Inbreeding Coefficient Calculator (Pedigree & Population)
Calculate the inbreeding coefficient F with Wright’s path formula: pick the parents’ relationship, list each common ancestor with its generations to the sire and dam, or paste a whole pedigree. Also gives the recessive-disease risk, the loss of heterozygosity and how F builds up in a small population.
How it works
Wright: F = Σ over paths (½)^(n₁ + n₂ + 1) × (1 + F_A), n₁ and n₂ = generations from the sire and from the dam up to the common ancestor (n₁ + n₂ + 1 = individuals in the loop) · pedigree: F = ½ a(sire, dam) from the tabular additive-relationship matrix · risk of a recessive disorder = q²(1 − F) + qF · population: ΔF = 1 ÷ (2 Ne); F_t = 1 − (1 − ΔF)ᵗ · Ne = 4 N_m N_f ÷ (N_m + N_f)
An individual is inbred when its two copies of a gene can both be traced to a single copy in a shared ancestor. The inbreeding coefficient F is the probability of that identity by descent. Sewall Wright showed it can be read off a pedigree: follow each loop from one parent up to the common ancestor and down to the other, halve the probability at every step, and add a little more if the ancestor was itself inbred. This calculator offers three ways to apply that. You can pick a standard relationship, or list each common ancestor with the number of generations back to it from the sire and from the dam. You can also paste a whole pedigree as animal, sire and dam, and the tabular method then finds every loop for you, along with the relationship between the parents. In whole populations the same thing accumulates at a rate set by the effective number of breeders. That is why small herds, island species and closed breeds drift toward homozygosity even when no close matings are planned. The cost is inbreeding depression, the exposure of harmful recessive alleles, which grows roughly in proportion to F.
Worked example
First-cousin parents share two grandparents. Each grandparent is two generations back from both the sire and the dam, so each loop has 2 + 2 + 1 = 5 individuals and F = 2 × (½)⁵ = 0.0625. That is a 6.25% loss of heterozygosity and about a 7-fold rise in the risk of a recessive disorder whose allele has a 1% frequency. In pedigree mode, a mating of two half-siblings that share Sire1 gives F = ½ × 0.25 = 0.125. A closed herd with an effective size of 50 accumulates ΔF = 1% per generation and reaches F ≈ 0.096 after ten generations. Ten generations of full-sib mating would reach F ≈ 0.886.
Sources: Wright, S. (1922) Coefficients of inbreeding and relationship. American Naturalist 56: 330–338
Frequently asked questions
How do I count n in the path method?
List every individual on the loop: parent 1, the chain up to the common ancestor, the ancestor, and the chain down to parent 2 — the offspring itself is not counted. Full sibs share two parents: two paths of n = 3 each, F = 2 × (½)³ = 0.25.
Is F the same as the coefficient of relationship?
No — the coefficient of relationship between two individuals is roughly twice the F of their offspring (siblings are related by 0.5, their child has F = 0.25).
How do I enter common ancestors?
One line per path, as name: generations to the sire, generations to the dam, and optionally the ancestor’s own F. A grandparent of both parents is "2, 2". A full-sib mating is two lines of "1, 1", one for each shared parent. If the same ancestor is reached by two different routes, list each route on its own line.
What does the pedigree mode do?
It builds the additive relationship matrix with the tabular method, the same calculation breed-registry software uses. F of the last animal is half the relationship between its sire and dam. Animals that appear only as parents are taken as unrelated founders, so the result is only as deep as the pedigree you enter.
What F is considered high?
As a rough guide, below 0.016 is negligible and around 0.0625 (first cousins) is moderate. From 0.125 on, most species show noticeable inbreeding depression. Breeding and conservation programmes usually aim to keep the increase below 1% per generation.
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