COI Methodology
How OpenStudbook calculates the Coefficient of Inbreeding and what it means
Algorithm
OpenStudbook calculates the Coefficient of Inbreeding (COI) using Wright's (1922) Path Coefficient method — the same algorithm used by OFA, BrAVO, and most breed health programs worldwide.
The formula is:
F(I) = Σ_A [ (0.5)^(n₁ + n₂ + 1) × (1 + F_A) ] Where: A = each common ancestor of sire and dam n₁ = number of generations from sire to ancestor A n₂ = number of generations from dam to ancestor A F_A = inbreeding coefficient of ancestor A (recursive)
The calculation traverses up to 10 generations of ancestors stored in the OpenStudbook database. Each ancestor not recorded in the system is treated as an unrelated founder with F = 0.
AVK — Ancestor Loss Coefficient
The AVK (Ahnenverlustkoeffizient), also called Ancestor Loss Coefficient, is the ratio of distinct ancestors to the total number of ancestor positions in the pedigree chart. It measures how many times the same dog appears in multiple positions — a direct indicator of family concentration. AVK of 1.0 means every ancestor position is a different dog; lower values indicate more repeated ancestry.
Pedigree Completeness
Pedigree completeness reports what percentage of ancestor slots in the chart contain a recorded animal. A completeness of 40% means 60% of ancestors are unknown to the system. COI is always underestimated when completeness is low — unrecorded ancestors may be closely related.
Evidence Levels and COI Accuracy
OpenStudbook labels every parent link with a source level:
- papers — documented by a registry or kennel club
- breeder record — recorded by the breeder in their own books
- oral tradition — reported by breeders or community knowledge, not written
- assumed — inferred or uncertain
The current COI calculation treats all evidence levels equally — an assumed link contributes the same as a papers link. This is a known limitation. A pedigree built entirely on assumed links should be interpreted with caution even if the COI value appears precise.
Important Limitations
- Pedigree COI ≠ Genomic inbreeding. Pedigree-based COI and ROH-based genomic inbreeding (FROH) diverge, especially in populations with a long history of undocumented breeding. Genomic methods (Kardos et al. 2015; Forutan et al. 2018) are more accurate but require SNP genotyping data not currently available on this platform.
- Founders assumed unrelated. Animals without recorded parents are treated as unrelated founders. If the founding population was actually related, COI will be underestimated for all descendants.
- 10-generation cap. Ancestors beyond 10 generations are not counted. This introduces a small downward bias for deeply inbred lineages.
- Missing ancestors. Any ancestor not entered in OpenStudbook is invisible to the calculation. Low pedigree completeness is a warning sign.
- No pedigree error detection. Impossible parent dates (dam younger than offspring) are not automatically flagged. Users should verify critical pedigree entries.
Interpretation Scale
| COI Range | Equivalent to | Assessment |
|---|---|---|
| < 0.5% | Unrelated large population | Negligible |
| 0.5% – 6.25% | Below first-cousin level | Low |
| 6.25% – 12.5% | First-cousin mating | Moderate — monitor |
| 12.5% – 25% | Half-sibling mating | High — increased recessive risk |
| > 25% | Sibling or parent × offspring | Very high — significant health risk |
References
- Wright, S. (1922). Coefficients of inbreeding and relationship. American Naturalist, 56(645), 330–338.
- Falconer, D.S. & Mackay, T.F.C. (1996). Introduction to Quantitative Genetics, 4th ed. Longman.
- Malécot, G. (1948). Les mathématiques de l'hérédité. Masson et Cie, Paris.
- Kardos, M., Luikart, G. & Allendorf, F.W. (2015). Measuring individual inbreeding in the age of genomics: marker-based measures are better than pedigrees. Heredity, 115, 63–72.
- Forutan, M. et al. (2018). Inbreeding and runs of homozygosity before and after the genomic era in six cattle breeds. Genetics Selection Evolution, 50, 11.
- Janssens, S. & Vandenberghe, J. (2013). Pedigree errors in pet animal studbooks. Animal, 7(12), 1934–1941.
- Wiggans, G.R. et al. (1995). Implementation of an animal model for genetic evaluations of dairy cattle in the United States. Journal of Dairy Science, 78(suppl. 2), 1–24.