Habier et al. Genetics Selection Evolution 2010, 42:5 http://www.gsejournal.org/content/42/1/5 a burn-in of 40,000 rounds. The GEBV of bull i, either in training or validation, was estimated as (1) K GEBVi = ∑ xikˆk , k=1 where ˆk is the estimated SNP effect of locus k. The BLUP animal model used to estimate genomic or pedi- gree-based EBVs is yi =  + g i + ei , wi where yi, ei and wi are defined as before, μ is the over- all mean, and gi is the breeding value of bull i in train- ing. Genomic BLUP (G-BLUP) EBVs of both training and validation bulls were obtained by mixed-model equations using the genomic relationship matrix, whereas pedigree-based BLUP (P-BLUP) EBVs were obtained by using the numerator relationship matrix [24,25]. The elements of the genomic relationship matrix were calculated as following [2,26], where xk is a column vector containing the SNP genotypes of training and validation bulls at locus k. ∑kK=1 x kx′k 2∑kK=1 pk(1−pk ) Generation of training and validation data sets Training and validation data sets were generated system- atically using the additive-genetic relationships between bulls derived from the pedigree in order to study the impact of additive-genetic relationship information on accuracy of GEBVs by cross-validation. The aim was to control the maximum additive-genetic relationship between bulls in training and validation denoted by amax; That is, given amax, no bull in training was allowed to have an additive-genetic relationship larger than amax with a bull in validation. This criterion allows to divide the family structure present in the data set such that validation bulls are allowed to have close relatives in training or not. Furthermore, the decay of additive- genetic relationships over generations, similar to that in simulation studies [1,2,14,27], can be mimicked. A sam- pling algorithm was implemented to generate training and validation data sets, which assigned bulls to both sets in a way that amax was not exceeded. For small amax values this can only be achieved by removing com- pletely some bulls from the analysis, where the algo- rithm was optimized to exclude as few bulls as possible. In general, the lower the amax, the smaller the number of bulls in validation. Therefore, several pairs of training and validation data sets were sampled, where repeated sampling of a bull into validation was not accepted. In addition, no more than two bulls out of one half sib Page 4 of 12 family were allowed to be in validation in order to reduce the dependency between validation bulls in each pair of data sets. Furthermore, fathers of training bulls were not allowed to be in validation, because the accu- racy of those bulls is not representative for the predic- tion of the GEBVs of future individuals as demonstrated by [2]. Relationships between training and validation data sets Four different scenarios with amax = 0.6, 0.49, 0.249 and 0.1249 were generated. These values were selected to exploit the family structure in the data as follows: The training data set contained fathers, full- and half sibs of the bulls in validation with amax = 0.6, only half sibs with amax = 0.49, and neither of those close relatives with amax = 0.249 and 0.1249. All scenarios had the same training size in order to exclude the effect of dif- ferent sizes on the accuracy of GEBVs. Because of diffi- culties to obtain large training data sets for the lowest amax in a structured dairy cattle population, the training sizes for the other scenarios were reduced to the average size of amax = 0.1249 by removing bulls randomly. Note, however, that for the scenarios with amax = 0.6 and 0.49 the half and full sibs or fathers of the bulls in validation were not removed from the training data. The training size for amax = 0.1249 was 2,096 bulls on average in 15 sampled pairs of training and validation data sets, hence the training size for the other scenarios was fixed at 2,096 bulls. Validation data sets of each sample for the first three scenarios were required to have at least 30 bulls, and for amax = 0.1249 at least 11 bulls. The corre- lation between EBVs and DYDs was also estimated for training bulls and denoted as scenario amax = 1. To study the effect of the size of the training data on accuracy at different amax values, training data sets were halved to a size of 1,048 by removing bulls randomly, except for fathers as well as full and half sibs of the bulls in validation. Thus, the number of close relatives between training and validation was kept constant in order to analyze the impact of the precision of SNP effects on accuracy rather than the number of relatives, which can already be observed with decreasing amax. Criterion for comparisons The correlation between true and estimated breeding values, g and gˆ , was estimated by the following formula: ˆ ggˆ = gˆgˆyy ×  gy =  gˆy × 1hy2 = ˆ ggˆyy , assuming  gˆy =  gˆg , where y denotes DYD, hy2 the heritability of DYDs and ˆ gy the correlation between the true breeding value and DYD averaged over bulls in validation. The latter was estimated from the accuracy of DYDs using