Basic Genetics

The basis for order in life lies in a very large molecule called deoxyribonucleic acid, mercifully abbreviated to DNA. A related molecule, ribonucleic acid (RNA) provides the genetic material for some microbes, and also helps read the DNA to make proteins.
Yes, read.
DNA has a shape rather like a corkscrewed ladder. The "rungs" of the ladder are of four different types. The information in DNA comes in how those types are ordered along the molecule, just as the information in Morse code comes in how the dashes and dots are ordered. The information in three adjacent rungs is "read" by a kind of RNA that hooks onto a particular triad of rungs at one end and grabs a particular amino acid at the other. Special triads say "start here" and "end here" and mark off regions of the DNA molecule we call discrete genes. The eventual result is a chain of amino acids that makes up a protein, with each amino acid corresponding to a set of three rungs along the DNA molecule. There are also genes that tell the cell when to turn on or turn off another gene. The proteins produced may be structural or they may be enzymes that facilitate chemical reactions in the body.
We now know that chromosomes are essentially DNA molecules. In an advanced (eukaryotic) cell, these chromosomes appear as threadlike structures packaged into a more or less central part of the cell, bound by a membrane and called the nucleus. What is more important is that the chromosomes in a body cell are arranged in pairs, one from the father and one from the mother. Further, the code for a particular protein is always on the same place on the same chromosome. This place, or location, is called a locus (plural loci.)
There are generally a number of slightly different genes that code for forms of the same protein, and fit into the same locus. Each of these genes is called an allele. Each locus, then, will have one allele from the mother and one from the father. How?
When an animal makes an egg or a sperm cell (gametes, collectively) the cells go through a special kind of division process, resulting in a gamete with only one copy of each chromosome. Unless two genes are very close together on the same chromosome, the selection of which allele winds up in a gamete is strictly random. Thus a dog who has one gene for black pigment and one for brown pigment may produce a gamete which has a gene for black pigment OR for brown pigment. If he's a male, 50% of the sperm cells he produces will be B (black) and 50% will be brown (b).
When the sperm cell and an egg cell get together, a new cell is created which once again has two of each chromosome in the nucleus. This implies two alleles at each locus (or, in less technical terms, two copies of each gene, one derived from the mother and one from the father,) in the offspring. The new cell will divide repeatedly and eventually create an animal ready for birth, the offspring of the two parents. How does this combination of alleles affect the offspring?
There are several ways alleles can interact. In the example above, we had two alleles, B for black and b for brown. If the animal has two copies of B, it will be black. If it has one copy of B and one of b, it will be just as black. Finally, if it has two copies of b, it will be brown, like a chocolate Labrador. In this case we refer to B as dominant to b and b as recessive to B. True dominance implies that the dog with one B and one b cannot be distinguished from the dog with two B alleles. Now, what happens when two black dogs are bred together?
We will use a diagram called a Punnett square. For our first few examples, we will stick with the B locus, in which case there are two possibilites for sperm (which we write across the top) and two for eggs (which we write along the left side. Each cell then gets the sum of the alleles in the egg and the sperm. To start out with a very simple case, assume both parents are black not carrying brown, that is, they each have two genes for black. We then have:
 B  B
B  BB (black)  BB (black)
B  BB (black)  BB (black)
All of the puppies are black if both parents are BB (pure for black.
Now suppose the sire is pure for black but the dam carries a recessive gene for brown. In this case she can produce either black or brown gametes, so
 B  B
B  BB (pure for black)  BB (pure for black)
b  Bb (black carrying brown)  Bb (black carrying brown)
This gives appoximately a 50% probability that any given puppy is pure for black, and a 50% probability that it is black carrying brown. All puppies appear black. We can get essentially the same diagram if the sire is black carrying brown and the dam is pure for black. Now suppose both parents are blacks carrying brown:
 B  b
B  BB (pure for black  Bb (black carrying brown)
b  Bb (black carrying brown)  bb (brown)
This time we get 25% probabilty of pure for black, 50% probability of black carrying brown, and - a possible surprise if you don't realize the brown gene is present in both parents - a 25% probability that a pup will be brown. Note that only way to distinguish the pure for blacks from the blacks carrying brown is test breeding or possibly DNA testing - they all look black.
Another possible mating would be pure for black with brown:
 B  B
b  Bb (black carrying brown)  Bb (black carrying brown)
b  Bb (black carrying brown)  Bb (black carrying brown)
In this case, all the puppies will be black carrying brown.
Suppose one parent is black carrying brown and the other is brown:
 B  b
b  Bb (black carrying brown)  bb (brown)
b  Bb (black carrying brown)  bb (brown)
In this case, there is a 50% probability that a puppy will be black carrying brown and a 50% probability that it will be brown.
Finally, look at what happens when brown is bred to brown:
 b  b
b  bb (brown)  bb (brown)
b  bb (brown)  bb (brown)
Recessive to recessive breeds true - all of the pups will be brown.
Note that a pure for black can come out of a mating with both parents carrying brown, and that such a pure for black is just as pure for black as one from ten generations of all black parentage. THERE IS NO MIXING OF GENES. They remain intact through their various combinations, and B, for instance, will be the same B no matter how often it has been paired with brown. This, not the dominant-recessive relationship, is the real heart of Mendelian genetics.
