Page 8 of 12 0.33 0.29 0.15 0.15 Training data size 2,096 1,048 Method BayesB G-BLUP BayesB G-BLUP Milk yield 0.41 0.21 0.24 0.13 Fat yield 0.47 0.38 0.31 0.33 0.29 0.17 0.23 0.10 Table 4 Accuracy of GEBVs due to LD estimated by equation (2) for milk, fat and protein yield as well as somatic cell score using training data sizes of 2,096 and 1,048 bulls. Protein yield Somatic cell score Habier et al. Genetics Selection Evolution 2010, 42:5 http://www.gsejournal.org/content/42/1/5 better for milk and protein yield. In comparison to the accuracies of GEBVs with 2,096 training bulls (Figure 3), differences between BayesB and G-BLUP became more distinct for the accuracies due to LD. In addition, the ranking of the traits according to their accuracies is dif- ferent. Milk and protein yield had clearly higher accura- cies of GEBVs than fat yield and somatic cell score, whereas fat yield had the highest accuracy due to LD and protein yield the lowest. Discussion The objective of this study was to analyze the impact of additive-genetic relationships between bulls in training and validation data sets on the accuracy of GEBVs and to estimate the accuracy due to LD. The accuracy of GEBVs obtained by both BayesB and G-BLUP decreased with maximum additive-genetic relationship between bulls in training and validation (amax) for all four traits analyzed. The decay of accuracy tended to be larger for G-BLUP and when training size was smaller. The differ- ences between BayesB and G-BLUP became more evi- dent considering the accuracy due to LD. BayesB clearly outperformed G-BLUP in sets of 2,096 training bulls. The LD found here is comparable to that reported by De Roos et al. [5] for the Dutch and Australian Holstein populations making the results of this study meaningful for other Holstein populations. Variability of accuracy of GEBVs Results of this study demonstrate that the accuracy of GEBVs is not constant for all selection candidates but can vary depending on the number of relatives in train- ing and the degree of additive-genetic relationships with training individuals (Figure 3 and 4). The impact of additive-genetic relationships also depends on the method used to estimate SNP effects [2], because the more SNPs fitted, the more additive-genetic relation- ships are captured by them. This may explain why G- BLUP tended to decrease more with amax than BayesB. In principle, the decay of accuracy with additive-genetic relationships is also expected to be higher with increas- ing heritability, but this could not be observed here. The accuracies of GEBVs reported in this study are representative for the prediction of GEBVs of future generations, in that fathers with offspring in training were not used for validation. Otherwise the accuracy would be higher because their Mendelian sampling terms could be inferred by utilizing the additive-genetic relationships captured by SNPs. In conclusion, the additive-genetic relationships between training individuals and a selection candidate must be known in order to provide a reliable GEBV accuracy of that candidate in practical application. As was shown with Figure 2, the average additive-genetic relationship for the amax scenarios 0.6, 0.49 and 0.249 did not differ, and thus is not helpful to describe the impact of additive-genetic relationships on accuracy, but rather amax. This criterion was selected here to exploit the family structure in the data, but other criteria should be found that are more useful in practice. One possibi- lity, which should be tested in subsequent studies, could be the expected accuracy of P-BLUP obtained from the- oretical calculations. To evaluate the expected variation in accuracy for young selection candidates, amax was calculated for bulls born in 2007 with respect to the full training data set of 3,863 bulls. Fortunately, all selection candidates have amax≥ 0.125, 83% have amax≥ 0.25, and one third even have ancestors and full sibs in training. The reason for these high genetic relationships are the long generation intervals in cattle and the low effective population size of 40-50 (personal unpublished studies, estimated from pedigree). This shows that the accuracy of GEBVs for current selection candidates is expected to vary due to different additive-genetic relationships with the training data. Accuracy due to LD Accuracy due to LD ranged between 0.29 for protein yield to 0.48 for fat yield using 2,096 training bulls and BayesB. With this number of training bulls, accuracy due to LD, which is expected to be fairly persistent over generations, appears to be too small to reduce trait phe- notyping, and progeny testing in particular if GS is applied. However, accuracy due to LD improved consid- erably with increasing training size and thus further stu- dies are necessary to evaluate the accuracy due to LD with the current training size of 3,863 bulls and beyond. Further improvements may be possible by varying the strong prior probability of fitting a SNP locus into the