The Chase Magazine
February, 1991
Page Two
Probabilities in Breeding and InBreeding
Ky W. White
2306 Jackson Lane
League City, TX 77573
I have written concerning dog breeding and some of the basic principles of genetics. This article came
about from a conversation with my father, O.M. “Hop” White,” about the benefits of maintaining a tight line
breeding. My father has been raising foxhounds in Texas for over forty years and all of his sons were
raised with pedigrees in hand.
A basic understanding of probabilities is essential to determine the chance of success in any breeding
program. This article will outline some basic principles and show how the chances of success can be
increased by judicious inbreeding and linebreeding. I have used the characteristics for show dogs in this
article, but it is just as important for those who breed RUNNING DOGS. You can substitute sense of smell
and stamina for coat color. We should all realize that we are not going to get good dogs without a firm
foundation in the dog’s ancestry. Let’s start with the basics.
The sex of the puppy is entirely determined by the sire. He carries both the X and the Y chromosomes
and will contribute one or the other to each ovum which will develop into a puppy. The dam contributes
only X chromosomes, one per ovum. If the spermatozoa with the X chromosome reaches the ovum first, it
will have a X-X combination and the puppy will be a bitch. If it is the spermatozoa with the Y chromosome
which reaches the ovum, then it will have an X-Y combination and that puppy will be a dog. It is a 50-50
chance. ½ of a litter should be dogs and the other ½ bitches.
Taking this a step further, let’s consider coat color. Each parent carries two genes for coat color, one
dominant and one recessive. The puppy will receive one gene from each parent and it’s coat color will be
determined by the dominant and recessive traits of the new combination.
To keep this fairly simple, assume the bitch is lemon and will therefore only donate lemon genes to each
unborn puppy. Since lemon is recessive to all other colors then the color will be determined by the male.
Assume he carries the dominant Black, White, Tan (BWT) gene and a recessive lemon gene. He will then
determine the puppy’s color in the same manner that he determines the sex. If he donates the BWT gene,
then the puppy will be BWT. If he donates his lemon gene, then the puppy will be LEMON.
Now for the probabilities, ½ of the puppies are male, ½ are female. Also coat color is determined in the
same way. ½ of the puppies will be BWT and ½ will be lemon. If you want a particular color and sex
combination then your chances will be ½ x ½ or ¼. Simply stated, you have a one in four chance of
getting the color puppy you want of the desired sex. The four combinations in this example are:
Male LEMON Female LEMON
Male BWT Female BWT
So much for the easy stuff.
Let’s assume you have a good quality bitch of sound type. She is of good breeding stock and has several
good qualities. Recognizing that there is no perfect Foxhound, you see that her best quality is her head
and that her weakest quality is her rear end.
Realizing that there are genes which control eye color and shape, length of muzzle, the bite, the jaw width,
and ears among others, I will lump all of these together under a broad category of just the head. I am not
qualified or knowledgeable enough to give the inheritance probabilities of all of the individual traits. Since
this is just a magazine article and not a doctoral thesis, I won’t go deeper than this. We must assume that
the bitch in question carries the genes for a good head and a weak rear end.
Now, the search for the stud dog begins. The dog selected also has excellent breed type and
soundness. His strength is his rear end. His head, though it is good, is not as good as the head of your
bitch. You desire the puppies to inherit his rear end and her head. Let us complicate things a little and
say that he is a BWT and she is Lemon. All things being equal then you want to keep a BWT male with
her head and his rear end. The puppies will be ½ male, ½ BWT, ½ her head, and ½ his rear end. The
right combination will be:
½ x ½ x ½ x ½ = 1/16
One puppy out of sixteen will be male and BWT with the sire’s rear end and the dam’s head. This is a
6.25% chance. Not many of us have litters of sixteen puppies every time. These are not very good odds
if you are unwilling to compromise on coat color or sex to get the conformation you desire. (Can you
name the sixteen possible combinations from the mating described above? They are included at the end
of the article).
A good breeder should strive to increase his chances for success. This can easily be done by inbreeding
and linebreeding. All of the probabilities discussed so far are good for dogs which are the result of a total
outcross with no shared genes.
Let’s modify the above scenario by stating that the sire and dam were half-brother and half-sister and that
they shared a common sire with a good head and a good rear end. This automatically doubles the
influence that the quality grandsire will have on the desired puppy. He will contribute one half of the
genetic makeup instead of one fourth.
In the following pedigree, I have shown the traits that we are looking for in capital letters and the undesired
ones in small letters. Look at the four grandparents. They are the key to understanding how the
probabilities have changed. By doubling up on the grandsire we have increased our chances of getting a
good head from ½ to ¾ and we have increased our chances of getting a good rear end desired by a like
amount. This desired puppy is as closely related to his quality grandsire as either of his two parents.
GRANDSIRE A (MALE-lemon-HEAD-REAR)
SIRE (MALE –BWT-head-REAR)
GRANDDAM B (female-BWT-head-REAR)
DESIRED PUPPY (MALE-BWT-HEAD-REAR)
GRANDSIRE A (MALE-lemon-HEAD-REAR)
DAM (female-lemon-HEAD-rear)
GRANDDAM C (female-lemon-HEAD-rear)
The probabilities can then be written as ½ male, ½ BWT, ¾ Head and ¾ rear end.
½ x ½ x ¾ x ¾ = 9/64
In the first example, the probability was one out of sixteen. 1/16 is equal to 4/64. Our chances are now 9
of 64 or 14%, which is more than double our previous chances. Our chances get even better if the two
granddames share some common ancestry in their pedigree.
If the dam and the sire of the desired puppy had both been BWT’s then the odds of having a BWT puppy
would have been ¾ as well instead of only 1/2., the calculated probabilities would have been:
½ x ¾ x ¾ x ¾ = 27/128
This is equal to a 21% chance or better than one puppy in five being exactly what we are looking for. This
is another 50% increase in probability than even the previous example.
Of course, one hears the fears of inbreeding and linebreeding as often as the success stories. If we can
increase our chances of getting good genes to 3 out of 4 then the chances of getting poor ones are only
one out of four. This type of reinforcement will increase the likelihood that we can consistently produce
the type and quality of dogs that we are all looking for.
The failure comes when dogs with common faults are inbred and this poor trait is reinforced. When
breeding closely dogs with any common faults at all should never be mated. Any failures should be culled
so that only the success can be used to reproduce.
POSSIBLE COMBINATIONS
MALE-BWT-HEAD-REAR FEMALE-BWT-HEAD-REAR
MALE-BWT-HEAD-rear FEMALE-BWT-HEAD-rear
MALE-BWT-head-REAR FEMALE-BWT-head-REAR
MALE-BWT-head-rear FEMALE-BWT-head-rear
MALE-lemon-HEAD-REAR FEMALE-lemon-HEAD-REAR
MALE-lemon-HEAD-rear FEMALE-lemon-HEAD-rear
MALE-lemon-head-REAR FEMALE-lemon-head-REAR
MALE-lemon-head-rear FEMALE-lemon-head-rear