Habier et al. Genetics Selection Evolution 2010, 42:5 http://www.gsejournal.org/content/42/1/5 ni + ni 4−h 2j , where ni is the h 2j the selection index formula number of daughters of a bull i and h 2j the heritability of a daughter record of trait j known from parameter estimations by Liu et al. [28,29]. The heritabilities for milk, fat and protein yield as well as somatic cell score were 0.53, 0.52, 0.51 and 0.23, respectively. The correla- tion  gˆy was calculated using the validation bulls from all replicates of a specified amax, after their EBVs were corrected by the mean EBV of their respective validation data set. Accuracy due to LD The accuracy due to LD was estimated using a regres- sion approach as suggested by Habier et al. [2]. In that study, the authors estimated the accuracy due to LD of generation j,  jLD , by using the accuracy of GEBVs obtained from four generations and the model  i = x1id j = x2i LjD + ei , where ri is the accuracy of GEBVs in generation i, x1i is the accuracy of P-BLUP in generation i divided by the accuracy of P-BLUP in generation j, which models the decay of P-BLUP accuracy due to the decline of addi- tive-genetic relationships, dj is the difference between the accuracy of GEBVs and the accuracy due to LD in generation j, x2i is the decay of LD over generations and ei is a residual term. In this study, accuracies of GEBVs from different generations were replaced by those from different amax values. Furthermore, the accuracy due to LD was assumed to be constant with different amax values, because the average birth year of training and validation bulls was nearly the same for all amax values and thus x2i is always 1. The equation used here was  amax =  LD + xamax d + eamax , (2) where  amax is the accuracy of GEBVs for amax (i.e., 0.6, 0.49, 0.249 and 0.1249) estimated by BayesB or G- BLUP, xamax is the accuracy of P-BLUP for amax divided by the accuracy of P-BLUP for amax = 0.6, d is the dif- ference between the accuracy of GEBVs for amax = 0.6 and the accuracy due to LD and eamax is a residual term. Results Linkage disequilibrium Figure 1 shows average r2 between syntenic SNP pairs against map distance of up to 1 megabase (Mb), which is roughly 1 centimorgan, as well as standard deviations of the average r2 values across all 30 chromosomes. Page 5 of 12 Figure 1 Average r2 (mid-point) as a measure of linkage disequilibrium between syntenic SNP pairs against map distance in megabase (Mb) as well as standard deviation of mean r2 values from all 30 chromosomes (upper and lower deviation from the mid-point). Average r2 decreased exponentially with increasing dis- tance between SNPs and was equal to 0.29, 0.23, 0.15 and 0.07 at distances of 0.02, 0.04, 0.1, and 1 Mb, respectively. Average distance and r2 of adjacent SNPs were 0.064 Mb and 0.22, respectively. Training and validation data Table 3 summarizes the number of bulls used for train- ing in each sampled pair of training and validation data sets as well as the total number of validation bulls over all samples for the specified amax values. Fifteen pairs of training and validation data sets were generated for each scenario with an average validation size of 33 bulls per sampled pair for amax = 0.6, 0.49 and 0.249, and 11 bulls for amax = 0.1249. To better understand the differ- ences in the accuracy of GEBVs between amax values in the following description of the results, the distributions of additive-genetic relationships between bulls in train- ing and validation depending on amax are depicted in Table 3 Average number of bulls used for training in each of the 15 sampled pairs of training and validation data sets and total number of validation bulls over all pairs for a maximum additive-genetic relationship between bulls of both data sets (amax) of 0.6, 0.49, 0.249 and 0.1249 No. of bulls in training 2,096 2,096 2,096 2,096 (± 28) validation 491 497 477 176 amax 0.60 0.49 0.249 0.1249