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Reproducing kernel Hilbert spaces regression procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are discussed from a theoretical perspective. It is argued that a nonparametric treatment may be needed for capturing the multiple and complex interactions potentially arising in whole-genome models, i.e., those based on thousands of single-nucleotide polymorphism (SNP) markers. After a review of reproducing kernel Hilbert spaces regression, it is shown that the statistical specification admits a standard mixed-effects linear model representation, with smoothing parameters treated as variance components. Models for capturing different forms of interaction, e.g., chromosome-specific, are presented. Implementations can be carried out using software for likelihood-based or Bayesian inference.

A total of 13,066 first-lactation test-day records of 2,277 Valle del Belice ewes from 17 flocks were used to estimate genetic parameters for somatic cell scores (SCS) and milk production traits, using a repeatability test-day animal model. Heritability estimates were low and ranged from 0.09 to 0.14 for milk, fat, and protein yields, and contents. For SCS, the heritability of 0.14 was relatively high. The repeatabilities were moderate and ranged from 0.29 to 0.47 for milk production traits. The repeatability for SCS was 0.36. Flock-test-day explained a large proportion of the variation for milk production traits, but it did not have a big effect on SCS. The genetic correlations of fat and protein yields with fat and protein percentages were positive and high, indicating a strong association between these traits. The genetic correlations of milk production traits with SCS were positive and ranged from 0.16 to 0.31. The results showed that SCS is a heritable trait in Valle del Belice sheep and that single-trait selection for increased milk production will also increase SCS.