Predicting genetic values: a kernel-based best linear unbiased prediction with genomic data

Genomic data provide a valuable source of information for modeling covariance structures, allowing a more accurate prediction of total genetic values (GVs). We apply the kriging concept, originally developed in the geostatistical context for predictions in the low-dimensional space, to the high-dimensional space spanned by genomic single nucleotide polymorphism (SNP) vectors and study its properties in different gene-action scenarios. Two different kriging methods ["universal kriging" (UK) and "simple kriging" (SK)] are presented. As a novelty, we suggest use of the family of Matérn covariance functions to model the covariance structure of SNP vectors. A genomic best linear unbiased prediction (GBLUP) is applied as a reference method. The three approaches are compared in a whole-genome simulation study considering additive, additive-dominance, and epistatic gene-action models. Predictive performance is measured in terms of correlation between true and predicted GVs and average true GVs of the individuals ranked best by prediction. We show that UK outperforms GBLUP in the presence of dominance and epistatic effects. In a limiting case, it is shown that the genomic covariance structure proposed by VanRaden (2008) can be considered as a covariance function with corresponding quadratic variogram. We also prove theoretically that if a specific linear relationship exists between covariance matrices for two linear mixed models, the GVs resulting from BLUP are linked by a scaling factor. Finally, the relation of kriging to other models is discussed and further options for modeling the covariance structure, which might be more appropriate in the genomic context, are suggested.