Starting Point
The two basic pigment colors, black and red

Color in mammals is caused by a pigment called
melanin.
In horses, melanin appears in two forms, eumelanin (black) and phaeomelanin
(orange-red). These two pigments are the source of every horse color. All of the
many shades and colors that can occur are caused by these two pigments
interacting with each other, and with the various "modifying" genes
that cause them to be lighter or darker or to have white added in various ways.
All horses have red pigment (although it may be modified or hidden), but only
some horses have black pigment. If a horse has black pigment, that doesn't
necessarily mean it will be black -- various other genes can modify or restrict
the black pigment.

The starting point for our understanding of horse
colors is the group called "basic colors".
In understanding this group of colors, it's important to remember that there
are two different genes at work, and they are inherited completely independently
from one another. Understanding this will explain how you can, for instance, get
a bay from a black x chestnut cross, even though bay is dominant to both black
and chestnut. Because of this interaction, we have chosen to cover these two
genes together in one section, rather than separately. Conventional terminology
refers to this group of colors as "base colors", or sometimes
"hard colors" (from an old time belief that lighter colors were
"weaker" and dark coats were "tougher"). It is also
important to understand that these are the "starting point" for every
other color, that, for instance, grey is not a color of its own, but rather a
grey horse started out as one of these colors and then had the grey gene added
on top of that "base color". As another example, buckskin is not a
color of its own, but rather, is a bay horse with a particular dilution gene
added, making it lighter.

The first gene is called the "E" gene.
It was named the "Extension" locus because the dominant allele,
E,
"extends" the eumelanin (black pigment). The recessive allele, e,
blocks the eumelanin, leaving only phaeomelanin (red pigment). When the black
pigment is present, it "covers up" the red pigment, so the horse looks
black (in the absence of any further modifying genes, which will be discussed
further). Therefore, ee
would give a red (chestnut) horse, EE would give a black horse which cannot produce a
chestnut foal, and Ee would give a black horse that can produce a chestnut foal.
There is now a DNA test which can tell you exactly which "E" genes
your horse is carrying. It's especially popular with breeders that are partial
to the color black, since a black horse that is EE will never have a chestnut
foal, and when bred to another black, will always have a black foal. But the
test can come in handy in solving some kinds of color mysteries, too, since some
colors can look very similar to each other.
Some older books have theorized that
there is a third allele, called ED, dominant to the other two, which would
explain the "non-fading black" which is rare, but occasionally seen.
However, more recent studies have discounted this theory. It is a fact that some
very few black horses do not fade in the sun, but it is unknown at this time
what genetic mechanism causes this. One theory that has been conclusively
disproved is that the "faders" are Ee, and the "non-faders"
are EE. Now that there is a test for the "E" genes, plenty of blacks
that fade terribly have been identified as EE, so that can't be the answer.

The second gene is called the "A" gene.
It was named the "Agouti" gene because it was thought to be
similar to the color of a South American rodent of the same name. The term was
used in mouse color genetics to refer to a gene that controls the distribution
of eumelanin, and apparently the name carried over to the horse
gene as well; however, it is now reasonably certain that this gene in horses does not
act the same as the one of the same name in mice. There have also been some differences
between various authors on just how many alleles there are at this locus. At this point
we are certain of at least two, but there are two more that are strongly
suspected, but not genetically proven yet, and it's possible there may be more. Very little research has been done on
this gene up to this point, although a new study from France has been enormously
helpful, having pinpointed the "a" allele. Perhaps soon there will be further research into what other alleles are at this locus.

