Reducing inbreeding rates with a breeding circle: Theory and practice in Veluws Heideschaap
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".