Reducing inbreeding rates with a breeding circle: Theory and practice in Veluws Heideschaap.

Breeding circles allow genetic management in closed populations without pedigrees. In a breeding circle, breeding is split over sub-populations. Each sub-population receives breeding males from a single sub-population and supplies breeding males to one other sub-population. Donor-recipient combinations of sub-populations remain the same over time. Here, we derive inbreeding levels both mathematically and by computer simulation and compare them to actual inbreeding rates derived from DNA information in a real sheep population. In Veluws Heideschaap, a breeding circle has been in operation for over 30 years. Mathematically, starting with inbreeding levels and kinships set to zero, inbreeding rates per generation (ΔF) initially were 0.29%-0.47% within flocks but later converged to 0.18% in all flocks. When, more realistically, inbreeding levels at the start were high and kinship between flocks low, inbreeding levels immediately dropped to the kinship levels between flocks and rates more gradually converged to 0.18%. In computer simulations with overlapping generations, inbreeding levels and rates followed the same pattern, but converged to a lower ΔF of 0.12%. ΔF was determined in the real population with a 12 K SNP chip in recent generations. ΔF in the real population was 0.29%, based on markers to 0.41% per generation based on heterozygosity levels. This is two to three times the theoretically derived values. These increased rates in the real population are probably due to selection and/or the presence of dominant rams siring a disproportionate number of offspring. When these were simulated, ΔF agreed better: 0.35% for selection, 0.38% for dominant rams and 0.67% for both together. The realized inbreeding rates are a warning that in a real population inbreeding rates in a breeding circle can be higher than theoretically expected due to selection and dominant rams. Without a breeding circle, however, inbreeding rates would have been even higher.