Guess the Genotype: Breakdown of Alleles

Since I haven't done this in full yet, I thought I should explain exactly what I am using for my Guess the Genotype posts. Here is the full list of known or theoretical genes that affect canine coat color and where the name of the locus originated from, at least it is as complete as I can make it. Where applicable, alleles are listed in order of dominance, i.e. most dominant to least dominant. They are in alphabetical order. As a rule, I try to not deal with genes that are theoretical, but I will mention them as I see necessary. For clarity, I have provided links to examples of dogs who express each phenotype.

You should also known that though I am using superscripts on this post, I do not use them on my GtG posts because it's difficult to get them to work in the posting box. However, the superscript is the more proper way to express the genes.

Dogs show remarkable amounts of variation when it comes to size, shape, color, and other aspects, as can be seen above. In this group of dogs the least number of loci necessary to produce the colors seen is five with at least eleven different alleles.  Image is from Flickr.com under a creative commons license

A locus: Agouti

This locus includes several alleles involving increasing amounts of black on a red base:
A^y - sable, which has hairs with black at the tip, the amount of black can vary greatly
a^w - "wild type" agouti, involving hairs banded with black
a^s - saddle marked, genetically the same as tan point, it is likely caused by as of yet unknown modifiers*. Often called "hound tricolor" when seen with white
a^t - tan point, black with tan at the cheeks, legs, above the eyes, on the chest, and under the tail
a - recessive black, the more unusual form of solid black, it is rarely seen in dogs
*Rather than combining them, I am retaining the old theorized genes for saddle mark and tan point until there is more information on what causes the difference in phenotype. I find it likely that what is called "capped tricolor" or "creeping tan" is an intermediate between saddle marked and tan point as controlled by the unknown modifiers.

B locus: Brown

What I usually refer to as liver, this gene turns any black on the dog to brown. It will also cause the eyes to become an amber color. There are two alleles:
B - non-brown, black will stay black
b - brown, black is diluted to brown, including the skin pigment

C locus: Colored (theorized from breeding data)
This is the theorized location of such genes as albino and chinchilla. It is believed to cause variation in the lightness of red in a dog's coat. Though this locus is known in other animals, it is quite possible that it is completely absent from dogs as no genetic testing has found evidence for the existence of the gene. If it is present, some sources think that the expression is only visible in recessive red dogs, which would explain such things as white German shepherds (which are always quite pale, even when born from fairly dark red parents). Regardless, numerous alleles are thought to possibly exist in dogs:
C - normal pigment, red stays red
c^ch - chinchilla, causing red in the coat to lighten in color
c^e - extreme chinchilla, further lightening of color, the existence of this is unclear
c^p - platinum, red will turn nearly or completely white
c - albino, either extreme rare or nonexistent in dogs

D locus: Dilution

The dilution gene turns any black in a coat to blue and any liver in a coat coat to fawn/Isabella. Blue dogs will have eyes that are a hazel-gray color and Isabella dogs will have eyes that are amber-gray and can often be quite pale. The nose will match the coat. There are two alleles:
D - non-dilute, normal color is maintained (i.e. black or liver)
d - dilute, color is diluted (i.e. black becomes blue and liver become Isabella)

E locus: Extension

This locus is an interesting one with several alleles, causing various changes to the coat:

E^M or E^m - masked, where a dog has black on its muzzle and around its eyes, amount of black varies
E^g - grizzle or domino, only visible when a dog has "a^t/a^t and no K^B or E^M", it appears to be exclusive to Salukis and Afghan hounds and is similar to sable or agouti in appearance
E - normal color, the dog is able to produce black pigment and is mask-less
e - recessive red, which makes the dog unable to produce any black pigment in its coat

G locus: Graying (theorized from breeding data)
Though this is another theoretical allele, the inheritance is pretty clear. There are two alleles:
G - gray, born dark and will lighten toward white with age
g - non-gray, normal color with no fading

H locus: Harlequin

This is one of the most recently confirmed genes. When combined with the merle gene, it causes the lighter patches caused by merle to be turned to white. It is lethal in the homozygous (HH) form and is probably exclusive to the great Dane. There are two alleles:
H - harlequin, light patches turn white
h - non-harlequin, light patches stay their normal color

I locus: Intensity (theorized from breeding data)
This is a theorized gene that is believed to affect the red in a dog's coat, making it lighter or darker depending on the genotype. Heterozygous dogs will be an intermediate between the two homozygous forms. It appears most sources are moving away from this theorized locus to the C locus for red intensity. There are two alleles:
I - intense, red will be dark
i - diluted, red will be light in color

K locus: blacK

The K locus determines the amount of black that covers up the A locus. Brindle can occur with any A allele, producing such phenotypes as saddled brindle and brindle pointed black (sometimes called trindle when it occurs with white). There are three alleles:
K (or K^B) - dominant black, turns the dog solid black in color and hides and A alleles
k^br - brindle, a pattern of black stripes over a red background
k - non-black or brindle, allows the agouti locus to show through in full

