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
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
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.
Copyright 2000 C. A. Sharp. All rights
reserved. C.A. Sharp
is editor of the "Double Helix Network News", the quarterly
newsletter for those interested in genetics and hereditary disease in the
Australian Shepherd.
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