Genetics Selection Evolution 2009, 41:35 http://www.gsejournal.org/content/41/1/35 0.95 0.9 y 0.85 rca 0.8 u cc 0.75 a 0.7 0.65 a. BayesB 500 1000 1500 N 2000 20 Ne/M 10 Ne/M 5 Ne/M 2 Ne/M 1 Ne/M anFAluiscgmcfuuobreaerBc3yaoyfoerfseBtcho(e3rpad)rseaidnidctthGieo-ntBrLoaUfingPine(ng3edbtai)ctavsasaelutfeu(snNco)tfioGn2oefinthdeividu- Accuracy of the prediction of genetic values of G2e individuals for BayesB (3a) and G-BLUP (3b) as a function of the number of records in the training data set (N). Estimation of the effective number of loci Using the results of Table 1 for a density of 20 Ne/M, the regression of PEV-1 on N was calculated as suggested in section 'Estimation of the effective number of segments'. For G-BLUP, the estimates of the intercept (α) and slope (β) were 1.388 and 1.551*10-3, respectively. For BayesB, these figures were 1.859 and 2.649*10-3, respectively. This results in estimates of the effective number of QTL of 516 and 302 for G-BLUP and BayesB, respectively. This value is expected to be lower for BayesB, since it concentrates on the loci with substantial effects whereas G-BLUP gives equal weight to all loci. The actual number of QTL was 120, which indicates that BayesB had to use several SNP to estimate the effect of each QTL. The derivation of God- dard [11] (see Section 'The scaling by Ne argument') pre- dicts that there are effectively 189 segments, which is considerably lower than the estimate of 516 by G-BLUP. Possibly the estimate of G-BLUP is biased by the deliber- ate exclusion of close relationships between the training and evaluation individuals. The estimates of the regres- sion coefficients α and β can also be used to predict PEV, and thus rG-BLUP and rBayesB for different sizes of the train- ing data set, N, than those used here. Using the prediction of 189 effective segments from [11], Equation (1) predicts accuracies of 0.946, 0.899, and 0.824, for N = 2000, 1000 and 500, respectively. This is reasonably close to the BayesB accuracies, but should in fact be compared to the G-BLUP (which was assumed to derive the 189 effective segments) accuracies, which are substantially lower (Table 1; 20 Ne/M results). This could be due to the training and estimation individuals being less related than when they were randomly sampled from the population. Lower heritability The effect of a reduced heritability was tested using a her- itability of 0.5 instead of 0.8. For N = 2000, this yielded accuracies of 0.789 and 0.859 for G-BLUP and BayesB, respectively (result not shown elsewhere). Equation (1) predicts that accuracy does not change if N*h2 remains the same, which is approximately the case for N = 1000 and h2 = 0.8, and yielded accuracies of 0.817 and 0.882 (Table 1). Thus, this prediction of Equation (1) seems to hold approximately, although the accuracy seems to decrease somewhat faster than predicted as h2 reduces. The latter may be because Equation (1) predicts basically the accu- racy of a single (effective) locus, whereas, if accuracy is high, all other loci are also predicted accurately. If herita- bility, and thus accuracy is reduced, the accuracy of the other loci reduces as well and the overall accuracy reduces more than expected from single locus predictions. The number of QTL and distribution of their effects The number of simulated QTL was quite large: 24 per Morgan, i.e. 720 for a 30 Morgan genome. In addition, the effective size was quite small, such that the expected LD between the QTL is substantial, i.e. from [22]: E(R2) = 4Ne1d +1 = 400 /124+1 = 0.06 where d is the dis- tance between the QTL. This implies that the effect of the previous QTL in part carries over to the next, and thus that there are measurable QTL effects everywhere across the genome. Thus, the genetic model resembles that of the infinitesimal model, which assumes that infinitely many small QTL are smeared across the genome. Results from large-scale genome-wide association studies in humans support this genetic model with relatively small and many QTL [4]. This genetic model with many, small QTL will especially be a disadvantage for BayesB, which attempts to estimate the variance of individual QTL, whereas G-BLUP a priori assumes that every marker has equal variance. Therefore, the results in Table 1, show a smaller advantage for BayesB relative to G-BLUP than Meuwissen et al. [2] found, who simulated only ~5 QTL per Morgan. However, in general, Page 7 of 9 (page number not for citation purposes)