Coefficient of Relatedness & Inbreeding Calculator

What r and F actually mean

r is the probability that, at a random locus, two individuals share an allele *by descent* — that is, inherited from the same ancestral copy, not just the same sequence. Two completely unrelated mice might share a lot of allele sequences by chance (they are both mice!), but r counts only the shared-by-descent fraction. r = 0.5 means 50% of loci are identical by descent; r = 0.125 means 12.5% (first cousins).

F is the probability that, at a random locus, an individual is *homozygous by descent* — that both of its alleles trace back to the same ancestral copy in its pedigree. For the offspring of two parents with relatedness r, F_offspring = r / 2. That is why full-sib mating (r = 0.5) gives F = 0.25: a quarter of the offspring's genome is homozygous by descent.

Inbreeding depression — reduced litter size, smaller pups, lower fertility — starts to become detectable around F $\approx$ 0.0625 in outbred stocks and gets progressively worse as F climbs. The NIH Guide for the Care and Use of Laboratory Animals treats the first-cousin threshold (F = 0.0625) as the practical boundary. Maintained inbred strains operate well above this by design and use the homozygosity as the whole point of the strain.

Wright's path coefficient method

For a pairwise relatedness between X and Y traced through a single common ancestor A:

r(X, Y) = (0.5)^L $\times$ (1 + f_A)

where L is the number of links (generation steps) in the path X → A → Y, and f_A is the inbreeding coefficient of the ancestor itself.

Full sibs share *two* common ancestors — both the dam and the sire. Each path is length 2 (X ← parent → Y), contributing (0.5)^2 = 0.25. Two paths sum to 0.5.

First cousins share one pair of grandparents. Each path is length 4 (X ← parent ← grandparent → parent → Y), contributing (0.5)^4 = 0.0625. Two paths (one through each grandparent) sum to 0.125.

If the common ancestor is itself inbred, the two alleles passed down the two sides of the pedigree are more likely to already be identical. This inflates r by a factor of (1 + f_A). For non-inbred founders, f_A = 0 and the correction vanishes — the standard textbook values assume this.