Table 9 WHEAT WHE5 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
0iFN0.309 (0.05)0.301 (0.05)0.610 (0.04)0.58 (0.03)0.619 (0.04)0.576 (0.04)0.645 (0.05)0.595 (0.05)
2iBN0.186 (0.06)0.191 (0.05)0.495 (0.04)0.453 (0.03)0.502 (0.04)0.449 (0.04)0.498 (0.06)0.469 (0.06)
5iBH0.23 (0.06)0.267 (0.05)0.678 (0.02)0.631 (0.04)0.685 (0.03)0.637 (0.03)0.684 (0.03)0.650 (0.04)
5iBN0.262 (0.05)0.256 (0.05)0.456 (0.04)0.430 (0.04)0.452 (0.04)0.406 (0.05)0.637 (0.04)0.618 (0.04)
5iFN0.266 (0.05)0.247 (0.05)0.418 (0.05)0.401 (0.05)0.407 (0.05)0.402 (0.04)0.603 (0.05)0.601 (0.05)
Proposed models without random effects l and f
EnvironmentMM-GKMM-GBMDs-GKMDs-GBMDe-GKMDe-GBMUC-GK MUC-GB
0iFN0.321 (0.05)0.303 (0.05)0.621 (0.03)0.572 (0.03)0.627 (0.04)0.574 (0.03)0.646 (0.05)0.595 (0.05)
2iBN0.215 (0.04)0.211 (0.05)0.49 (0.05)0.451 (0.04)0.491 (0.05)0.459 (0.04)0.497 (0.06)0.470 (0.06)
5iBH0.248 (0.06)0.284 (0.05)0.675 (0.02)0.646 (0.03)0.677 (0.03)0.631 (0.03)0.684 (0.03)0.649 (0.04)
5iBN0.255 (0.04)0.245 (0.05)0.452 (0.04)0.407 (0.04)0.440 (0.05)0.409 (0.05)0.635 (0.04)0.598 (0.04)
5iFN0.251 (0.05)0.245 (0.05)0.405 (0.04)0.394 (0.04)0.408 (0.04)0.384 (0.04)0.607 (0.05)0.577 (0.05)
  • * Environments are described by a sequence of codes: 0i, 2i and 5i denote the number of irrigation cycles; B/F denotes whether the planting system was ‘bed’ (B) or ‘flat’ (F); N/H denotes whether planting date was normal (N) or late (H, simulating heat).