Multivariate Genomic Hybrid Prediction with Kernels and Parental Information
Abstract
:1. Introduction
2. Results
2.1. Trait DTF
2.2. Trait DTH
2.3. Trait YIELD
2.4. Across Traits
3. Discussion
4. Materials and Methods
4.1. Phenotypic Data
4.2. Genotypic Data
4.3. Multivariate Statistical Model
4.4. Evaluation of Prediction Performance
4.5. Kernel Methods
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Type | Kernel | Year | NRMSE | RE__Ker | RE_Env |
---|---|---|---|---|---|
BV | AC_1 | 1 | 0.675 | 0.000 | 0.000 |
BV | AC_2 | 1 | 0.675 | 0.000 | 0.000 |
BV | AC_3 | 1 | 0.675 | 0.000 | 0.000 |
BV | AC_4 | 1 | 0.675 | 0.000 | 0.000 |
BV | GK | 1 | 0.675 | 0.000 | 0.000 |
BV | Linear | 1 | 0.665 | 1.534 | 0.000 |
NO_Cov | AC_1 | 1 | 0.703 | 0.000 | 0.000 |
NO_Cov | AC_2 | 1 | 0.703 | 0.000 | 0.000 |
NO_Cov | AC_3 | 1 | 0.703 | 0.000 | 0.000 |
NO_Cov | AC_4 | 1 | 0.703 | 0.000 | 0.000 |
NO_Cov | GK | 1 | 0.703 | 0.000 | 0.000 |
NO_Cov | Linear | 1 | 0.693 | 1.428 | 0.000 |
Pmean | AC_1 | 1 | 0.670 | 0.000 | 0.000 |
Pmean | AC_2 | 1 | 0.670 | 0.000 | 0.000 |
Pmean | AC_3 | 1 | 0.670 | 0.000 | 0.000 |
Pmean | AC_4 | 1 | 0.670 | 0.000 | 0.000 |
Pmean | GK | 1 | 0.670 | 0.000 | 0.000 |
Pmean | Linear | 1 | 0.666 | 0.706 | 0.000 |
BV | AC_1 | 2 | 0.654 | 0.000 | 3.321 |
BV | AC_2 | 2 | 0.654 | 0.000 | 3.321 |
BV | AC_3 | 2 | 0.654 | 0.000 | 3.321 |
BV | AC_4 | 2 | 0.654 | 0.000 | 3.321 |
BV | GK | 2 | 0.654 | 0.000 | 3.321 |
BV | Linear | 2 | 0.640 | 2.125 | 3.922 |
NO_Cov | AC_1 | 2 | 0.683 | 0.234 | 3.048 |
NO_Cov | AC_2 | 2 | 0.683 | 0.234 | 3.048 |
NO_Cov | AC_3 | 2 | 0.683 | 0.234 | 3.048 |
NO_Cov | AC_4 | 2 | 0.683 | 0.234 | 3.048 |
NO_Cov | GK | 2 | 0.683 | 0.234 | 3.048 |
NO_Cov | Linear | 2 | 0.684 | 0.000 | 1.359 |
Pmean | AC_1 | 2 | 0.645 | 0.000 | 3.955 |
Pmean | AC_2 | 2 | 0.645 | 0.000 | 3.955 |
Pmean | AC_3 | 2 | 0.645 | 0.000 | 3.955 |
Pmean | AC_4 | 2 | 0.645 | 0.000 | 3.955 |
Pmean | GK | 2 | 0.645 | 0.000 | 3.955 |
Pmean | Linear | 2 | 0.644 | 0.062 | 3.290 |
BV | AC_1 | 3 | 0.606 | 0.000 | 11.382 |
BV | AC_2 | 3 | 0.606 | 0.000 | 11.382 |
BV | AC_3 | 3 | 0.606 | 0.000 | 11.382 |
BV | AC_4 | 3 | 0.606 | 0.000 | 11.382 |
BV | GK | 3 | 0.606 | 0.000 | 11.382 |
BV | Linear | 3 | 0.592 | 2.330 | 12.255 |
NO_Cov | AC_1 | 3 | 0.617 | 0.616 | 13.950 |
NO_Cov | AC_2 | 3 | 0.617 | 0.616 | 13.950 |
NO_Cov | AC_3 | 3 | 0.617 | 0.616 | 13.950 |
NO_Cov | AC_4 | 3 | 0.617 | 0.616 | 13.950 |
NO_Cov | GK | 3 | 0.617 | 0.616 | 13.950 |
