Expected performance under repeated hybrid male cross and crisscross mating systems

The expected performance of two crossbreeding systems, the crisscross (CC) and repeated hybrid male cross (RHMC) was compared. These systems are of particular interest for less prolific species such as dairy cattle. Under the CC, the expected performance fluctuated over generations while under the RHMC, performance was constant after the F1 generation. After a few generations of crossing, the ratio of the average performance of the two alternative CCs to the performance under RHMC approached (6+4H)/ (6+3 H) where H was a coefficient indicating the degree of heterosis. When the parent breed difference (D) was small (10%) and heterosis (H) substantial (30%), the CC involving the first back cross to the superior sire breed was expected to exceed the RHMC by 6% after a few generations of crossing. The expected performance under CC and RHMC for various values of D and H was calculated.