Applications of Machine Learning Methods to Genomic Selection in Breeding Wheat for Rust Resistance.

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.

Applications of Genomic Selection in Breeding Wheat for Rust Resistance.

There are a lot of methods developed to predict untested phenotypes in schemes commonly used in genomic selection (GS) breeding. The use of GS for predicting disease resistance has its own particularities: (a) most populations shows additivity in quantitative adult plant resistance (APR); (b) resistance needs effective combinations of major and minor genes; and (c) phenotype is commonly expressed in ordinal categorical traits, whereas most parametric applications assume that the response variable is continuous and normally distributed. Machine learning methods (MLM) can take advantage of examples (data) that capture characteristics of interest from an unknown underlying probability distribution (i.e., data-driven). We introduce some state-of-the-art MLM capable to predict rust resistance in wheat. We also present two parametric R packages for the reader to be able to compare.

Genome-enabled prediction using probabilistic neural network classifiers.

BACKGROUND: Multi-layer perceptron (MLP) and radial basis function neural networks (RBFNN) have been shown to be effective in genome-enabled prediction. Here, we evaluated and compared the classification performance of an MLP classifier versus that of a probabilistic neural network (PNN), to predict the probability of membership of one individual in a phenotypic class of interest, using genomic and phenotypic data as input variables. We used 16 maize and 17 wheat genomic and phenotypic datasets with different trait-environment combinations (sample sizes ranged from 290 to 300 individuals) with 1.4 k and 55 k SNP chips. Classifiers were tested using continuous traits that were categorized into three classes (upper, middle and lower) based on the empirical distribution of each trait, constructed on the basis of two percentiles (15-85 % and 30-70 %). We focused on the 15 and 30 % percentiles for the upper and lower classes for selecting the best individuals, as commonly done in genomic selection. Wheat datasets were also used with two classes. The criteria for assessing the predictive accuracy of the two classifiers were the area under the receiver operating characteristic curve (AUC) and the area under the precision-recall curve (AUCpr). Parameters of both classifiers were estimated by optimizing the AUC for a specific class of interest. RESULTS: The AUC and AUCpr criteria provided enough evidence to conclude that PNN was more accurate than MLP for assigning maize and wheat lines to the correct upper, middle or lower class for the complex traits analyzed. Results for the wheat datasets with continuous traits split into two and three classes showed that the performance of PNN with three classes was higher than with two classes when classifying individuals into the upper and lower (15 or 30 %) categories. CONCLUSIONS: The PNN classifier outperformed the MLP classifier in all 33 (maize and wheat) datasets when using AUC and AUCpr for selecting individuals of a specific class. Use of PNN with Gaussian radial basis functions seems promising in genomic selection for identifying the best individuals. Categorizing continuous traits into three classes generally provided better classification than when using two classes, because classification accuracy improved when classes were balanced.

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

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.