This type of dominant-recessive inheritance is common (and at times frustrating if you are trying to breed out a recessive trait, as you can't tell by looking which pups are pure for the dominant and which have one dominant and one recessive gene.) Note that dominant to dominant can produce recessive, but recessive to recessive can only produce recessive. The results of a dominant to recessive breeding depends on whether the dog that looks to be the dominant carries the recessive. A dog that has one parent expressing the recessive gene, or that produces a puppy that shows the recessive gene, has to be a carrier of the recessive gene. Otherwise, you really don't know whether or not you are dealing with a carrier, bar genetic testing or test breeding.
One more bit of terminology before we move on - an animal that has matching alleles (BB or bb) is called homozygous. An animal that has two different alleles at a locus (Bb) is called heterozygous.
A pure dominant-recessive relationship between alleles implies that the heterozygous state cannot be distinguished from the homozygous dominant state. This is by no means the only possibility, and in fact as DNA analysis advances, it may become rare. Even without such analysis, however, there are many loci where three phenotypes (appearances) come from two alleles. An example is merle in the dog. This is often treated as a dominant, but in fact it is a type of inheritance in which there is no clear dominant - recessive relationship. It is sometimes called overdominance, if the heterozyote is the desired state. I prefer incomplete dominance, recognising that in fact neither of the alleles is truly dominant or recessive relative to the other.
As an example, we will consider merle. Merle is a diluting gene, not really a color gene as such. If the major pigment is eumelanin, a dog with two non-merle genes (mm) is the expected color - black, liver, blue, tan-point, sable, recessive red. If the dog is Mm, it has a mosaic appearance, with random patches of the expected eumelanin pigment in full intensity against a background of diluted eumelanin. Phaeomelanin (tan) shows little visual effect, though there is a possibility that microscopic examination of the tan hair would show some effect of M. Thus a black or black tan-point dog is a blue merle, a brown or brown tan-point dog is red merle, and a sable dog is sable merle, though the last color, with phaeomelanin dominating, may be indistinguishable from sable in an adult. (The effect of merle on recessive red is unknown, and I can't think of a breed that has both genes.) What makes this different from the black-brown situation is that an MM dog is far more diluted than is an Mm dog. In those breeds with white markings in the full-color state the MM dog is often almost completely white with a few diluted patches, and has a considerable probablity of being deaf, blind, and/or sterile. Even in the daschund, which generally lacks white markings, the so-called double dapple (MM) has extensive white markings and may have reduced eye size. Photographs of Shelties with a number of combinations of merle with other genes are available on this site, but the gene also occurs in Australian Shepherds, Collies, Border Collies, Cardiganshire Welsh Corgis, Beaucerons (French herding breed), harlequin Great Danes, Catahoula leopard dogs, and Daschunds, at the least.
Note that both of the extremes - normal color and double merle white - breed true when mated to another of the same color, very much like the Punnett squares above for the mating of two browns or two pure for blacks. I will skip those two and go to the more interesting matings involving merles.
First, consider a merle to merle mating. Remember both parents are Mm, so we get:
 M  m
M  MM (sublethal double merle)  Mm (merle)
m  Mm (merle)  mm (non-merle)
Assuming that merle is the desired color, this predicts that each pup has a 25% probability of inheriting the sublethal (and in most cases undesirable by the breed standards) MM combination, only 50% will be the desired merle color, and 25% will be acceptable full-color individuals. (In fact there is some anecdotal evidence that MM puppies make up somewhat less than 25% of the offspring of merle to merle breedings, but we'll discuss that separately.) Merle, being a heterozygous color, cannot breed true.
Merle to double merle would produce 50% double merle and is almost never done intentionally. The Punnet square for this mating is:
 M  M
M  MM (sublethal double merle)  MM (sublethal double merle)
m  Mm (merle)  Mm (merle)
Merle to non-merle is the "safe" breeding, as it produces no MM individuals:
 m  m
M  Mm (merle)  Mm (merle)
m  mm (non-merle)  mm (non-merle)
We get exactly the same probability of merle as in the merle to merle breeding (50%) but all of the remaining pups are acceptable full-colored individuals.
There is one other way to breed merles, which is in fact the only way to get an all-merle litter. This is to breed a double merle (MM) to a non-merle (mm). This breeding does not a use a merle as either parent, but it produces all merle puppies. (The occasional exception will be discussed elsewhere.) In this case,
 M  M
m  Mm (merle)  Mm (merle)
m  Mm (merle)  Mm (merle
The problem with this breeding is that it requires the breeder to maintain a dog for breeding which in most cases cannot be shown and which may be deaf or blind. Further, in order to get that one MM dog who is fertile and of outstanding quality, a number of other MM pups will probably have been destroyed, as an MM dog, without testing for vision and hearing, is a poor prospect for a pet. In Shelties, the fact remains that several double merles have made a definite contribution to the breed. This does not change the fact that the safe breeding for a merle is to a nonmerle.
Thus far, we have concentrated on single locus genes, with two alleles to a locus. Even something as simple as coat color, however, normally involves more than one locus, and it is quite possible to have more than two alleles at a locus. What happens when two or more loci are involved in one coat color?