Prediction of inbreeding in commercial females maintained by rotational mating with partially isolated sire lines

The solution to the inbreeding problem for livestock breeds in commercial use is often complicated by hierarchical population structure, in which favourable genes are accumulated in the upper level of the hierarchy (breeding population) by artificial selection and the genetic progress achieved is transferred to the lower level through migration of males. When the breeding population is subdivided into several isolated lines, rotational mating with the lines has been shown to be quite an effective system to reduce the short‐ and long‐term inbreeding of commercial females in the lower level. In practice, however, some amount of migration should be allowed among the lines to reduce the rate of inbreeding in each line. In this study, we developed the recurrence equation for the inbreeding coefficient of the commercial females maintained by the rotational mating with partially isolated lines. Numerical computations were carried out to evaluate the effect of the migration on the efficiency of the rotational mating. It was shown that even with a small amount of migration among the lines, the inbreeding of commercial females is substantially inflated. However, when four or five lines are available, the inbreeding coefficient of commercial females can be suppressed to an acceptable level, irrespective of the effective size of line and the migration rate. Application of the mating system to the population of Japanese Black cattle was also examined.