Understanding Inbred
Pedigrees by Suzon
You just bought a purebred, papered animal. You’re
proud of that animal, those papers, that pedigree. You’re thinking
about breeding. Now you’ve got to do your homework. Now it’s time to
take that pedigree apart and understand what you’ve got in terms of
genetics, in terms of blood. It’s time to think about the genetics
you’re going to be producing when you cross that pedigree with
another. Questions begin to form in your mind. Should your program
include inbreeding or avoid such practices? But exactly what is
inbreeding and why is it important? And why should you pay attention
to it in your own breeding program?
Most man-developed purebred breeds are the product of
“inbreeding.” Inbreeding by definition is the mating of two animals
more closely related than the general population. In creating a breed,
breeders cross individuals with desirable characteristics to other
closely related individuals with those same characteristics to
increase the regularity with which those traits are passed on.
Eventually a distinct line of animals comes into being with set
characteristics that are passed on without fail. This is what is
called prepotency, the ability to stamp one or many traits on
offspring regularly, even offspring that is the result of crossing to
animals outside the breed. Prepotency most often (though not always)
comes from a high number of genes that are homozygous. Homozygosity is
what inbreeding is all about.
OK, so what is homozygosity anyway? Each parent of an individual
contributes one set of chromosomes to the genetic makeup of that
individual. These pairs are the map that defines all the
characteristics of that individual. Each chromosome is made up of
individual genes. The genes on one set of chromosomes match up with
genes at the same location on the other set. When the two genes are
identical they are said to be “homozygous,” and when they are
different, they are “heterozygous.” In purebred animals, the starting
assumption is that 50% of all an individual’s genes are homozygous.
Genes are either “dominant” or
“recessive.” In heterozygous pairs, if there is a dominant and a
recessive gene, the dominant gene is the one that is expressed. However,
if a gene pair is homozygous and dominant, you are given a 100% chance
of passing that trait on, no matter what. If you have a recessive
quality and you raise your percentage of homozygous genes in a breed
population, you raise your chances of pairing up those recessive genes,
allowing their qualities to be expressed. The rub, unfortunately, comes
in regard to these recessive genes. As you raise the number of
homozygous pairs, you raise your chances of matching recessive genes
whose traits are less than desirable (infertility, deformities,
immune-deficiencies, et cetera).
There are schools of thought that state any amount of
inbreeding is going to decrease the “vigor” of an individual. Other
schools argue that until total homozygosity has reached 65% there is
little danger. Breeders need to come to terms with how much
homozygosity they are willing to create in order to produce the stock
desired.
This is where
analyzing a pedigree comes in. There are many ways to do this.
The first to be discussed makes a
simple distinction between “inbred” and “line bred.” In this system
inbreeding is defined as the crossing of very closely related
individuals (such as half-brother/sister), with line breeding to mean
the crossing of less closely related individuals (for example, having
the same great-grandparent on both sides). The distinction is made
between the two with a simple formula of “generation numbers.”
Each generation is given a numerical value. The parents are given the
number 1, the grandparents 2, great-grandparents 3 and so on. Then for
any ancestors appearing in both the paternal and maternal sides of the
pedigree, the values are added and a total reached. If this number is
below 6, the individual is said to be inbred, if the number is between 6
and 9 then the individual is classified line bred, beyond 9 it is
considered to be effectively out crossed.
For Example:
| |
F1 |
F2 |
F3 |
F4 |
F5 |
|
Fedon |
Beaux Arts |
Orgueilleux |
Diviseur |
Quicko |
Gringalet |
| Italienne |
|
Vigoureuse |
Bourbacky |
| Mirza |
|
Irma |
Polo |
Bacchus |
| Hermione |
|
Etincelle |
Trompeur |
| Amande |
|
Tyrolienne |
Galois |
Questeur |
Ultra |
| Rola |
|
Tulipe |
Neptune |
| Jonquille |
|
Etincelle |
Trompeur |
Bacchus |
| Parfait |
|
Amande |
Millefore |
| Vervienne |
|
Hirondelle |
Arcol du Bourg |
Diviseur |
Quicko |
Gringalet |
| Italienne |
|
Vigoureuse |
Bourbacky |
| Mirza |
|
Irma |
Polo |
Bacchus |
| Hermione |
|
Etincelle |
Trompeur |
| Amande |
|
Utopie du Bourg |
Diviseur |
Quicko |
Gringalet |
| Italienne |
|
Vigoureuse |
Bourbacky |
| Mirza |
|
Oba |
Diviseur |
Quicko |
|
Vigoureuse |
|
Victoire |
Printemps |
| Jonquille |
This pedigree is fictitious,
but it is an excellent example of both an inbred and a line-bred
pedigree. In looking at the numbers we see that Fedon has Diviseur in
the third generation in both the paternal and maternal side. 3 + 3=6;
therefore this individual can be considered mildly “inbred.” If
Diviseur had appeared as a grand parent on both sides, then the
combined values would equal four and the degree of inbreeding would be
more acute. Then we see that Fedon has Etincelle in the third
generation on the paternal side and in the fourth generation on the
maternal side. 3 + 4=7, so Fedon is considered linebred to Etincelle.
However, we also see he has Jonquille in the fifth generation on both
sides. 5+5=10, which is greater than nine; so this pairing is
considered to be too far away to have any bearing on the pedigree.
Remember, inbreeding indicates a higher degree of homozygosity. This
method is good to quickly determine the general degree of inbreeding
in a pedigree, but it does not give us an accurate idea of the degree
of increased homozygosity that could be present in this individual.
For that, you will need the next method.
In his work, Systems of Breeding, Sewell Wright
developed a formula to determine the degree of homozygosity likely to be
present in an inbred individual. The number, which is calculated by this
formula, is called the coefficient of inbreeding. It is an estimate of
the percentage of homozygous pairs above and beyond the assumed 50% for
a purebred animal.
Fx=Σ (1/2)a+b
(1+Fa)
Wright’s Formula states that the coefficient of
inbreeding is equal to the sum of one-half raised to a power equal to
the number of generations from the sire to the common ancestor and back
to the dam times one plus the coefficient of inbreeding, if any, of the
common ancestor. In other words, if we start with the base 50%, Wrights
Formula tells us what percentage we must add to that to have an accurate
idea of the increased homozygosity of the individual. If an animal has a
coefficient of 25% it would mean that 25% of the REMAINING 50% (or 12.5%
of the total) are likely to be homozygous. So the total gene pairs that
are homozygous would be 50% + 12.5% or 62.5%.
However, if you’re sane, you forgot your algebra shortly after you
learned it. Fear not, there’s a slightly longer means of calculating
this formula by hand that requires only addition and the use of the
table below.
Calculating the co-efficient of inbreeding:
|
|
F1 |
F2 |
F3 |
F4 |
F5 |
F6 |
F7 |
|
F1 |
50% |
25% |
12.5% |
6.25% |
3.13% |
1.56% |
.78% |
|
F2 |
25% |
12.5% |
6.25% |
3.13% |
1.56% |
.78% |
.39% |
|
F3 |
12.5% |
6.25% |
3.13% |
1.56% |
.78% |
.39% |
.19% |
|
F4 |
6.25% |
3.13% |
1.56% |
.78% |
.39% |
.19% |
.095% |
|
F5 |
3.13% |
1.56% |
.78% |
.39% |
.19% |
.1% |
.05% |
|
F6 |
1.56% |
.78% |
.39% |
.19% |
.1% |
.05% |
.025% |
Each pedigree is divided into generations just as in
the previous method. The parents are expressed as generation F1, the
grandparents as F2, the great-grandparents as F3 et cetera. To use the
above chart, simply identify the common ancestor(s) in a pedigree. For
example: In the pedigree used as an example previously we find Diviseur
on the paternal side in the F3 generation. We also find him on the
maternal side twice in the F3 generation and once in F4. For each
combination (from paternal to maternal) we must calculate the
percentages and add them together (in other words, coefficients are
collective).
F3 + F3=3.13%
F3 + F3= 3.13%
F3 + F4=1.56%
So Diviseur has contributed 7.81% of the remaining 50% to the increased
homozygosity . But we cannot stop there. We also find Irma in the F3
generation of both the sire and dam. So to our total we must add another
3.13% to make 10.94% of the remaining 50%. But wait, we need to look a
little farther. We see that Etincelle is the mother of Irma. We have
already calculated Irma so there is no need to calculated Etincelle,
EXCEPT that Etincelle ALSO appears in a different context as the mother
of Tyrolienne. This makes her a separate factor and we must now
calculate for her as well. On the Paternal side, she appears in the F3
generation as the mother of Tyrolienne. On the maternal side she appears
in the F4 generation as the mother of Irma.
F3 + F4 = 1.56%
Our final calculation looks like this: Diviseur 7.81% + Irma 3.13% +
Etincelle 1.56%, for a grand total of 12.50% of the remaining 50% or
6.25% of the total. 50% + 6.25% =56.25% homozygous. Get it? Work through
several on your own and it will begin to be clear. The secret is to keep
a sharp eye for ALL the combinations. Remember you are only looking for
matches between the two sides of the pedigree; matches on the same side
are irrelevant. Work backwards from the individual whose pedigree it is.
Once you find a common ancestor, there is no need to also calculate for
all of his ancestors (which are also on the pedigree as many times as he
is) UNLESS they appear in a different relationship.
Finally we come to Percentage of Blood. This
calculation assumes that any individual is the product of the sum of its
genetic makeup. In this method, all generations in the pedigree together
are equal to 100%. So the parents would each contribute 50% of the total
genetic material, the grandparents 25% and so on. In an inbred pedigree
each incident of a given individual must be added together to give the
total of his contribution to the whole. This method differs from
Wright’s Formula in that the coefficient of inbreeding expresses the
percentage of homozygosity (the percentage of both genes in a pair being
alike) while percentage of blood only calculates the probability of one
of the genes of any given pair is present in the individual, passed down
from the ancestor in question.
Using the values in the following table will allow
you to quickly calculate the percentage of blood for any given ancestor.
When the ancestor only appears once then his contribution will be the
basic value for the generation in which he appears. However, if he
appears more than once, then you must add together all the values for
each and every time he appears in the pedigree.
Percentage of Blood:
|
F1 |
F2 |
F3 |
F4 |
F5 |
F6 |
F7 |
|
50% |
25% |
12.5% |
6.25% |
3.13% |
1.56% |
.78% |
Let’s look at our sample pedigree again. Beaux Arts
and Hirondelle, as parents, each contribute 50%. Each grandparent (Orgueilleux,
Tyrolienne, Arcol du Bourg and Utopie du Bourg) contributes 25%. Now
things start to need a bit of addition.
Diviseur appears 3 times in the F3 generation and
once in F4 which makes his total contribution 12.5% x 3 + 6.25% = 43.75%
(in other word, for any gene pair, there is a 43.75% chance that one of
the pair descended directly from Diviseur). Irma appears twice in the F3
generation, making her total contribution 25%. Etincelle appears once in
F3 and twice in F4 for a total of 25%. Quicko appears 3 times in the F4
generation for a contribution of 18.75%. You should be getting the
picture now. Finish the calculations for each individual on your own to
become an expert.
Now that you’ve looked at all that, you’re back to
square one. Now you must personally decide how much homozygosity you
want to deal with in your animals. Remember, homozygosity is not
necessarily bad. That’s how purebreds get to be uniform in the first
place. If an individual has perfect genes, it can, in theory, be 100%
homozygous without consequence...however, no individual is perfect.
Somewhere lurking in there are genes none of us want to know about. But
to decide whether inbreeding is beneficial or detrimental to your goals,
look at your stock, or the stock your stock came from. Is it well
conformed? Does it have any growth problems? Is its over-all health
good? Does it seem to have a degree of intelligence? Is it fertile? Have
a good life span? Is the size staying consistent or is it getting
smaller with each generation? Are you producing a few outstanding
individuals, but also a lot of culls? Do buyers shy away from your stock
because it’s inbred?
By now you may have an opinion on inbreeding. Perhaps
after looking at all the individuals that make up one animal you’ve
either decide inbreeding is too risky or produces stock you don’t want
and can’t sell. Perhaps you’ll find it works well for one or two
generations and then needs to be out crossed. Maybe you’re of the
opinion that a mild form of inbreeding (line breeding) is the way to go.
It could be that you’re dead set against it, or 100% for it. The point
is every breeding operation is as individual as it’s animals and what
works with the stock at one farm might not work at another. But I hope
I’ve given you a little food for thought and that it will help you find
what’s best for you and your animals.
***
