View Full Table | Close Full ViewTable 1.

Range of disease severity (%) on the six parental lines of wheat used in the present study.

 
Parental line Stem rust (Kenya)† Yellow rust (Kenya) Yellow rust (Toluca)
PBW343 60–70 15–20 10–15
Kingbird 0–5 0–5 0–5
Juchi 5–15 20–30 15–20
Muu 5–10 5–10 15–20
Pavon 10–15 10–15 15–20
Kenya Nyangumi 0–5 40–50 0–5
Disease severity in the main and off seasons was not statistically different at the 0.05 level.



View Full Table | Close Full ViewTable 2.

Numbers of individuals evaluated for rust resistance in a single population × environment (season) combination and across environments (seasons), variance component estimation, heritability, and genetic correlation between environments.

 
Stem Rust
Yellow Rust
Population Off season Main season σg2 σge2 σe2 H2 rg Njoro (Kenya) Toluca (Mexico) σg2 σge2 σe2 H2 rg
PBW343 × Juchi 92 92 96.9 49.7 103.6 0.72 0.47 92 90 100.0 111.1 9.0 0.66 0.52
PBW343 × Kingbird 90 90 287.3 45.5 88.2 0.90 0.74 90 90 32.1* 74.8 10.0 0.45 0.35
PBW343 × K-Nyangumi 191 176 309.0 69.4 122.6 0.85 0.66 –‡ 189
PBW343 × Muu 148 148 247.8 31.6 83.9 0.90 0.75 148 148 21.1* 75.5 16.3 0.66 0.21
PBW343 × Pavon76 180 176 181.23 38.5 95.6 0.83 0.64 147 180 76.8 107.9 18.3 0.56 0.48
σg2, genotypic variance; σge2, genotype × environment interaction; σe2, residual variance; H2, broad-sense heritability; rg, genetic correlation between both environments (seasons).
Yellow rust analysis of population PBW343 × K-Nyangumi is not presented because there was only one trial.



View Full Table | Close Full ViewTable 3.

Pearson’s correlation (ρ) between observed and predicted stem rust values using four genomic selection models trained under three different conditions in five wheat populations evaluated in two seasons.

 
Model†
Population BL SVR-linear SVR-RBF RR BL SVR-linear SVR-RBF RR
Case AঠTRN = TST = Off TRN = TST = Main
PBW343 × Juchi 0.38 0.26 0.41 0.41 0.55 0.55 0.52 0.56
PBW343 × Kingbird 0.75** 0.66 0.64 0.68 0.69** 0.61 0.59 0.60
PBW343 × K-Nyangumi 0.59** 0.52 0.55 0.56 0.39 0.39 0.32 0.37
PBW343 × Muu 0.57* 0.50 0.53 0.56 0.62* 0.53 0.57 0.61
PBW343 × Pavon76 0.68** 0.55 0.58 0.60 0.60** 0.46 0.50 0.52
Case B§¶ TRN = Main + Off TST = Off TRN = Main + Off TST = Main
PBW343 × Juchi 0.49 (28.9) 0.39 (50.0) 0.39 (−0.01) 0.53** (29.3) 0.58** (5.5) 0.45 (−18.2) 0.45 (−13.5) 0.47 (−16.1)
PBW343 × Kingbird 0.85** (13.3) 0.78 (18.2) 0.69 (7.8) 0.82 (20.6) 0.80 (15.9) 0.76 (24.6) 0.59 (0.0) 0.81* (35.0)
PBW343 × K-Nyangumi 0.74 (25.4) 0.66 (26.9) 0.78** (41.8) 0.65 (16.1) 0.70** (79.5) 0.67 (71.8) 0.62 (93.8) 0.62 (67.6)
PBW343 × Muu 0.72 (26.3) 0.72 (44.0) 0.55 (3.8) 0.75** (33.9) 0.78** (25.8) 0.75 (41.5) 0.60 (5.3) 0.72 (18.0)
PBW343 × Pavon76 0.78** (8.8) 0.66 (20.0) 0.71 (22.4) 0.72 (20.0) 0.70 (16.7) 0.67 (45.7) 0.64 (28.0) 0.70 (34.6)
Case C¶ TRN = Main TST = Off TRN = Off TST = Main
PBW343 × Juchi 0.47 0.47 0.47 0.5 0.5 0.47 0.48 0.47
PBW343 × Kingbird 0.81 0.77 0.77 0.79 0.80 0.77 0.77 0.80
PBW343 × K-Nyangumi 0.61 0.64 0.62 0.62 0.62 0.67 0.67 0.61
PBW343 × Muu 0.77 0.77 0.77 0.80 0.80 0.77 0.80 0.77
PBW343 × Pavon76 0.70 0.68 0.68 0.68 0.70 0.69 0.63 0.68
*Best result for each environment × population combination is statistically significant at the 0.05 probability levels.
**Best result for each environment × population combination is statistically significant at the 0.01 probability levels.
BL, Bayesian least absolute shrinkage and selection operator (LASSO); SVR-linear, support vector regression with linear kernel; SVR-RBF, support vector regression with radial basis function kernel; RR, ridge regression; TRN training set; TST, testing set; Off, off season; Main, main season.
The first two upper sections show the mean Pearson’s correlation (ρ) between observed and predicted stem rust values of 50 random partitions of the data for four models in five wheat populations evaluated in two seasons, off and main seasons. Models were trained and tested using three different combinations of training set (TRN) and testing set (TST). Case A: training and testing in the same environment. Case B: training in main plus off season and testing only in off season or only in main season. Case C: training in one season and predicting in the other.
§Numbers in parenthesis denote the percentage increase (or decrease) in the models’ prediction ability for Case B compared to their respective models in Case A.
Nonsignificant differences are not indicated.



