Breeder's Notebook: Do the Math
First published in Dog World, June 2004
by D. Caroline Coile, Ph.D.
You see it all the time; ads for litters touting multiple relationships to a breed great. Litter A boasts “Sir Pantsalot appears 10 times in his pedigree” while litter B claims “Sir Pantsalot is behind his dam 14 times.” How can you compare such claims?
Given this sort of information, you can't. Counting appearances in a pedigree isn't enough. When in the pedigree does Sir Pantsalot appear? If the 10 appearances are all 10 generations back, his influence will be very small. And where does he appear? If all 14 appearances are behind the dam, and none behind the sire, then this litter is not inbred on the great Sir Pantsalot at all. Inbreeding requires that a common ancestor be behind both the sire and dam.
Simply counting appearances isn't informative; nor is classifying litters as “outcrossed,” “inbred,” “really inbred,” and “really, really inbred” satisfactory. There's a better way. You can quantify the degree of inbreeding. Wright's Coefficient of Inbreeding gives the probability that two alleles (alternate forms of a gene) are identical by descent. That is, the same allele is inherited through both the sire and dam. It's a function of the how many common ancestors are behind a litter's sire and dam, and how closely related those ancestors are to the litter in question.
Here's where a lot of people get mixed up. A common ancestor must behind both parents. No matter how many times the same ancestor appears behind just one parent, it doesn't make the target litter inbred. Breeding an inbred male to an inbred female won't produce inbred progeny unless the male and female share a common ancestor. To take it to extremes, breeding a dog of one breed (which can be considered an inbred strain of dogs) to a dog of another breed produces a litter of non-inbred mixed breeds. However, breeding two mixed-breed littermates together produces inbred mixed-breeds.
To get a true feel for how the COI works, take the time to compute a few by hand. It's easy as long as you're just doing a few generations. Start with the simple case of Boscoe, a dog from a half brother-sister mating. Both Boscoe's sire and dam are in turn sired by the great stud Barky. Instead of using the traditional pedigree, redraw it without the dogs that aren't common ancestors (that is, don't appear behind both sire and dam) and with the common ancestor's name (Barky) appearing only once.
What we want to know is the probability of Boscoe inheriting the identical allele coming down from Barky through (or by way of) both Bowser and Buffy. Assuming Barky is a heterozygote, that is, has both an A and a allele, there is a 50% chance that he will pass the same allele (either A or a) to both Bowser and Buffy. There is also a 50% chance that Bowser will pass on whichever allele he got from Barky to Boscoe, and a 50% chance Buffy will pass on whichever allele she got from Barky to Boscoe.
Before your head starts reeling, all you have to do is multiply these probabilities by counting the number of individuals (excluding Boscoe) in the simplified pedigree you drew and multiply 0.5 times itself that many times; in other words, with three individuals, you would multiply 0.5 x 0.5 x 0.5, which would equal 12.5 percent."
Pedigrees are seldom this simple. What if Bertha was a Barky daughter? You would have to do a separate simplified pedigree that included her relationship to Barky and Boscoe, and add the COI from it to the COI from the original simplified pedigree. So you would have four individual in that simplified pedigree for a 6.25% probability, added to the 12.5% you already had, for a total of 18.75%.
What if Barky were himself inbred? You would have to figure out his inbreeding coefficient first—let's say it's 10%, or 0.10. You add that to 1.0 and multiply the sum by Boscoe's COI due to Barky. So now you multiply 18.75% (or 0.1875) X (1 + 0.10) to get a COI of 0.20625, or roughly 21 percent.
The more generations you consider, the more likely you are to find shared ancestors with complicated lines of relationship, and the more likely you are to go back to just saying “really inbred.” Fear not. Computer programs will rescue you from the mire of calculations. All you have to do is type in the pedigree and voila! Instant COI! Most of the pedigree programs available will calculate COIs for you, but check before you buy.
Because COI tends to increase with more generations, when describing a COI it should be in context of generations included. For example, Bowser has a COI of 0.21 in a two generation pedigree.
Now you have a number. What will you do with it? At one time it was almost fashionable to have “realy inbred” dogs. Now more breeders attempt to keep COIs as low as possible because of evidence that high COIs decrease hardiness. How low? That part is open to debate. Some advocate keeping it below 0.10 in 10 generations, which is a challenge in most breeds. Before contemplating a breeding or buying a puppy, calculate the COI and consider it in your decision as strongly as you would any other important trait.