NO_Cov | Linear | 3 | 0.621 | 0.000 | 11.659 |
Pmean | AC_1 | 3 | 0.567 | 0.000 | 18.139 |
Pmean | AC_2 | 3 | 0.567 | 0.000 | 18.139 |
Pmean | AC_3 | 3 | 0.567 | 0.000 | 18.139 |
Pmean | AC_4 | 3 | 0.567 | 0.000 | 18.139 |
Pmean | GK | 3 | 0.567 | 0.000 | 18.139 |
Pmean | Linear | 3 | 0.567 | 0.106 | 17.434 |
BV | AC_1 | Global | 0.645 | 0.000 | 4.688 |
BV | AC_2 | Global | 0.645 | 0.000 | 4.688 |
BV | AC_3 | Global | 0.645 | 0.000 | 4.688 |
BV | AC_4 | Global | 0.645 | 0.000 | 4.688 |
BV | GK | Global | 0.645 | 0.000 | 4.688 |
BV | Linear | Global | 0.632 | 1.982 | 5.149 |
NO_Cov | AC_1 | Global | 0.668 | 0.000 | 5.337 |
NO_Cov | AC_2 | Global | 0.668 | 0.000 | 5.337 |
NO_Cov | AC_3 | Global | 0.668 | 0.000 | 5.337 |
NO_Cov | AC_4 | Global | 0.668 | 0.000 | 5.337 |
NO_Cov | GK | Global | 0.668 | 0.000 | 5.337 |
NO_Cov | Linear | Global | 0.666 | 0.225 | 4.088 |
Pmean | AC_1 | Global | 0.627 | 0.000 | 6.822 |
Pmean | AC_2 | Global | 0.627 | 0.000 | 6.822 |
Pmean | AC_3 | Global | 0.627 | 0.000 | 6.822 |
Pmean | AC_4 | Global | 0.627 | 0.000 | 6.822 |
Pmean | GK | Global | 0.627 | 0.000 | 6.822 |
Pmean | Linear | Global | 0.626 | 0.304 | 6.395 |
Type | Kernel | Env | NRMSE | RE_Ker | RE_Env |
---|---|---|---|---|---|
BV | AC_1 | 1 | 0.651 | 0.000 | 0.000 |
BV | AC_2 | 1 | 0.651 | 0.000 | 0.000 |
BV | AC_3 | 1 | 0.651 | 0.000 | 0.000 |
BV | AC_4 | 1 | 0.651 | 0.000 | 0.000 |
BV | GK | 1 | 0.651 | 0.000 | 0.000 |
BV | Linear | 1 | 0.641 | 1.577 | 0.000 |
NO_Cov | AC_1 | 1 | 0.678 | 0.000 | 0.000 |
NO_Cov | AC_2 | 1 | 0.678 | 0.000 | 0.000 |
NO_Cov | AC_3 | 1 | 0.678 | 0.000 | 0.000 |
NO_Cov | AC_4 | 1 | 0.678 | 0.000 | 0.000 |
NO_Cov | GK | 1 | 0.678 | 0.000 | 0.000 |
NO_Cov | Linear | 1 | 0.670 | 1.224 | 0.000 |
Pmean | AC_1 | 1 | 0.645 | 0.000 | 0.000 |
Pmean | AC_2 | 1 | 0.645 | 0.000 | 0.000 |
Pmean | AC_3 | 1 | 0.645 | 0.000 | 0.000 |
Pmean | AC_4 | 1 | 0.645 | 0.000 | 0.000 |
Pmean | GK | 1 | 0.645 | 0.000 | 0.000 |
Pmean | Linear | 1 | 0.642 | 0.468 | 0.000 |
BV | AC_1 | 2 | 0.630 | 0.000 | 3.204 |
BV | AC_2 | 2 | 0.630 | 0.000 | 3.204 |
BV | AC_3 | 2 | 0.630 | 0.000 | 3.204 |
BV | AC_4 | 2 | 0.630 | 0.000 | 3.204 |
BV | GK | 2 | 0.630 | 0.000 | 3.204 |
BV | Linear | 2 | 0.619 | 1.875 | 3.507 |
NO_Cov | AC_1 | 2 | 0.659 | 0.410 | 2.991 |
NO_Cov | AC_2 | 2 | 0.659 | 0.410 | 2.991 |
NO_Cov | AC_3 | 2 | 0.659 | 0.410 | 2.991 |
NO_Cov | AC_4 | 2 | 0.659 | 0.410 | 2.991 |
NO_Cov | GK | 2 | 0.659 | 0.410 | 2.991 |
NO_Cov | Linear | 2 | 0.661 | 0.000 | 1.331 |
