Playing COI: Using inbreeding Coefficients
First printed in Double Helix Network News, Spring 2000

by C.A. Sharp

FX  =  å [ {½) n1+n2+1 (1 + FA)]

Breeding dogs is a numbers game. Even though math problems are the last thing on your mind, what you are doing when you breed is calculating the best odds for getting a desired result. But a little applied mathematics, in the form of a coefficient of inbreeding (COI) can be helpful and even enlightening. Now that technology allows even the mathematically challenged to put them to use, they are a tool that should be applied by every breeder.

Research in the fields of genetics, immunology, and veterinary medicine, is turning up more and more information indicating that high levels of inbreeding can have deleterious effects on health. Inbreeding depression, a complex of behavioral and physical reproductive problems, have long been recognized. Inbreeding can increase the frequency of a disease in a population, sometimes quite rapidly. Inbreeding leads to increased incidence of immune-mediated disease and cancer.

But, all pure breeds of domestic animals are inbred. (Keep in mind that to a scientist “inbreeding” means the breeding of related animals, which would include what we call “linebreeding.”) But how much is too much? Without it, the breeds could never have been developed and would not breed true to type.

However, almost all breeds of purebred dog already have well-established type. There is no mistaking a
Chihuahua for a St. Bernard. Or even a Greyhound from a Whippet. Given this, breeders would be well advised to retain as much genetic diversity as possible within the existing breed population in order to avoid or reduce such unwanted health problems as those mentioned above. Along with screening and maintaining detailed health records, another tool available to you is the Coefficient of Inbreeding. Track COIs on your breeding stock. Calculate them on proposed matings, with an eye to keeping the numbers low if they already are or lowering them where possible.

So, how is this done? Via a formula called Wright’s Coefficient of Inbreeding. It appears directly beneath the title of this article. Before you drop this publication in a math-phobic panic attack, be advised that the only practical way to use it is with a computer. For those who enjoy math or want more detailed background, there is an excellent discussion of applying the formula hands-on in Malcolm Willis’ Genetics of the Dog, pages 320-326. For the rest of you, there are other options.

The easiest way to incorporate COIs into your strategy is to purchase a pedigree database program that will calculate them. CompuPed (which I use), Breeders Standard and Breedmate all have functions for calculating COIs. Other breeder software may offer this feature as well. You will also need a comprehensive pedigree database, including as many of the ancestors of present-day dogs as possible. Some vendors can provide starter databases for various breeds.

Now that we’ve soothed the math anxiety, what exactly is a COI? It is the probability that a homozygous gene pair will be identical by descent from both sides of a pedigree. In the formula, FX is your dog’s COI, FA is that of the ancestor common to both sides of the pedigree. n1 and n2 are the numbers of generations on each side between your dog and that ancestor. In other words, if your dog Flux is a double-grandson of FAbulous it tells you how likely it is you can get exactly the same gene passed down to Flux through each of his parents. (In case you are wondering, the probability is 12.5%.) If FAbulous happened to be a Collie Eye Anomaly carrier, Flux would have a 12.5%, or a one in eight chance, of having CEA thanks to Old Granddad. Total actual risk would be dependent on whether there were any other carrier or affected individuals in the remainder of the pedigree, but whatever that might be, it is evident that FAbulous provided a significant part of it.

Multiply this times a dog’s 80-100K genes and it is apparent how quickly you can concentrate some genes—both good and bad—while others drift out of your kennel’s gene puddle. Multiply that by all the people breeding a particular kind of dog and it can have remarkable effects on the breed’s gene pool, especially if large numbers of them are making similar mating selections via the use of popular sires or heavy linebreeding on the product of successful kennels.

COIs can be calculated on any number of generations, the simple two-generation example of Flux and FAbulous was useful to make a point (and keep the math simple) but few purebred dogs have only one common ancestor on both sides of the pedigree and the more generations that can be included in the calculation the more common ancestors will be found and the more accurate the COI will be. The typical three to five generation pedigrees in common use are often insufficient. In my breed, the Australian Shepherd, five generations may appear ot be loosely linebred or even out-crossed, but pedigrees extended to 10 generations, especially in show lines, will prove this is often not the case.

But how far should you go? Even with a computer the complexity of reviewing many thousands of ancestors and calculating large numbers of common ancestors can take hours on the average PC. Since calculating all available information may not be practical, how do you know where to draw the line?

How many generations to use will vary from breed to breed, depending on how many founders a breed had, how populous the breed is, whether there have been genetic bottlenecks, whether “new blood” has been introduced, and how long the breed has been in existence.

Some breeds descend from a very few individuals, who are it’s genetic founders. Samoyeds, for example, go back to about 20 dogs. Tracing everyone back to the founders in such a situation will result in COIs that may vary only by tiny fractions of a percent. Therefore selecting some intermediate number of generations for the calculation is the best option, unless the breed is very recent in origin and only a handful of generations away from those few founders.

For breeds with large populations, sufficient generations should be calculated that the results will have leveled out, so only small numerical differences will be achieved by pushing the calculation back a generation further. For example, if a one-generation COI is calculated on good old Flux, the COI would be 0%. You are considering only his sire and dam who, obviously, aren’t going to be the same dog. Extending it far enough to include FAbulous (two generations) produced the 12.5% we saw earlier. What if the sire’s dam was one of FAbulous.’s daughters? Going into the third generation would tell us the COI was 18.75%. If the dam’s dam was out of FAbulous.’s full brother (linebreeding on the cross that produced FAbulous.), we go back to the 4th generation to include FAbulous’s parents behind his brother the COI becomes 23.4%.

With each additional generation the COI will tend to climb but at some point the increase from one generation to the next will be negligible. COIs should be calculated over sufficient generations so that most current dogs will be at this point.

