Genomic Prediction of Breeding Values of Maize and Wheat Using Linear and Non-linear 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 regressions, and non-parametric methods are used. Interactions between marker alleles at two or more loci can be accommodated in a linear model by using appropriate contrasts. However, this is feasible only when the number of markers (p) is moderate. In GS, however, p is usually large, making parametric modeling of complex epistatic interactions unfeasible. An alternative is to use semi-parametric regressions and non-parametric methods, such as kernel-based methods with the expectation that such procedures can capture complex higher order interaction patterns. In this presentation we show how to use kernel methods for prediction with dense molecular markers. We illustrate the use of linear and non-linear on simulated data and on real maize line genotyped with 55k markers and evaluated for several trait-environment combinations. We also show results from wheat multi trait multi environments trials. The empirical results indicated that the models have similar prediction accuracy, with slight superiority of the kernel models over linear  model. Non-linear models may be capturing epistatic effects and showed slight and consistent prediction accuracy superiority over the linear model.