Model averaging for genome-enabled prediction with reproducing kernel Hilbert spaces: a case study with pig litter size and wheat yield.

Predictive ability of yet-to-be observed litter size (pig) grain yield (wheat) records of several reproducing kernel Hilbert spaces (RKHS) regression models combining different number of Gaussian or t kernels was evaluated. Predictive performance was assessed as the average (over 50 replicates) predictive correlation in the testing set. Predictions from these models were combined using three different types of model averaging: (i) mean of predicted phenotypes obtained in each model, (ii) weighted average using mean squared error as weight or (iii) using the marginal likelihood as weight. (ii) and (iii) were obtained in a validation set with 5% of the data. Phenotypes consisted of 2598, 1604 and 1879 average litter size records from three commercial pig lines and wheat grain yield of 599 lines evaluated in four macro-environments. SNPs from the PorcineSNP60 BeadChip and 1447 DArT markers were used as predictors for the pig and wheat data analyses, respectively. Gaussian and univariate t kernels led to same predictive performance. Multikernel RKHS regression models overcame shortcomings of single kernel models (increasing the predictive correlation of RKHS models by 0.05 where 3 Gaussian or t kernels were fitted in the RKHS models simultaneously). None of the proposed averaging strategies improved the predictive correlations attained with single models using multiple kernel fitting.