Pmean | AC_1 | 2 | 0.625 | 0.000 | 3.103 |
Pmean | AC_2 | 2 | 0.625 | 0.000 | 3.103 |
Pmean | AC_3 | 2 | 0.625 | 0.000 | 3.103 |
Pmean | AC_4 | 2 | 0.625 | 0.000 | 3.103 |
Pmean | GK | 2 | 0.625 | 0.000 | 3.103 |
Pmean | Linear | 2 | 0.625 | 0.000 | 2.607 |
BV | AC_1 | 3 | 0.607 | 0.000 | 7.201 |
BV | AC_2 | 3 | 0.607 | 0.000 | 7.201 |
BV | AC_3 | 3 | 0.607 | 0.000 | 7.201 |
BV | AC_4 | 3 | 0.607 | 0.000 | 7.201 |
BV | GK | 3 | 0.607 | 0.000 | 7.201 |
BV | Linear | 3 | 0.592 | 2.448 | 8.120 |
NO_Cov | AC_1 | 3 | 0.619 | 0.679 | 9.667 |
NO_Cov | AC_2 | 3 | 0.619 | 0.679 | 9.667 |
NO_Cov | AC_3 | 3 | 0.619 | 0.679 | 9.667 |
NO_Cov | AC_4 | 3 | 0.619 | 0.679 | 9.667 |
NO_Cov | GK | 3 | 0.619 | 0.679 | 9.667 |
NO_Cov | Linear | 3 | 0.623 | 0.000 | 7.611 |
Pmean | AC_1 | 3 | 0.565 | 0.000 | 14.048 |
Pmean | AC_2 | 3 | 0.565 | 0.000 | 14.048 |
Pmean | AC_3 | 3 | 0.565 | 0.000 | 14.048 |
Pmean | AC_4 | 3 | 0.565 | 0.000 | 14.048 |
Pmean | GK | 3 | 0.565 | 0.000 | 14.048 |
Pmean | Linear | 3 | 0.564 | 0.142 | 13.678 |
BV | AC_1 | Global | 0.629 | 0.000 | 3.385 |
BV | AC_2 | Global | 0.629 | 0.000 | 3.385 |
BV | AC_3 | Global | 0.629 | 0.000 | 3.385 |
BV | AC_4 | Global | 0.629 | 0.000 | 3.385 |
BV | GK | Global | 0.629 | 0.000 | 3.385 |
BV | Linear | Global | 0.617 | 1.955 | 3.770 |
NO_Cov | AC_1 | Global | 0.652 | 0.000 | 4.065 |
NO_Cov | AC_2 | Global | 0.652 | 0.000 | 4.065 |
NO_Cov | AC_3 | Global | 0.652 | 0.000 | 4.065 |
NO_Cov | AC_4 | Global | 0.652 | 0.000 | 4.065 |
NO_Cov | GK | Global | 0.652 | 0.000 | 4.065 |
NO_Cov | Linear | Global | 0.651 | 0.067 | 2.876 |
Pmean | AC_1 | Global | 0.612 | 0.000 | 5.384 |
Pmean | AC_2 | Global | 0.612 | 0.000 | 5.384 |
Pmean | AC_3 | Global | 0.612 | 0.000 | 5.384 |
Pmean | AC_4 | Global | 0.612 | 0.000 | 5.384 |
Pmean | GK | Global | 0.612 | 0.000 | 5.384 |
Pmean | Linear | Global | 0.610 | 0.202 | 5.106 |
Type | Kernel | Env | NRMSE | GRE_Entre_Ker | GRE_Entre_Env |
---|---|---|---|---|---|
BV | AC_1 | 1 | 0.810 | 0.099 | 0.000 |
BV | AC_2 | 1 | 0.810 | 0.099 | 0.000 |
BV | AC_3 | 1 | 0.810 | 0.099 | 0.000 |
BV | AC_4 | 1 | 0.810 | 0.099 | 0.000 |
BV | GK | 1 | 0.810 | 0.099 | 0.000 |
BV | Linear | 1 | 0.811 | 0.000 | 0.000 |
NO_Cov | AC_1 | 1 | 0.828 | 0.000 | 0.000 |
NO_Cov | AC_2 | 1 | 0.828 | 0.000 | 0.000 |
NO_Cov | AC_3 | 1 | 0.828 | 0.000 | 0.000 |
NO_Cov | AC_4 | 1 | 0.828 | 0.000 | 0.000 |
NO_Cov | GK | 1 | 0.828 | 0.000 | 0.000 |
NO_Cov | Linear | 1 | 0.827 | 0.169 | 0.000 |
