Efficient design of crossbreeding experiments

The efficiencies of different experimental configurations for estimating additive (A) and heterotic (H) effects in purebred and crossbred populations derived from two parent breeds are examined. Allocation of resources over six groups is considered: the two parental breeds, the F1, the F2 and the backcrosses to the two parental breeds. Additive and heterotic effects are best estimated by allocating resources to the two parental groups and F1 in the proportions 35%, 35%, 30% and for many practical situations, an experiment involving numbers in the region 250-300 is reasonable. If it is not possible to include all three groups, other combinations involving a subset of them and some of the other three groups can be used to give estimates of A and H. However, even the best of these alternatives requires over twice the resources to give the same precision as the optimal design and, further, these estimates may be correlated. Relatively modest reallocation of resources to the F2 to estimate or test for an epistatic effect (E) leads to a minor reduction in the precision of estimates of A and H while giving reasonable precision for the estimate of E. The inclusion of maternal effects in the model greatly reduces the efficiency of estimation of A and H. Where one of the breeds is introduced through the sire line only, optimal allocation gives roughly equal replication to the pure lines and F1 but about 63% of allocation is placed in equal amounts on the two backcrosses produced through crossing F1 dams with pure sires of both breeds. The relevance of these results to the planning of livestock crossbreeding trials, particularly those involving a local and an exotic or imported breed, is discussed.