Compute Wright's coefficient of relatedness (r) and the offspring inbreeding coefficient (F) for common pedigree relationships. Flags matings that cross the first-cousin threshold (F > 0.0625).
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Standard pairwise relationships. For complex pedigrees with multiple shared ancestors, sum the r values from each independent path.
Default 0 for outbred founders. Scales r by (1 + fA).
Two paths of length 4 (X → parent → grandparent → parent → Y), each (0.5)^4 = 0.0625, summing to 0.125.
| Relationship | r | F (offspring) | Above 0.0625? |
|---|---|---|---|
| Parent ↔ offspring | 0.5000 | 0.2500 | Yes |
| Full siblings (same dam & sire) | 0.5000 | 0.2500 | Yes |
| Half siblings (one shared parent) | 0.2500 | 0.1250 | Yes |
| Uncle / aunt ↔ niece / nephew | 0.2500 | 0.1250 | Yes |
| Double first cousins (both parents are siblings) | 0.2500 | 0.1250 | Yes |
| First cousins | 0.1250 | 0.0625 | No |
| First cousins once removed | 0.0625 | 0.0313 | No |
| Second cousins | 0.0313 | 0.0156 | No |
| Unrelated (independent founders) | 0.0000 | 0.0000 | No |
When to use
Do not use for
Two unrelated mice from the same inbred background will have identical DNA at many loci but r = 0 between them in a fresh pedigree — the shared alleles are from strain fixation, not recent descent. When you switch from "unrelated outbred" founders to "two C57BL/6J founders" you must flip the inbred-strain toggle; otherwise the math is meaningless.
The first-cousin threshold only makes sense when you start from a non-inbred base. For maintained inbred strains, every sib-mating already has F = 0.25, and that is the entire point of the strain. Do not let the warning scare you away from sib-mating C57BL/6J — you *want* F = 1.
If X and Y share both a grandfather AND a grandmother (unusual, but happens in close lines), the r contributions from the two paths add: 2 (0.5)^4 = 0.125 for first cousins, 4 (0.5)^4 = 0.25 for double first cousins. A common mistake is to multiply the single-path value, which underestimates relatedness by an order of magnitude.
HS (Heterogeneous Stock) and Collaborative Cross mice have complex mosaic ancestries where r between two animals depends on the specific recombination events in their lineages. For those lines, use a genotyped-based kinship matrix (kinship2 or GEMMA), not the textbook path-coefficient values.
Implements Wright (1922) path coefficient method. r(X, Y) = Σ (0.5)^L (1 + f_A), summed over all paths through common ancestors A. F_offspring = r_parents / 2. Standard textbook values are precomputed for parent-offspring (0.5), full sib (0.5), half sib (0.25), first cousin (0.125), double first cousin (0.25), first cousin once removed (0.0625), second cousin (0.03125). Ancestor inbreeding f_A is applied as a (1 + f_A) scale factor on r. The warning threshold 0.0625 corresponds to the first-cousin F and is suppressed for maintained inbred strains where F 1 is by design.
Last validated 2026-04-07. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.
ConductScience Coefficient of Relatedness & Inbreeding Calculator (v1.5.0). ConductScience, Inc. 2026. Available at: https://conductscience.com/tools/coefficient-of-relatedness-calculator
Wright S. Coefficients of inbreeding and relationship. Am Nat. 1922;56:330-338.
Falconer DS, Mackay TFC. Introduction to Quantitative Genetics. 4th ed. Longman; 1996.
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 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.
For a pairwise relatedness between X and Y traced through a single common ancestor A:
r(X, Y) = (0.5)^L (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.
Logs every breeding pair with its full pedigree, computes r and F automatically, and warns before you cross the first-cousin threshold.
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