What a coefficient of inbreeding actually tells you

Almost everything else attached to a pedigree is a record of something that happened. A registration, a health test, a date of birth, a name. The coefficient of inbreeding is not. It is an estimate of a probability, produced by a piece of arithmetic, and it is the only figure on the page that changes depending on how the sum was set up.

That is not a criticism of it. Used properly it is one of the more useful things a breeder can look at before a mating, and one of the few genuinely comparative numbers a buyer can ask for. But it is quoted far more often than it is explained, and a percentage handed over without its method attached tells you very little.

What the number is

The coefficient of inbreeding — usually written COI, and originally Wright's coefficient — is the probability that, at any given point in an animal's genome, the two copies it carries are identical by descent. That is, that they are not merely the same in effect, but are literally the same piece of DNA, inherited twice over from a single common ancestor standing on both sides of the pedigree.

The classical figures follow from that definition. A mating between full siblings, or between a parent and its offspring, produces a COI of 25 per cent. Half-siblings, 12.5. First cousins, 6.25. Those numbers are exact, and they are also, in a slightly awkward way, hypothetical: they describe what happens when the animals concerned are otherwise unrelated. In a closed studbook, they almost never are.

Why this matters is the whole of the rest of this piece.

The depth problem

Every COI is calculated over a defined number of generations, and the calculator assumes that the animals at the far edge of that window are unrelated to each other. They are, of course, no such thing. They simply lie beyond where the sum was told to stop.

The practical consequence is severe. In many pedigree breeds there are no repeated ancestors at all in the first five generations, so a five-generation COI comes out near zero. Go back ten and the same pedigree may show a materially higher figure. Go back twenty or thirty, into the era when the studbook was a few dozen animals, and the same animal is heavily inbred by any measure. Nothing about the dog or the pony has changed. Only the window did.

So "his COI is 1.2 per cent" is not a statement about an animal. It is a statement about an animal and a method, and without the second half it cannot be compared with anything. Two breeders quoting figures calculated over different depths are not disagreeing; they are answering different questions.

The Kennel Club's own calculators, on Mate Select, sidestep this by using all the pedigree records held on its database rather than a fixed five or ten generations, which is why a Mate Select figure for a registered dog will often look higher than a number a breeder has worked out from the paper pedigree in a drawer. Both can be honestly arrived at. Only one of them is comparable to the breed average published alongside it.

That is the first question worth asking, and it is not an aggressive one: over how many generations, and from which database?

What it is for

The number is not meant to be read on its own. It is meant to be read against the breed.

The Kennel Club publishes an average COI for each pedigree breed, recalculated annually from the dogs registered in the preceding year, and its guidance to breeders is straightforward: where possible, produce puppies with a coefficient at or below the breed average, and ideally as low as you can manage. That is a sound instruction, and it is the correct use of the figure — as a comparator within a population, not as a grade out of a hundred.

It follows that a COI means nothing across breeds. A figure that would be unremarkable in a numerically small native breed would be a warning in a breed registering tens of thousands a year, because the two populations start from entirely different places. Comparing them is like comparing two temperatures without saying which scale.

The underlying concern is real and well evidenced. Higher inbreeding is associated, at the population level, with smaller litters, reduced fertility, weaker immune function and shorter lives — the cluster of effects usually gathered under the heading of inbreeding depression. None of that is speculative. What is easy to get wrong is the direction of the inference.

What it is not

It is not a health test. A health test asks a specific question about a specific animal and returns an answer about that animal, as I set out in how to read a health-testing certificate. A COI does no such thing. It is a statement of risk across a distribution. A puppy with a low coefficient can still inherit two copies of a recessive and be affected by it; a puppy with a high one may live seventeen unremarkable years. The number moves the odds. It does not settle the case.

It is not a verdict on the breeder. This is worth saying plainly, because the figure is increasingly used as a stick. A slightly elevated coefficient can be the result of a considered decision — to use a stallion or a stud dog who brings something the population badly needs, to keep a bloodline in the book that would otherwise vanish, to accept a known and manageable cost in exchange for something else. In the numerically small breeds we spend most of our time on, that trade is made deliberately and often, for reasons I have written about at length in why rare breeds don't breed the carriers out. A breeder who can explain the trade has thought about it. A breeder who cannot is a different matter.

It is not a measurement. It is a prediction from a pedigree, and pedigrees predict imperfectly, because inheritance is a lottery each time. Two full siblings have precisely the same pedigree and therefore precisely the same COI, and they do not carry the same genome. Genomic measures — which look at actual runs of homozygosity in the DNA rather than inferring them from ancestry — will separate those two siblings, and can differ noticeably from the pedigree estimate in either direction. Where such testing is available and affordable it is the better instrument. It is also, at present, far from universal, which is why the pedigree calculation remains the working tool.

And it is not an absolute. Because the calculator resets the clock at the edge of the records, every COI you will ever see measures inbreeding accumulated since the studbook opened, not the total relatedness of the animals concerned. Every closed registry is, viewed from far enough away, a small and related population. The figure is a measure of drift within that population, not a measure of distance from the wild.

Horses and ponies

The arithmetic is identical, but the record-keeping is often better. Equine studbooks tend to be older, deeper and more consistently maintained than the canine equivalents, and several of the native breed societies hold pedigree data in Grassroots databases that members can search directly — the Fell Pony Society, for instance, points members to its Grassroots records for exactly that purpose.

Depth is a double-edged advantage. A deeper studbook produces a more honest coefficient, and a more honest coefficient in a native breed with a few hundred registrations a year is usually a higher one. That is not the breed doing badly. It is the arithmetic finally telling the truth about a small population, which is precisely the thing the societies are managing rather than pretending away. As with why heritage breeds are worth building for, the honest number is the one you can plan against.

If you are buying

Ask for the coefficient. Most breeders working seriously will have it to hand and many will offer it before you ask.

Then ask the two questions that make it mean something. First: over what depth, and from which database — so you know whether the figure can be compared with the breed average at all. Second, and more revealing: what was the breed average, and what were you aiming for? The answer to that is a small window into how the mating was planned. "Below breed average, and I chose this dog partly for that" is a considered reply. So, in a rare breed, is "slightly above, and here is why I judged it worth it." What should give you pause is a number produced with no idea what it is being compared to, or a breeder who has clearly never looked.

If the figure is recorded anywhere, keep it with the animal rather than in a folder that gets lost at the point of sale. That is one of the things our free health record exists to hold, and it costs nothing to use.

The last word on the number

A coefficient of inbreeding is a good instrument pointed at a genuine problem, and it is routinely asked to do work it cannot do. It cannot tell you whether an individual animal is healthy. It cannot be compared across breeds, or across methods, and most of the arguments about it are really arguments between two people using different windows.

What it can do is tell you, within a breed, roughly where a proposed mating sits against everything else that breed is doing — and, more usefully than that, give you something specific to ask a breeder about. The number is worth having. The conversation it opens is worth more.

— Rene