Genomic Prediction in Wheat and Maize Breeding Populations

Selection of the bandwidth parameter h in the Gaussian kernel is a challenging problem. Recently a Bayesian method for selecting the bandwidth parameter (h) of a Gaussian kernel was developed by assigning a prior p(h) and obtaining a posterior point estimate of h. Also recently, a marker x environment interaction model (MxE) in the context of the GBLUP model was proposed that allows decomposing marker effects and genomic variance into components that are stable across environments (main effect) and components that are environment specific (interaction terms). In the MxE model the genetic covariance between any pair of environments can be represented by the variance of the main effect; therefore it is restricted to being positive (homogeneous or heterogeneous across environments). The approach for selecting the bandwidth parameter h can be implemented in conjunction with the MxE model to examine accuracies of different prediction problems. Furthermore, the reaction norm model, also recently developed for assessing genotype x environment interaction (GxE), allows genomic prediction using highly dimensional marker, pedigree and environmental covariables matrices. Results of two wheat data sets using the MxE model with the Gaussian kernel Bayesian estimation of h, show increases in prediction accuracies over the standard MxE of about 7% and10%. Other results include the analyses of GxE incorporated in the reaction norm model using 20,000 wheat lines genotyped with genotyping-by sequencing. For predicting about 500 wheat lines in several international environments (in two different years), environmental covariables of the environments to be predicted were included. The prediction accuracy of these international environments shows promising results.