Periodic rotational crosses. I. Breed and heterosis utilization

Periodic rotational crosses differ from conventional rotations by using sire breeds an unequal number of generations but in a regular sequence. Formulas for breed composition and heterosis in offspring from periodic rotations at equilibrium averaged over all generations of a cycle and for each generation of the cycle are presented. Coefficients of squares and products of breed differences and heterosis used to calculate inter-generational variance are also derived. Several specific periodic rotations utilizing a range of breed proportions were found to use from 70 to 95% as much heterosis as conventional rotations using the same number of breeds equally. Estimates of swine and cattle additive breed and heterosis effects taken from the literature were applied to the formulas. In both the swine and cattle examples, periodic rotations were found that equaled or exceeded the conventional rotations using the same number of breeds and also had lower inter-generational variance.