M locus: Merle

Merle usually only affects the black in a dog's coat (including black hairs that have been diluted by the B or D genes), causing pale patches to form on an otherwise darker coat. It will also effect skin pigment and eye color, resulting in pink patches on the skin and blue eyes. It usually will not effect red hairs and as such can cause "cryptic merles," which are usually red dogs that don't show that they have a merle gene. In the homozygous (MM) form, merle can be extremely detrimental, causing high incidence of deafness, blindness, and even the loss of eyes. There are two alleles:
M - merle, coat will be patchy
m - non-merle, coat will not be patchy

R locus: Roan (theorized from breeding data)
Roan is believed to be a modifying gene that is associated with the ticking gene, causing a fairly even distribution of colored hairs in white areas rather than spots. It is only visible if one of the white spotting genes is in effect. Puppies will have white areas at birth that will fill with colored hairs as they age. There are two alleles:
R - roan, dog will have a more even distribution of colored hairs
r - non-roan, dog will have spots or ticking

S locus: Spotting

This is what causes white areas to appear on a dog's coat, from bits of white on the toes and chest to a dog that may have no evidence of color at all. Though it seems very simple, it is more complicated than you would think as different combinations of genes can cause somewhat unexpected phenotypes. For example, a dog with one solid gene and one extreme white gene will appear Irish white. If a dog has white that either touches or completely covers an eye, it is quite possible for that eye to be blue in color. White will cover any color or pattern except for ticking and roaning (which add colored hairs back into a white area). There are numerous alleles: 
S - solid, dog will have no white or will have some "residual white" on the toes and chest
sⁱ - Irish, white occurs on the legs, chest, and tail tip*
 * collared Irish is caused by the same gene but adds a white collar to the above
s^p - piebald, can be similar to collared Irish, but white will cross the dog's "topline" or back
s^w - extreme piebald, a dog that is nearly all white with few small spots of color or none at all

T locus: Ticking (theorized from breeding data)
Ticking is spotting on a coat in areas that would otherwise be solid white. It is only visible if one of the spotting genes is in effect. The white will be clear at birth, and spots will appear with age. There are two alleles:
T - ticked, dog will have spots in the white areas of their coat
t - non-ticked, the white will be devoid of spots

V locus: silVer (theorized from breeding data)
This is a theorized gene that might be exclusive to poodles. Its effect is similar to the Graying locus, but it is recessive rather than dominant. It is also incomplete dominant, meaning that a dog that carries one copy of the recessive would be lighter in color than a dog who is homozygous dominant. There are two alleles:
V - non-silver, dog will remain dark throughout its life
v - silver, dog is born dark and lightens with age

W locus: tWeed (theorized from breeding data)
Tweed is another modifier to the merle gene, which causes extra shades of color to appear in a dog's coat. Tweed is rather unusual, and may be exclusive to the Australian shepherd. I have also seen this gene represented as Tw, but I prefer W to avoid confusion with the ticking gene. There are two alleles:
W - tweed, merle will include extra shades of color
w - non-tweed, merle will have only the normal two shades (excluding tan point or white)

X locus: urajiro (?) (theorized from breeding data)
Urajiro is a term used to refer to the pale areas seen in the red of Japanese dogs such as the Shiba Inu, and this same pattern is sometimes called "ghosting". The location is similar in placement to the tan markings seen in tan pointed dogs. Some theorize that this gene is associated with the C locus, while others believe it is a separate gene. It is believed to be a recessive, though other sources refer to it as polygenic. Similar pale areas are sometimes seen in other breeds, and this may or may not be controlled by the same gene. I suspect that it is. I have seen at least one source refer to urajiro as the X locus, and that is what I use for this theorized simple inheritance:
X - normal coloring, no pale points, and pale areas are those commonly seen in the red on dogs
x - urajiro, pale points will be present

Miscellaneous other factors

There are numerous other as of yet unknown factors that affect coat color. What determines the intensity of a mask? Or the degree of Irish white? Or the difference between saddle marked and tan point? Or what causes "bad black" or "seal" to occur in dogs that are genetically dominant black? Why are only some breeds prone to such problems as blue dilution alopecia while others are clear? Why are some double merles completely fine while others are deaf and were born without eyes?

There are also other alleles that are associated to such things as coat type (wire, long, short, curled, hairless, etc.), eye color (mainly just blue eyes that are not associated with genes such as merle and white spotting), ear type and set (drop, prick, semi-prick, rose, button, etc.), leg length, muzzle length, and tail type (curled, straight, bobtail, gay, sabre, etc.). The inheritance of some of these alleles are well known or at least mostly understood (like bobtail, hairlessness, and wire hair), but others are so polygenic that it is difficult to tell the exact nature of how the inheritance works. This is why I talk about coat color and will only occasionally mention other genes when I feel that it is a necessary addition.

An example
Now, let's guess at a genotype with a full representation of genes for this dog. Note that common notation for an unknown gene is to use a dash, as you can see below:

Ay- BB C- DD E- gg hh I? kk Mm si- Tt V? Ww XX or Irish white tweed sable merle with ticking

Sources for this post are: one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen.