The accuracy of marker-assisted selection for quantitative traits within populations in linkage equilibrium

Using the concept of conditional coancestry, given observed markers, an explicit expression of the accuracy of marker-based selection is derived in situations of linkage equilibrium between markers and quantitative trait loci (QTL), for the general case of full-sib families nested within half-sib families. Such a selection scheme is rather inaccurate for moderate values of family sizes and QTL variance, and the accuracies predicted for linkage disequilibrium can never be reached. The result is used to predict the accuracy of marker-assisted combined selection (MACS) and is shown to agree with previous MACS results obtained by simulation of a best linear unbiased prediction animal model. Low gains in accuracy are generally to be expected compared to standard combined selection. The maximum gain, assuming infinite family size and all QTLs marked, is about 50%.