View Full Table | Close Full ViewTable 4.

Pairwise Pearson’s correlation (without reciprocals) between observed and predicted stem rust values of four different models. Algorithms were trained in one population (across both environments) and evaluated on the other population.

 
Testing or training†
PBW343 × Juchi PBW343 × Kingbird PBW343 × K-Nyangumi PBW343 × Muu PBW343 × Pavon76
Training or testing‡ PBW343 × Juchi 0.48 0.14 0.28 0.31 Bayes LASSO
PBW343 × Kingbird 0.53 0.29 0.25 0.54
PBW343 × K-Nyangumi 0.14 0.30 0.28 0.28
PBW343 × Muu 0.18 0.30 0.33 0.29
PBW343 × Pavon76 0.37 0.51 0.22 0.33
Ridge regression
Testing or training§
PBW343 × Juchi PBW343 × Kingbird PBW343 × K-Nyangumi PBW343 × Muu PBW343 × Pavon76
Training or testing PBW343 × Juchi 0.28 0.32 0.48 0.32 SVR-linear
PBW343 × Kingbird 0.28 0.45 0.53 0.59
PBW343 × K-Nyangumi 0.35 0.31 0.25 0.39
PBW343 × Muu 0.14 0.58 0.26 0.55
PBW343 × Pavon76 0.35 0.64 0.41 0.67
SVR-RBF
The upper-right triangle of the first section of the table has the results of Bayes least absolute shrinkage and selection operator (LASSO), with the rows indicating the training population and the columns the testing population.
The lower-left triangle gives the results of ridge regression, with the columns indicating the training population and the rows the test population.
§The second section of the table shows similar results in the upper-right and lower-left triangles but considers support vector regression with linear kernel (SVR-linear) and support vector regression with radial basis function kernel (SVR-RBF).



View Full Table | Close Full ViewTable 5.

Pearson’s correlation (ρ) between observed and predicted yellow rust values for four models trained under three different conditions in five wheat populations evaluated in two sites Njoro (Kenya) and Toluca (Mexico).