Pmean | AC_1 | 1 | 0.793 | 0.000 | 0.757 |
Pmean | AC_2 | 1 | 0.793 | 0.000 | 0.757 |
Pmean | AC_3 | 1 | 0.793 | 0.000 | 0.757 |
Pmean | AC_4 | 1 | 0.793 | 0.000 | 0.757 |
Pmean | GK | 1 | 0.793 | 0.000 | 0.757 |
Pmean | Linear | 1 | 0.793 | 0.000 | 0.769 |
BV | AC_1 | 2 | 0.800 | 0.075 | 1.162 |
BV | AC_2 | 2 | 0.800 | 0.075 | 1.162 |
BV | AC_3 | 2 | 0.800 | 0.075 | 1.162 |
BV | AC_4 | 2 | 0.800 | 0.075 | 1.162 |
BV | GK | 2 | 0.800 | 0.075 | 1.162 |
BV | Linear | 2 | 0.801 | 0.000 | 1.186 |
NO_Cov | AC_1 | 2 | 0.818 | 0.281 | 1.333 |
NO_Cov | AC_2 | 2 | 0.818 | 0.281 | 1.333 |
NO_Cov | AC_3 | 2 | 0.818 | 0.281 | 1.333 |
NO_Cov | AC_4 | 2 | 0.818 | 0.281 | 1.333 |
NO_Cov | GK | 2 | 0.818 | 0.281 | 1.333 |
NO_Cov | Linear | 2 | 0.820 | 0.000 | 0.878 |
Pmean | AC_1 | 2 | 0.799 | 0.013 | 0.000 |
Pmean | AC_2 | 2 | 0.799 | 0.013 | 0.000 |
Pmean | AC_3 | 2 | 0.799 | 0.013 | 0.000 |
Pmean | AC_4 | 2 | 0.799 | 0.013 | 0.000 |
Pmean | GK | 2 | 0.799 | 0.013 | 0.000 |
Pmean | Linear | 2 | 0.799 | 0.000 | 0.000 |
BV | AC_1 | 3 | 0.722 | 0.194 | 12.162 |
BV | AC_2 | 3 | 0.722 | 0.194 | 12.162 |
BV | AC_3 | 3 | 0.722 | 0.194 | 12.162 |
BV | AC_4 | 3 | 0.722 | 0.194 | 12.162 |
BV | GK | 3 | 0.722 | 0.194 | 12.162 |
BV | Linear | 3 | 0.723 | 0.000 | 12.056 |
NO_Cov | AC_1 | 3 | 0.742 | 0.054 | 11.659 |
NO_Cov | AC_2 | 3 | 0.742 | 0.054 | 11.659 |
NO_Cov | AC_3 | 3 | 0.742 | 0.054 | 11.659 |
NO_Cov | AC_4 | 3 | 0.742 | 0.054 | 11.659 |
NO_Cov | GK | 3 | 0.742 | 0.054 | 11.659 |
NO_Cov | Linear | 3 | 0.742 | 0.000 | 11.410 |
Pmean | AC_1 | 3 | 0.706 | 0.071 | 13.128 |
Pmean | AC_2 | 3 | 0.706 | 0.071 | 13.128 |
Pmean | AC_3 | 3 | 0.706 | 0.071 | 13.128 |
Pmean | AC_4 | 3 | 0.706 | 0.071 | 13.128 |
Pmean | GK | 3 | 0.706 | 0.071 | 13.128 |
Pmean | Linear | 3 | 0.707 | 0.000 | 13.063 |
BV | AC_1 | Global | 0.777 | 0.120 | 4.164 |
BV | AC_2 | Global | 0.777 | 0.120 | 4.164 |
BV | AC_3 | Global | 0.777 | 0.120 | 4.164 |
BV | AC_4 | Global | 0.777 | 0.120 | 4.164 |
BV | GK | Global | 0.777 | 0.120 | 4.164 |
BV | Linear | Global | 0.778 | 0.000 | 4.142 |
NO_Cov | AC_1 | Global | 0.796 | 0.054 | 4.079 |
NO_Cov | AC_2 | Global | 0.796 | 0.054 | 4.079 |
NO_Cov | AC_3 | Global | 0.796 | 0.054 | 4.079 |
NO_Cov | AC_4 | Global | 0.796 | 0.054 | 4.079 |
NO_Cov | GK | Global | 0.796 | 0.054 | 4.079 |
NO_Cov | Linear | Global | 0.796 | 0.000 | 3.847 |
Pmean | AC_1 | Global | 0.766 | 0.026 | 4.296 |
Pmean | AC_2 | Global | 0.766 | 0.026 | 4.296 |
