Genomic-enabled prediction with classification algorithms.

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 and RE for each algorithm depended strongly on the selection percentile. Based on the results, we propose classification method as a promising alternative for GS in plant breeding.