Habier et al. Genetics Selection Evolution 2010, 42:5 http://www.gsejournal.org/content/42/1/5 model, π, or by treating it as another variable model parameter. The accuracy due to LD may be a lower bound for the accuracy of an individual that is unrelated to the train- ing population. However, if LD is primarily due to selec- tion and recent drift rather than historic mutations, the accuracy for unrelated individuals might be even lower. This could be the case if selection candidates descend from a population having an LD structure that is differ- ent from that in the training data. This may apply to individuals either from families that did not contribute to the actual German Holstein Friesian population or from Holstein populations of other regions, such as Australia, New Zealand or the United States. The classical inheritance model in quantitative genet- ics divides the breeding value into parent average and a Mendelian sampling term. The advantage of GS is that the latter can be inferred without its own or progeny performance [30]. In general, LD information contri- butes to both parts of the breeding value, and thus the accuracy due to LD is not necessarily the accuracy to predict Mendelian sampling terms. This accuracy is of great interest in order to evaluate future inbreeding and effective selection intensity when selecting on GEBVs. For this purpose and to test to what extent the accuracy due to LD obtained in this study corresponds to the accuracy to predict Mendelian sampling, cross-valida- tions should be conducted with Mendelian sampling terms estimated from DYDs of bulls and yield deviations of dams. The persistence of the accuracy due to LD over gen- erations might depend on the source of LD that is uti- lized in estimating SNP effects, which should also be analyzed in further studies. Muir [14] showed that accu- racy of GEBVs is not only persistent due to historic mutations and drift, but also when LD originates only from recent drift and selection. Furthermore, when selecting on GEBVs both the extent of LD between SNPs and QTL and the size of the QTL effects deter- mine the fixation of QTL alleles [31] and thereby a pos- sible decay of accuracy due to LD over generations. Inference of the genetic model The number of QTL affecting a quantitative trait was estimated by Hayes et al. [32] to be in the range of 100- 200. Goddard [33], however, pointed out that there are probably many more, because there is a limit to the size of the effect that can be detected. These findings are consistent with conclusions from GS studies [10,12], namely, that there are only a few major genes, but many with a small effect. Results of this study confirm these conclusions because BayesB did not perform much bet- ter than G-BLUP in the accuracy of GEBVs. BayesB was even inferior to G-BLUP for somatic cell score with a Page 9 of 12 training size of 1,048 bulls. In simulations [1,2], how- ever, in which the genetic variance was mainly deter- mined by a few QTL with a large effect, BayesB utilized LD information considerably better than G-BLUP. The question arises why G-BLUP was mostly as good as BayesB and superior to P-BLUP despite the underlying prior assumptions for SNP effects, causing strong shrinkage. Goddard [33] pointed out that GS works in part by using deviations of the realized relationships from that expected from the pedigree, where these deviations are only useful if there is LD between SNPs and QTL or cosegregation. Those deviations seem to be estimated better if more SNPs are fitted in the model and therefore G-BLUP has advantages compared to BayesB if SNP effects and/or LD are small. This may explain why G-BLUP worked better than BayesB for somatic cell score with 1,048 training bulls. However, if more SNPs are fitted in BayesB, e.g. by altering π to 5 or 10%, that difference may disappear. The accuracy due to LD gives more insight into the differences of the genetic determination of quantitative traits. Because this accuracy was higher for fat and milk yield than for pro- tein yield and somatic cell score, milk and fat yield are determined either by QTL with larger effects or the LD between SNPs and QTL is higher than for protein yield and somatic cell score. However, heritability of somatic cell score is lower than that of the yield traits [19], redu- cing the ability to detect QTL. One reason for the dif- ference between protein and the other two yield traits may be DGAT1 [34,35], but this locus is already well estimated with the lower training size and thus the increasing difference with more training individuals results most likely from the fact that more QTL are detected. Comparison with simulation results Meuwissen et al. [1] fitted 2-SNP haplotypes with BayesB and obtained an accuracy for the offspring of training individuals of 0.85 and 0.75 based on 2,200 and 1,000 training individuals, respectively. Solberg et al. [13] and Habier et al. [2,27], in contrast, fitted single SNPs and found an accuracy of 0.7 with 1,000 training individuals, where the accuracy due to LD was estimated to be 0.55 [2]. Although training data sets were compar- able in size to this study, accuracies from simulations tended to be higher, which might have two main rea- sons. First, in simulations every offspring had two par- ents in the training data set so that the additive-genetic relationship information between training and validation data sets is expected to be higher at first sight, but more half sib relationships are present in real cattle popula- tions. Second, there might be a discrepancy between the simulated genetic models and the genetic architecture (number of QTL, distribution of QTL effects, LD