Proposed models without random effects l and f
EnvironmentMM-GKMM-GBMDs-GKMDs-GBMDe-GKMDe-GBMUC-GK MUC-GB
P-LN0.50 (0.06)0.315 (0.06)0.524 (0.07)0.325 (0.06)0.52 (0.06)0.32 (0.05)0.536 (0.07)0.318 (0.06)
P-IN0.53 (0.05)0.358 (0.06)0.554 (0.05)0.368 (0.05)0.56 (0.05)0.365 (0.06)0.563 (0.05)0.361 (0.07)
A-LN0.463 (0.07)0.332 (0.07)0.476 (0.06)0.334 (0.07)0.478 (0.06)0.33 (0.07)0.496 (0.06)0.333 (0.06)
A-IN0.584 (0.06)0.438 (0.07)0.612 (0.05)0.447 (0.05)0.607 (0.04)0.445 (0.06)0.61 (0.05)0.439 (0.06)
  • * Environments are: Anhumas ideal N (A-IN), Anhumas low N (A-LN), Piracicaba ideal N (P-IN) and Piracicaba low N (P-LN).