Pmean | AC_3 | Global | 0.766 | 0.026 | 4.296 |
Pmean | AC_4 | Global | 0.766 | 0.026 | 4.296 |
Pmean | GK | Global | 0.766 | 0.026 | 4.296 |
Pmean | Linear | Global | 0.766 | 0.000 | 4.281 |
Phenotypic covariance | |||
yield_blue | DTH_blue | DTF_blue | |
yield_blue | 0.943 | 3.318 | 2.981 |
DTH_blue | 3.318 | 35.301 | 33.398 |
DTF_blue | 2.981 | 33.398 | 31.872 |
Phenotypic correlation | |||
yield_blue | DTH_blue | DTF_blue | |
yield_blue | 1.000 | 0.575 | 0.544 |
DTH_blue | 0.575 | 1.000 | 0.996 |
DTF_blue | 0.544 | 0.996 | 1.000 |
Genetic covariance | |||
yield_blue | DTH_blue | DTF_blue | |
yield_blue | 2.787 × 10−10 | 1.726 × 10−10 | 1.142 × 10−10 |
DTH_blue | 1.726 × 10−10 | 5.383 × 10−9 | 5.147 × 10−9 |
DTF_blue | 1.142 × 10−10 | 5.147 × 10−9 | 5.037 × 10−9 |
Genetic correlation | |||
yield_blue | DTH_blue | DTF_blue | |
yield_blue | 1.000 | 0.141 | 0.096 |
DTH_blue | 0.141 | 1.000 | 0.988 |
DTF_blue | 0.096 | 0.988 | 1.000 |
Residual covariance | |||
yield_blue | DTH_blue | DTF_blue | |
yield_blue | 0.144 | −0.017 | −0.009 |
DTH_blue | −0.017 | 1.575 | 1.531 |
DTF_blue | −0.009 | 1.531 | 1.619 |
Residual correlation | |||
yield_blue | DTH_blue | DTF_blue | |
yield_blue | 1.000 | −0.035 | −0.019 |
DTH_blue | −0.035 | 1.000 | 0.958 |
DTF_blue | −0.019 | 0.958 | 1.000 |
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Montesinos-López, O.A.; Crossa, J.; Saint Pierre, C.; Gerard, G.; Valenzo-Jiménez, M.A.; Vitale, P.; Valladares-Cellis, P.E.; Buenrostro-Mariscal, R.; Montesinos-López, A.; Crespo-Herrera, L. Multivariate Genomic Hybrid Prediction with Kernels and Parental Information. Int. J. Mol. Sci. 2023, 24, 13799. https://doi.org/10.3390/ijms241813799
Montesinos-López OA, Crossa J, Saint Pierre C, Gerard G, Valenzo-Jiménez MA, Vitale P, Valladares-Cellis PE, Buenrostro-Mariscal R, Montesinos-López A, Crespo-Herrera L. Multivariate Genomic Hybrid Prediction with Kernels and Parental Information. International Journal of Molecular Sciences. 2023; 24(18):13799. https://doi.org/10.3390/ijms241813799
Chicago/Turabian StyleMontesinos-López, Osval A., José Crossa, Carolina Saint Pierre, Guillermo Gerard, Marco Alberto Valenzo-Jiménez, Paolo Vitale, Patricia Edwigis Valladares-Cellis, Raymundo Buenrostro-Mariscal, Abelardo Montesinos-López, and Leonardo Crespo-Herrera. 2023. "Multivariate Genomic Hybrid Prediction with Kernels and Parental Information" International Journal of Molecular Sciences 24, no. 18: 13799. https://doi.org/10.3390/ijms241813799