 
Model†
Population BL SVR-linear SVR-RBF RR BL SVR-linear SVR-RBF RR
Case AঠTRN = TST = Njoro TRN = TST = Toluca
PBW343 × Juchi 0.33 0.42* 0.41 0.33 0.37 0.37 0.34 0.37
PBW343 × Kingbird 0.23** 0.16 0.14 0.20 0.49 0.42 0.48 0.49
PBW343 × K Nyangumi 0.30** 0.24 0.23 0.15
PBW343 × Muu 0.17 0.19 0.20* 0.12 0.49 0.45 0.46 0.49
PBW343 × Pavon76 0.26 0.20 0.33** 0.25 0.63** 0.54 0.58 0.59
Case B§¶ TRN = Njoro + Toluca TST = Njoro TRN = Njoro + Toluca TST = Toluca
PBW343 × Juchi 0.56 (69.7) 0.53 (26.2) 0.52 (26.9) 0.56 (69.7) 0.63 (70.3) 0.60 (62.2) 0.60 (44.1) 0.52 (40.5)
PBW343 × Kingbird 0.36** (60.9) 0.30 (100) 0.33 (135.7) 0.32 (60.0) 0.50* (2.0) 0.31 (−26.1) 0.47 (−14.6) 0.45 (−8.2)
PBW343 × Muu 0.19 (11.8) 0.15 (−21.1) 0.20 (0.0) 0.14 (16.7) 0.29 (−40.8) 0.34 (−24.0) 0.06 (−87.0) 0.26 (−47.0)
PBW343 × Pavon76 0.46 (76.9) 0.46 (130.0) 0.46 (39.4) 0.45 (80.0) 0.62** (−1.6) 0.47 (−13.0) 0.56 (−3.45) 0.60 (1.69)
Case C¶ TRN = Toluca TST = Njoro TRN = Njoro TST = Toluca
PBW343 × Juchi 0.52 0.52 0.52 0.54 0.52 0.52 0.52 0.56
PBW343 × Kingbird −0.09 0.30 0.31 −0.10 −0.16 0.34 0.42 0.10
PBW343 × Muu 0.18 0.13 0.13 0.18 0.17 0.15 0.15 0.17
PBW343 × Pavon76 0.48 0.47 0.47 0.48 0.47 0.44 0.41 0.45
*Best result for each environment × population combination is statistically significant at the 0.05probability levels.
**Best result for each environment × population combination is statistically significant at the 0.01 probability levels.
BL, Bayesian least absolute shrinkage and selection operator (LASSO); SVR-linear, support vector regression with linear kernel; SVR-RBF, support vector regression with radial basis function kernel; RR, ridge regression; TRN, training set; TST, testing set.
The two upper sections show the mean Pearson’s correlation (ρ) between observed and predicted yellow rust values of 50 random partitions of the data for four models in five wheat populations evaluated in two sites Njoro (Kenya) and Toluca (Mexico). Models were trained and tested using three different combinations of training set (TRN) and testing set (TST). Case A: training and testing in the same environment. Case B: training in Njoro plus Tolca and testing only in Njoro or only in Toluca. Case C: training in one environment and predicting in the other.
§Numbers in parentheses denote the percentage increase (or decrease) in the models’ predictive ability for Case B compared to their respective models in Case A.
Nonsignificant differences are not indicated.



View Full Table | Close Full ViewTable 6.

Pairwise Pearson’s correlation (without reciprocals) between observed and predicted yellow rust values for four different models. The algorithms were trained in one population (across both environments) and evaluated in the other population.

 
Testing or training
PBW343 × Juchi PBW343 × Kingbird PBW343 × Muu PBW343 × Pavon76
Training or testing PBW343 × Juchi 0.12 0.06 0.09 Bayesian LASSO†
PBW343 × Kingbird 0.06 0.16 0.14
PBW343 × Muu 0.05 0.16 0.07
PBW343 × Pavon76 0.10 0.14 0.09
Ridge regression‡
Testing or training
PBW343 × Juchi PBW343 × Kingbird PBW343 × Muu PBW343 × Pavon76
Training or testing PBW343 × Juchi 0.09 0.05 0.07 SVR-linear§
PBW343 × Kingbird 0.09 0.04 0.21
PBW343 × Muu 0.09 0.11 0.09
PBW343 × Pavon76 0.12 0.18 0.12
SVR-RBF
The upper-left triangle in the first section of the table shows the results of Bayesian least absolute shrinkage and selection operator (LASSO), with the rows indicating the training population and the columns the testing population.
The lower-left triangle shows the results of ridge regression, with the columns indicating the training population and the rows the test population.
§The second section of the table shows similar results in the upper and lower triangles but considering support vector regression with linear kernel (SVR-linear) and support vector regression with radial basis function (SVR-RBF) kernel.