Coefficient of inbreeding (COI): how to calculate it and what counts as safe

What COI actually measures

The coefficient of inbreeding is not a vague sense of how closely related two cats are. It is a defined probability: pick any locus in this cat, and COI is the chance that its two alleles are copies of the same gene in the same shared ancestor.

That definition explains the risk. Harmful recessive mutations exist throughout every population, and carrying one copy usually causes nothing. Inbreeding raises the chance that sire and dam each pass down the same copy from the same ancestor, so the recessive becomes homozygous and expresses. What breeders then see is familiar: early embryonic resorption, stillbirths, low birth weights, poorer survival, weaker immunity, and reduced fertility in the next generation. Collectively that is inbreeding depression.

One point of vocabulary. COI describes the offspring, not the pair. When breeders say "this pairing has a COI of 12.5%", strictly they mean the kittens from that pairing would have a COI of 12.5%, which is derived from the relationship between the two parents. The table below and every calculator worth using report the figure on that basis.

Wright's path method: the formula and a worked check

The method comes down to three things: find the common ancestors, count the generations, and add up the paths. The formula is not hard. Not missing a path is, and that is why anything beyond three generations belongs in software.

The standard form is F(X) = Σ (1/2)^(n1 + n2 + 1) × (1 + F(A)). A is one common ancestor of the sire and dam, n1 is the number of generations from the sire back to A, n2 the number from the dam back to A, and F(A) is the coefficient of inbreeding of that ancestor itself (zero, and so the term becomes 1, if the ancestor is not itself inbred). Run it once for each independent path through each common ancestor and sum the results.

By hand: write out both pedigrees three to five generations deep, mark every cat that appears on both sides, count the generations on each side for each of them, substitute into the formula, and total the contributions. If one ancestor appears more than once on a side — as a maternal grandsire and again as a great-grandsire, say — each appearance is a separate path and each must be counted. That is where hand calculations go wrong most often.

A worked example you can check yourself. A full-sibling pairing has two common ancestors, the shared sire and the shared dam. Through the sire, n1 = n2 = 1, contributing (1/2)^3 = 12.5%. The dam contributes another 12.5% the same way. Total 25%, matching the table below — a useful way to verify that your procedure is right before you trust it on a real pedigree.

Two thresholds that matter: 12.5% and 25%

Read 12.5% as the point where the pairing needs a reason, and 25% as the point where it needs an exceptional one. Neither number is arbitrary: they are the values produced by half-sibling and full-sibling pairings, the two situations catteries actually run into.

Below 6.25% — first cousins and more distant — a single pairing adds very little homozygosity risk. Treat it as a normal mating decision and put your attention on health screening and how the two cats complement each other.

Between 6.25% and 12.5% is acceptable, but it is worth having breed-appropriate genetic screening results for both parents in hand, and worth recording weights and survival more closely in that litter. Problems in this band rarely look like defects; they look like a smaller-than-usual litter and slow gainers, both of which are easy to write off as bad luck.

Between 12.5% and 25%, proceed with caution. Half-sibling and grandparent pairings sit here. There is normally only one legitimate reason to make one: a planned single backcross to fix a specific, identified trait, with a decided plan for how the next generation brings the coefficient back down. Without that follow-up plan, you are simply accumulating load in your lines.

At 25% and above the risk is high. Offspring of full siblings or parent-offspring pairings are homozygous by descent at roughly a quarter of their loci on average; stillbirth, defect and immune-deficiency rates rise materially, and the litter pushes the inbreeding level of the whole cattery up in one step. Outside conservation programs with professional genetic support, it does not belong in a working cattery.

One measure matters more than any single pairing: the cumulative coefficient across your cats. You can hold every individual mating under 6% and still watch the average climb into dangerous territory over a few generations if all your breeding stock traces to one line. Reviewing pedigree overlap across the whole group tells you more about real risk than any one number does.

Line breeding vs inbreeding: intent, not a number

There is no numerical border between line breeding and inbreeding. They are the same mechanism at different intensities, practised differently. The real difference is that line breeding has a named target trait, a selection standard, and a route back out; inbreeding often just means "these are the two cats I have".

Line breeding concentrates on one proven ancestor, letting that cat recur in the pedigree while keeping the coefficient of any individual mating relatively low — commonly under 10% — and culling hard from the breeding program each generation. It depends entirely on that ancestor being genuinely proven: not merely good-looking, but with documented health screening and a record of how its offspring turned out. Line breeding on an unproven cat replicates and amplifies whatever unknown recessives it carries.

Inbreeding puts two very close relatives together — full siblings, parent and offspring — and reaches 25% in a single step. It has legitimate genetic uses, mainly exposing recessives quickly and fixing traits fast, but the cost is health risk across the whole litter and the responsibility of dealing appropriately with affected individuals. That is not a cost structure commercial breeding should be carrying.

The practical test is blunt. If you cannot name the specific trait this mating is meant to fix, and you cannot name the outcross you intend to use in the next generation to bring the coefficient down, then whatever the number says, this is not line breeding.

Five ways to use COI in day-to-day pairing decisions

COI earns its keep before the mating, not after the kittens arrive. These five habits are what turn it from a retrospective explanation into an actual input.

None of this replaces veterinary and genetic advice. Which DNA panels apply to your breed, and how to read a result, are questions for your veterinarian or a genetics service.

• Calculate before the breeding plan is fixed. Run every candidate combination, put the coefficients next to the health screening results, and choose from that comparison rather than from availability.
• Ask for three generations when importing. Two generations of pedigree will not reveal a shared ancestor; three is the minimum needed to judge whether a new cat can be paired with what you already have.
• Verify that same-named ancestors are the same cat. Where similar names appear in a pedigree, confirm identity by registration number or cattery prefix. One misidentification distorts the entire result.
• Write the coefficient into the breeding record. Log the figure and the pedigree it was based on at the time of each mating, so that reviewing the direction of your lines a few generations later rests on data instead of recall.
• Review the group, not just the mating. Once a year, look at pedigree overlap across all your breeding cats and plan when an outcross goes in — rather than reacting after litter sizes start dropping.

Calculating in practice: relationship lookup or full pedigree

For the common relationships within three generations, the table above is enough — look the pairing up and you have the number. Beyond three generations, or wherever the same cat recurs in different positions, hand enumeration will miss paths, and the question is only how many.

If your cats are already recorded in FanMeowy Cattery Manager (free on the App Store, core features included), the coefficient comes from the pedigree you already have: the app computes COI between any two cats in the cattery and flags the risk band when you set up a breeding plan, so you are not rebuilding a family tree by hand for each candidate pairing.

Whatever you calculate with, remember what the output is. COI is a probability, not a verdict on a litter, and it is only as good as the pedigree depth and identity accuracy behind it. A number produced from two generations of an unverified pedigree is not a safety margin.