Birth year 1981-1989 1990-1997 1998 1999 2000 2001 2002 2003 2004 Table 1 Distribution of genotyped bulls (n = 3,863) by birth year and average number of phenotyped daughters per bull (s.e.) No. of bulls No. of daughters 140 455 378 446 484 482 485 830 163 5,969 (± 886) 4,473 (± 356) 567 (± 115) 297 (± 42) 142 (± 11) 107 (± 2) 116 (± 2) 93 (± 1) 62 (± 2) Table 2 Family structure of genotyped bulls. Number (n), average size ( x ), standard deviation (s), minimum (Min) and maximum (Max) size of paternal half and full sib families as well as number of genotyped fathers and summary statistics for the number of their genotyped sons Family type Half sib Full sib Father-son n 646 168 114 x 6.0 2.2 10.7 s 10.9 0.4 19 Min 1 2 1 Max 102 5 109 Genotypes of SNPs located on the X chromosome, but outside the pseudo-autosomal region, were set to miss- ing if the genotype of a bull was heterozygous. Missing genotypes were imputed by fastPhase [16]. Furthermore, the haplotypes obtained by fastPhase were utilized in Haploview [17] to estimate r2 as a mea- sure of LD between SNPs. Haplotypes of all genotyped bulls were used in this calculation, because the aim was to evaluate the LD that can be utilized to estimated SNP effects, and this LD may have also been caused by cose- gregation, recent drift and selection. Pedigree information The pedigree consisted of genotyped bulls as well as their ancestors born between 1950 and 1998, yielding a total of 21,591 individuals. This pedigree was used to generate training and validation data sets with a speci- fied maximum additive-genetic relationship between bulls in both data sets and to estimate breeding values with the standard BLUP-methodology. Phenotypes Daughter yield deviations (DYDs) [18] for the quantita- tive traits milk yield, fat yield, protein yield and somatic cell score were available for both genotyped bulls and their male ancestors in the pedigree. They were esti- mated from the test-day yields of daughters corrected Habier et al. Genetics Selection Evolution 2010, 42:5 http://www.gsejournal.org/content/42/1/5 Page 3 of 12 for fixed and permanent environmental effects as well as half the breeding value of the daughter’s dam [19]. Phe- notypes and estimated effects were taken from the April 2009 evaluation for the German Holstein Friesian popu- lation. Additive-genetic and residual variances,  g2 and  e2 , used as prior information in the statistical analyses, were estimated by ASReml [20] utilizing all phenotyped bulls in the pedigree. A sire model was used for this purpose in which residual terms were weighted by the reliability of a bull’s DYD. Statistical models Three statistical models were used to evaluate the impact of additive-genetic relationships on the accu- racy of GEBVs. These were 1) BayesB [1], 2) BLUP animal model using the genomic relationship matrix [21], which is equivalent to RR-BLUP [2,22,23], and 3) BLUP animal model using the numerator relationship matrix [24,25] to estimate standard BLUP breeding values. These models are described in more detail below. The statistical model for BayesB can be written as yi =  + ∑K xik k k + ei , k=1 wi where yi is the DYD of bull i in training, a is an inter- cept, K = 40, 588 SNPs, xik is the SNP genotype, bk is the effect and δk is a 0/1-indicator variable, all for SNP k, ei is the residual effect with mean zero and variance  e2 , and wi is the reliability of yi. SNP genotypes are coded as the number of copies of one of the SNP alleles, i.e. 0, 1 or 2. The prior for a was 1, for  e2 scaled inverse chi-square with degrees of freedom νe = 4.2 and scale Se2 =  e2(4.2−2) , and for δk the probability that 4.2 SNP k is fitted in the model, π = Pr(δk = 1), which was set to 0.01. SNP effects are treated as random and are sampled from N (0,  2 ), where  2 k k inverse chi-square prior with νb has a scaled = 4.2 and S2 =  2 (44..22−2) . The variance  2 was calculated as  g2 , where pk is the allele frequency at  ∑kK=12pk(1−pk ) SNP k. MCMC-sampling was used to infer model para- meters, where a, bk and  e2 were sampled with Gibbs steps and δk and  2 with a Metropolis-Hastings step. k The MCMC-sampler was run for 50,000 iterations with