Genomic selection (GS) facilitates the rapid selection of superior genotypes and accelerates the breeding cycle. In this review, we discuss the history, principles, and basis of GS and genomic-enabled prediction (GP) as well as the genetics and statistical complexities of GP models, including genomic genotype×environment (G×E) interactions. We also examine the accuracy of GP models and methods for two cereal crops and two legume crops based on random cross-validation. GS applied to maize breeding has shown tangible genetic gains. Based on GP results, we speculate how GS in germplasm enhancement (i.e., prebreeding) programs could accelerate the flow of genes from gene bank accessions to elite lines. Recent advances in hyperspectral image technology could be combined with GS and pedigree-assisted breeding.

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

The availability of high density panels of molecular markers has prompted the adoption of genomic selection (GS) methods in animal and plant breeding. In GS, parametric, semi-parametric and non-parametric regressions models are used for predicting quantitative traits. This article shows how to use neural networks with radial basis functions (RBFs) for prediction with dense molecular markers. We illustrate the use of the linear Bayesian LASSO regression model and of two non-linear regression models, reproducing kernel Hilbert spaces (RKHS) regression and radial basis function neural networks (RBFNN) on simulated data and real maize lines genotyped with 55,000 markers and evaluated for several trait–environment combinations. The empirical results of this study indicated that the three models showed similar overall prediction accuracy, with a slight and consistent superiority of RKHS and RBFNN over the additive Bayesian LASSO model. Results from the simulated data indicate that RKHS and RBFNN models captured epistatic effects; however, adding non-signal (redundant) predictors (interaction between markers) can adversely affect the predictive accuracy of the non-linear regression models.

New methods and algorithms are being developed for predicting untested phenotypes in schemes commonly used in genomic selection (GS). The prediction of disease resistance in GS has its own peculiarities: a) there is consensus about the additive nature of quantitative adult plant resistance (APR) genes, although epistasis has been found in some populations; b) rust resistance requires effective combinations of major and minor genes; and c) disease resistance is commonly measured based on ordinal scales (e.g., scales from 1-5, 1-9, etc.). Machine learning (ML) is a field of computer science that uses algorithms and existing samples to capture characteristics of target patterns. In this paper we discuss several state-of-the-art ML methods that could be applied in GS. Many of them have already been used to predict rust resistance in wheat. Others are very appealing, given their performance for predicting other wheat traits with similar characteristics. We briefly describe the proposed methods in the Appendix.

Pearson's correlation coefficient (ρ) is the most commonly reported metric of the success of prediction in genomic selection (GS). However, in real breeding ρ may not be very useful for assessing the quality of the regression in the tails of the distribution, where individuals are chosen for selection. This research used 14 maize and 16 wheat data sets with different trait–environment combinations. Six different models were evaluated by means of a cross-validation scheme (50 random partitions each, with 90% of the individuals in the training set and 10% in the testing set). The predictive accuracy of these algorithms for selecting individuals belonging to the best α=10, 15, 20, 25, 30, 35, 40% of the distribution was estimated using Cohen's kappa coefficient (κ) and an ad hoc measure, which we call relative efficiency (RE), which indicates the expected genetic gain due to selection when individuals are selected based on GS exclusively. We put special emphasis on the analysis for α=15%, because it is a percentile commonly used in plant breeding programmes (for example, at CIMMYT). We also used ρ as a criterion for overall success. The algorithms used were: Bayesian LASSO (BL), Ridge Regression (RR), Reproducing Kernel Hilbert Spaces (RHKS), Random Forest Regression (RFR), and Support Vector Regression (SVR) with linear (lin) and Gaussian kernels (rbf). The performance of regression methods for selecting the best individuals was compared with that of three supervised classification algorithms: Random Forest Classification (RFC) and Support Vector Classification (SVC) with linear (lin) and Gaussian (rbf) kernels. Classification methods were evaluated using the same cross-validation scheme but with the response vector of the original training sets dichotomised using a given threshold. For α=15%, SVC-lin presented the highest κ coefficients in 13 of the 14 maize data sets, with best values ranging from 0.131 to 0.722 (statistically significant in 9 data sets) and the best RE in the same 13 data sets, with values ranging from 0.393 to 0.948 (statistically significant in 12 data sets). RR produced the best mean for both κ and RE in one data set (0.148 and 0.381, respectively). Regarding the wheat data sets, SVC-lin presented the best κ in 12 of the 16 data sets, with outcomes ranging from 0.280 to 0.580 (statistically significant in 4 data sets) and the best RE in 9 data sets ranging from 0.484 to 0.821 (statistically significant in 5 data sets). SVC-rbf (0.235), RR (0.265) and RHKS (0.422) gave the best κ in one data set each, while RHKS and BL tied for the last one (0.234). Finally, BL presented the best RE in two data sets (0.738 and 0.750), RFR (0.636) and SVC-rbf (0.617) in one and RHKS in the remaining three (0.502, 0.458 and 0.586). The difference between the performance of SVC-lin and that of the rest of the models was not so pronounced at higher percentiles of the distribution. The behaviour of regression and classification algorithms varied markedly when selection was done at different thresholds, that is, κ a...