Eventing competitions in Great Britain (GB) comprise three disciplines, each split into four grades, yielding 12 discipline-grade traits. As there is a demand for tools to estimate (co)variance matrices with a large number of traits, the aim of this work was to investigate different methods to produce large (co)variance matrices using GB eventing data. Data from 1999 to 2008 were used and penalty points were converted to normal scores. A sire model was utilised to estimate fixed effects of gender, age and class, and random effects of sire, horse and rider. Three methods were used to estimate (co)variance matrices. Method 1 used a method based on Gibbs sampling and data augmentation and imputation. Methods 2a and 2b combined sub-matrices from bivariate analyses; one took samples from a multivariate Normal distribution defined by the covariance matrix from each bivariate analysis, then analysed these data in a 12-trait multivariate analysis; the other replaced negative eigenvalues in the matrix with positive values to obtain a positive definite (co)variance matrix. A formal comparison of models could not be conducted; however, estimates from all methods, particularly Methods 2a/2b, were in reasonable agreement. The computational requirements of Method 1 were much less compared with Methods 2a or 2b. Method 2a heritability estimates were as follows: for dressage 7.2% to 9.0%, for show jumping 8.9% to 16.2% and for cross-country 1.3% to 1.4%. Method 1 heritability estimates were higher for the advanced grades, particularly for dressage (17.1%) and show jumping (22.6%). Irrespective of the model, genetic correlations between grades, for dressage and show jumping, were positive, high and significant, ranging from 0.59 to 0.99 for Method 2a and 0.78 to 0.95 for Method 1. For cross-country, using Method 2a, genetic correlations were only significant between novice and pre-novice (0.75); however, using Method 1 estimates were all significant and low to moderate (0.36 to 0.70). Between-discipline correlations were all low and of mixed sign. All methods produced positive definite 12 × 12 (co)variance matrices, suitable for the prediction of breeding values. Method 1 benefits from much reduced computational requirements, and by performing a true multivariate analysis.

Reliable selection criteria are required for young riding horses to increase genetic gain by increasing accuracy of selection and decreasing generation intervals. In this study, selection strategies incorporating genomic breeding values (GEBVs) were evaluated. Relevant stages of selection in sport horse breeding programs were analyzed by applying selection index theory. Results in terms of accuracies of indices (rTI) and relative selection response indicated that information on single nucleotide polymorphism (SNP) genotypes considerably increases the accuracy of breeding values estimated for young horses without own or progeny performance. In a first scenario, the correlation between the breeding value estimated from the SNP genotype and the true breeding value (= accuracy of GEBV) was fixed to a relatively low value of rmg = 0.5. For a low heritability trait (h2 = 0.15), and an index for a young horse based only on information from both parents, additional genomic information doubles rTI from 0.27 to 0.54. Including the conventional information source ‘own performance’ into the before mentioned index, additional SNP information increases rTI by 40%. Thus, particularly with regard to traits of low heritability, genomic information can provide a tool for well-founded selection decisions early in life. In a further approach, different sources of breeding values (e.g. GEBV and estimated breeding values (EBVs) from different countries) were combined into an overall index when altering accuracies of EBVs and correlations between traits. In summary, we showed that genomic selection strategies have the potential to contribute to a substantial reduction in generation intervals in horse breeding programs.