Is the use of formulae a reliable way to predict the accuracy of genomic selection?

We studied four formulae used to predict the accuracy of genomic selection prior to genotyping. The objectives of our study were to investigate the impact of the parameters of each formula on the values of accuracy calculated using these formulae, and to check whether the accuracies reported in the literature are in agreement with the formulae. First, we computed the marginal distribution of accuracy (by integration) for each parameter of all four formulae: heritability h(2), reference population size T, number of markers M and number of effective segments in the genome M-e. Then, we collected 145 accuracies and corresponding parameters reported in 13 publications on genomic selection (mainly in dairy cattle), and performed analysis of variance to test the differences between observed and predicted accuracy with effects of formulae and parameters. The variation of accuracy for different values of each parameter indicated that two parameters, T and M-e,M- had a significant impact and that considerable differences existed between the formulae (mean accuracies differed by up to 0.20 point). The results of our meta-analysis showed a big formula effect on the accuracies predicted using each formula, and also a significant effect of the value obtained for M-e calculated from N-e (effective population size). Each formula can therefore be demonstrated to be optimal depending on the assumption used for M-e. In conclusion, no rules can be applied to predict the reliability of genomic selection using these formulae.