If breed population is small, preserving its remaining genetic diversity is vital. Calculate COI’s back far enough to reach founders and then, working together, breeders can use them to equalizing representation of those founders in the over-all breed population. For example, if a breed had ten founders but most present individuals descended only from three of them, much of the genetic potential of the breed’s gene pool is at risk of being lost as genes from the less-represented founders fail to get passed down by their fewer descendents. Equalizing founder representation by giving breeding preference to individuals that do not descend from the most-represented founders and in avoiding crossing their descendents to each other will help preserve those under-represented genes. Since low-population breeds are at greater risk from genetic disease, due to “no place to go,” maximizing genetic potential in this manner may be the line between extinction and survival. In fact, it is the very technique used by zoos and others who are trying to preserve endangered species in captivity.

Some breeds have suffered genetic bottlenecks. By the end of World War II, many European breeds, including the English Mastiff and French Poodle, were reduced to a handful of survivors. Today these breeds trace their pedigrees back to those dogs, who are therefore effective founders. Even though known pedigree exists behind them, there is little point in extending a COI calculation them. The only reason would be to determine how inbred those effective founders were themselves and what their inter-relationships might have been.

Sometimes a breed’s gene pool may receive infusions of new genetic material. Some European registries allow registration of decendants of unpapered dogs brought in from the country of breed origin, such as a desert-bred Saluqi from
Arabia. Occasionally, even such conservative registries as the AKC will, at a parent club’s request, open a registry to new, undocumented, individuals. This happened about 20 years ago when a few Basenjis were imported from Africa. Obviously, such “new blood” could have significant effects on the average COIs in a kennel or even throughout the breed, depending on how many dogs are added and how often. How much and with whom they are used in breeding will determine their contribution of new genes..

If a breed is long-established and has pedigree documentation going back tens of generations without bottlenecks, you would need a big mainframe computer to compute a full COI in a reasonable amount of time. Since most of us operate PCs and we don’t want to leave them doing nothing but crunching COI numbers for hours on end, some more-or-less arbitrary number of generations must be selected beyond the “leveling-off” point mentioned earlier..

In calculating Australian Shepherd COIs, I use 10 generations because beyond that point my software is known to slow down considerably. A secondary reason is because Aussie pedigrees are rarely complete to ten generations due to the breed’s recent origin. By running 10 generatrions, I get pretty much all there is to get for that particular breed.

Once you have a PC, software that does COIs, a good breed database, and sufficient knowledge of your breed’s history to decide how many generations to use in your calculations, it’s time to put it all to work.

First run COIs on all your own dogs. Since few dogs will have such diverse pedigrees that only one common ancestor will be found, the COI will be a reflection of all the ancestors common to both sides of the pedigree. In order to have a handle on what the numbers you will get mean, in terms of level of inbreeding, it is helpful to keep in mind what various percentages would be equivalent to, if there were only one common ancestor or pair of ancestors in the pedigree:

25.00% - parent/offspring or full brother/sister cross
12.50% - half brother/sister, grandparent/grandpup, or double first cousins crosses
9.75% - great uncle or aunt/great niece or nephew cross
6.25% - first cousins

Think back to our pal Flux and his 23.4% COI. He is very nearly the equivalent of a parent/offspring mating. If you bred him to his sister, given their already high level of inbreeding, the pups’ COI would be 44.4%. Anybody glancing at Flux’s pedigree would probably consider him inbred, and certainly heavily linebred. But it is possible to achieve high COIs without this kind of close breeding. Linebreeding on dogs several generations back can result in elevated numbers if the dogs appear frequently enough on both sides of the pedigree. While this inbred cross of FAbulous’s grandpups might serve the breeder’s short-term goals, it significantly increases the risk of turning up something unpleasant. And so would a linebreeding with a similar COI.

What’s a breeder to do? We are breeding dogs not numbers and many factors other than COIs need to be considered when planning a mating. Even so, whenever possible you should try to achieve COIs in the puppies that are at or below the average COI of the two parents. Thus, if the sire had a COI of 20% and the dam was 10%, you would want the pups’ COI to be 15% or lower. If a kennel or line’s average COIs have crept dangerously high, serious consideration should be given to avoiding further crosses to dogs descending from the most frequently seen names in the pedigrees and, as much as possible, to finding mates which are significant outcrosses.

The nice thing about COIs is that they can’t be a secret. If you have a dog’s pedigree, you can calculate the COI. In the privacy of your own computer station, you can figure out the COIs of all the prominent dogs in your breed. You can play with hypothetical matings between any two dogs you choose and see what the pups’ COI would be.

For a real-life example, my dog Tank is the result of a father/daughter mating and has a COI of 40.9%. No doubt about it, he’s inbred. Using my pedigree software I can set up all kinds of hypothetical social activity for the old boy and see where the COI goes. He is heavily linebred on a particular stud dog of a number of years back. However, that dog is not common in most show-line Australian Shepherd pedigrees, so I can easily find mates—even those with fairly high COIs themselves—who will give him puppies with much lower COIs. If I’m really determined I can hypothetically mate him to working-line Aussie bitches and in many cases I will drop the COI to less than 5%. All of this without having to risk finding out what any of the owners of those bitches (especially the working breeders!) think of the idea of poor old Tank having a fling with their girls.

Getting reliable hereditary disease history on your dog’s ancestors and on his potential mates can be difficult to impossible. If you know your dog has family background for a disease and there is no available testing to let you know whether he might be carrying the genes for it, breeding for low COIs may reduce your risk of producing the problem. With a lower COI you are lowering the probability of doubling up on those unwanted genes you know are back there somewhere.

Coefficients of inbreeding are an important tool to apply to your breeding program. Whatever the needs of your kennel or your breed, COIs provide you with a vital bit of information that should be part of your decision-making process.

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