Genetics Selection Evolution 2009, 41:35 http://www.gsejournal.org/content/41/1/35 where rG-BLUP (rT-BLUP) is the accuracy using G-BLUP (T- BLUP), (1-rT-BLUP) denotes the inaccuracy of rG-BLUP, and ρG-BLUP is the proportion of the inaccuracy that could be explained by G-BLUP. Since, rG-BLUP and rT-BLUP are known, ρG-BLUPcan be calculated from the simulation results and Equation (2). Using these ρG-BLUP values, a method to pre- dict the accuracies from traditional BLUP (e.g. [20]), and Equation (2), we can predict rG-BLUP in situations where there may be very different relationships between the training and evaluation individuals, than assumed in the presented simulations. Similarly, the accuracy of BayesB can be predicted for different relationships between train- ing and evaluation individuals. To test these predictions, a simulation was conducted where the training data set was composed of G1t individ- uals, the number of which was increased to N, and the evaluation individuals originated from G1e. Hence, the training and evaluation individuals were two generations less separated (one generation in each of the lines). Estimation of the effective number of segments By combining the simulation results and Equation (1), the effective number of segments can be derived as fol- lows. Let PEV = 1-rG-BLUP2, then it can be seen from Equa- h2 tion (1) that the E(PEV-1) = 1+β*N, where β = 4NeLν . Hence, the regression of PEV-1 on N is linear, and the regression coefficient is a function of h2, which is known, and the effective number of segments, 4NeLν. Results and discussion Effect of number of markers and training records Figure 2 shows the accuracy of the predicted breeding val- ues of the G2e individuals, as a function of the marker density expressed in terms of the linkage disequilibrium between adjacent markers (following Calus et al. [21]). The linkage disequilibrium between adjacent markers was calculated as R2 = 1/(4Ned+1) [22], where d is the distance between the adjacent markers. As can be seen from Figure 2, accuracy increases approximately linearly with |R| over a 20-fold increase in marker density. However, increasing the density from 10 to 20 Ne/M hardly increased the accu- racy of selection (and also the |R| between adjacent mark- ers). For G-BLUP, the slope of the increase with increasing density was clearly smaller, which indicates that the supe- riority of BayesB increases with increasing density. This may be expected since with increasing density it becomes more important to filter the SNP that are in strong LD with the QTL from all the others, instead of spreading the effects over all SNP as G-BLUP does, which results in very small effects for the single SNP. The differences between BayesB and MIXTURE are very small (Table 1), but slightly in favour of BayesB, which is probably due to the informative prior distribution that was used in BayesB. G-BLUP yielded clearly lower accu- racy at high density, which was especially the case for low N. This may be explained by the fact that as N goes to infinity all methods will reach perfect predictions of SNP effects, as can be seen from Equation (1). At low density (1 Ne/M) G-BLUP yielded only a 0.02–0.06 fold lower accuracy than BayesB. For T-BLUP, the accuracies varied between 0.19 and 0.23 as N increased from 500 to 2000 (result not shown else- where). Thus T-BLUP was much less accurate than BayesB (varied from 0.83 – 0.93) because (i) it does not make use of the marker data; and (ii) it uses pedigree-based rela- tionships to predict the EBV of the evaluation individuals from the phenotyped of the training individuals which were generally low, on average 0.01. The accuracy of G-BLUP increases more than that of BayesB when the number of records increases (Figure 3). Thus, G-BLUP requires more records, N, to achieve high accuracy than BayesB. In other words, BayesB seems espe- cially superior to G-BLUP in situations with small num- bers of records and high marker density. In these situations, the prior knowledge about QTL effects used by BayesB partly overcomes the low information content of the data, and the high marker density results in marker effects reflecting better the effects of QTL. The effect of increasing the number of records, N, is smaller at low marker densities, especially for G-BLUP at density 1 Ne/ M. For high densities, the accuracy keeps increasing as the number of records increases. Hence, to take advantage of high-density SNP genotyping, large data sets are needed to estimate the marker effects. Larger genome sizes Table 2 shows the effect of doubling the genome size and simultaneously doubling the number of G2t individuals (N). From Equation (1), it was expected that accuracy would not be affected by this doubling. This is approxi- mately the case, but not quite: for G-BLUP the accuracy decreases on average by 0.014 per doubling of genome sizes and for BayesB this figure is on average 0.0075. The mechanics of doubling genome size and numbers of training records may become clearer, if we consider two replicated simulations containing one chromosome each, and obtain an average accuracy of r. Now, if we combine the two chromosomes of the two replicates into one rep- licate with two chromosomes, it becomes clear that we also have to combine the phenotypic recordings of both replicates to predict marker effects and thus breeding val- ues with the same accuracy. However, 2N records on two chromosomes are only as informative as N records on 1 Page 5 of 9 (page number not for citation purposes)