Breeding dogs is a numbers game.

Even though it may be the last thing on our mind, what we are doing when we 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 and is a tool that can be used 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 behavioural 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.

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, breeds such as the Cesky Terrier would never have been developed and would not breed true to type. 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, the Coefficient of Inbreeding is a valuable tool. You can track COIs on your breeding stock and calculate them on proposed matings, with an eye to keeping the numbers as low as possible.

This is done via a formula called Wright’s Coefficient of Inbreeding.

FX = Sum [ {½) n1+n2+1 (1 + FA)]

Before you close this window in a maths-phobic panic attack don’t worry, because the only practical way to use the formula is with a computer. The easiest way to incorporate COIs into your strategy is to purchase a pedigree database program that will calculate them. Most programs incorporate this facility. You will also need a comprehensive pedigree database, including as many of the ancestors of present-day dogs as possible. Alternatively the Cesky Terrier Archive gives COIs for each dog, and also has the facility to calculate figures for test matings.

So 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, it tells you how likely it is you can get exactly the same gene passed down to your dog through each of his parents. Multiply this by a dog’s 80-100,000 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 pool. Multiply that by all the people breeding Cesky Terriers and it can have remarkable effects on the breed’s gene pool, especially if many of them are making similar mating selections via the use of popular sires or heavy linebreeding to successful show dogs.

COIs can be calculated on any number of generations, 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 the Cesky Terrier, five generations may appear to be loosely linebred or even out-crossed, but pedigrees extended to 10 generations, will prove this is never the case.

Even with a computer the complexity of 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 its genetic founders. Cesky Terriers go back to just three founding dogs – two Sealyhams and a Scottie, with another Sealyham introduced 35 years later. 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 (10 is the most commonly used)for the calculation is the best option.

If a breed population is small, preserving its remaining genetic diversity is vital. 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.

It is often said that the ideal COI is one that is less than 6.25% (ie. equivalent to the mating of first cousins). Many Cesky Terrier COIs are in the 60%+ range.

So what can we do? We are breeding dogs, not numbers, and many factors other than COIs need to be considered when planning a litter. Even so, whenever possible we 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 80% and the dam was 60%, we would want the pups’ COI to be 70% or lower. Serious consideration should be given to avoiding further crosses to dogs descending from the most frequently seen names in the pedigree and, as much as possible, to finding mates which are significant outcrosses.

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