Durable resistance to the rust diseases of wheat (Triticum aestivum L.) can be achieved by developing lines that have racenonspecifi c adult plant resistance conferred by multiple minor slow-rusting genes. Genomic selection (GS) is a promising tool for accumulating favorable alleles of slow-rusting genes. In this study, fi ve CIMMYT wheat populations evaluated for resistance were used to predict resistance to stem rust (Puccinia graminis) and yellow rust (Puccinia striiformis) using Bayesian least absolute shrinkage and selection operator (LASSO) (BL), ridge regression (RR), and s upport vector regression with linear or radial basis function kernel models. All parents and populations were genotyped using 1400 Diversity Arrays Technology markers and different prediction problems were assessed. Results show that prediction ability for yellow rust was lower than for stem rust, probably due to differences in the conditions of infection of both diseases. For within population and environment, the correlation between predicted and observed values (Pearson's correlation [ρ]) was greater than 0.50 in 90% of the evaluations whereas for yellow rust, ρ ranged from 0.0637 to 0.6253. The BL and RR models have similar prediction ability, with a slight superiority of the BL confi rming reports about the additive nature of rust resistance. When making predictions between environments and/or between populations, including information from another environment or environments or another population or populations improved prediction.

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...

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BackgroundMulticlass classification of microarray data samples with a reduced number of genes is a rich and challenging problem in Bioinformatics research. The problem gets harder as the number of classes is increased. In addition, the performance of most classifiers is tightly linked to the effectiveness of mandatory gene selection methods. Critical to gene selection is the availability of estimates about the maximum number of genes that can be handled by any classification algorithm. Lack of such estimates may lead to either computationally demanding explorations of a search space with thousands of dimensions or classification models based on gene sets of unrestricted size. In the former case, unbiased but possibly overfitted classification models may arise. In the latter case, biased classification models unable to support statistically significant findings may be obtained.ResultsA novel bound on the maximum number of genes that can be handled by binary classifiers in binary mediated multiclass classification algorithms of microarray data samples is presented. The bound suggests that high-dimensional binary output domains might favor the existence of accurate and sparse binary mediated multiclass classifiers for microarray data samples.ConclusionsA comprehensive experimental work shows that the bound is indeed useful to induce accurate and sparse multiclass classifiers for microarray data samples.