The Agouti alleles that are definitely known to exist are:
A, which is dominant, and causes the eumelanin (black) to be restricted to
the horse's points (mane, tail, legs), leaving the rest of the body red, and
giving us a bay horse. This is the most common horse color in many
breeds.
a, which is recessive, and which does not restrict the eumelanin in any
way, but allows it to be fully expressed all over the horse's body, thus giving
us a black horse. It is more common in some breeds and less common in others.
Considering these two alleles, we can see that AA would give us a bay
horse that can never have a black foal, Aa would give us a bay horse that can
have a black foal, and aa would give us a black horse.
There is now a test available for the a
allele. It can tell you if your horse has one a,
two of them, or none. Anything not a
is labeled A by
default, because the test is only detecting the a
allele. So, if there are indeed (as believed by many) more than two
possible Agouti alleles, the test will not distinguish between the three (or
however many there are) non-a
alleles. Therefore, it can't distinguish between bay and brown. It
is useful in many cases, though.
At, which would be dominant to
a but recessive to the other
alleles, which would cause seal brown. This was the most common theory for some
years, then in the 1990s it lost favor to another popular theory which has since
been disproved, so now is gaining favor again. Hopefully the research
will soon be done to find out for certain if this allele exists.
The allele which is theorized, but not genetically
proven at this point in time are:
A+, which is dominant over all the other alleles at the A
locus. It is called "wild type" bay, and gives a much lighter horse
with shading that makes them look much lighter on the underbelly, and the
black on the legs is much less extensive (perhaps only up to the ankles).
Some books specify the color of the Przewalski's Horse as an example of this
gene, but pictures of them show that they are actually dun. Perhaps they are A+
and dun, both. It is possible that this gene was once the most common color in
all horses, but has been almost completely bred out of the modern horse population.
Currently, the various Agouti genes are believed to affect only the eumelanin in
the horse's coat, and therefore would have no visible effect on a chestnut
horse, which has no black pigment to be affected. There are some who believe
that the various A alleles may affect the shade of a chestnut, but at this point
there is no evidence one way or another. Anecdotal evidence does suggest that
black (aa) horses seem more likely to produce very dark chestnuts (liver chestnuts)
when they do have chestnut foals, and vice versa, so there may be something to
the idea. However, the one study that was done by the researchers who isolated
the a allele showed no statistically significant difference in the shades of
chestnuts whether they were AA,
Aa or aa.
Hopefully more
research will be done in this area soon.

Descriptions and examples of our four "base colors", then:
1. Chestnut (ee,
with any combination of A genes)
Body
color any shade of red, reddish-brown, or orangey-red, points may be lighter or
darker than the body, or the same color, but never black. This is a typical
medium chestnut; they can be much lighter or darker.
2. Bay (AA, Aa,
or AAt, plus EE or
Ee)
Body
color red, ranging from light to dark, but some shade of red or reddish-brown;
points black. Dark bays may have an "overlay" of black hairs on the
body (see "sooty" for details) but the color
underneath will still be some shade of red.
3. Brown (AtAt
or Ata,
plus EE or
Ee)
There
is now a DNA test to differentiate this color from bay or black. It's definitely a
separate and distinct color meriting a category of its own. The color is called
"black and tan" in some countries, which is an apt description. The
basic appearance is that of a black horse with tan highlights in
specific areas -- the muzzle, flanks, underbelly, and girth areas. The darkest
shades of seal brown would be almost all black except for a little tan at the
muzzle and flank, while the lighter ones look more like a tan horse with an
overlay of black covering a good deal of the body, and the very lightest shades
of seal brown might look very much like some bays. At one time a theory
was proposed that seal brown was caused by a solid black base color with a 'pangare'
gene, however, this theory was disproved when the a
allele was isolated and a test for it developed -- since none of the seal browns
that have been tested turned out to be aa,
they could not be "black plus" anything.
4. Black (EE
or Ee, plus aa)
The
horse is black all over, including the muzzle, flanks and underbelly. Blacks are
notorious for fading and bleaching when exposed to the sun, so it can be hard to
identify a black horse that has been out in the sun.... they might look more
like some strange shade of bay, brown or even dun! But once the new coat comes
in, they will be all black again (for awhile, at least).

What you can get when crossing these colors:
(x = "crossed with")
Chestnut x chestnut will always give a chestnut foal.
Black x black will always give a black foal if at least one parent is
EE.
If both parents are Ee, then the chance of black is 75% and the remaining 25%
would be chestnut.
Brown x brown may be expected to produce brown, black, or
chestnut, but not bay.
Bay x bay can produce any of these colors. If one parent is
EE, AA then
every foal will be bay. If both parents are Ee,
Aa then the chances are 56.25%
bay, 18.75% black, and 25% chestnut.
Chestnut x any of the other three "black-based" colors gives the
potential of producing any of the base colors, since there is no way of knowing
which of the "A" genes that chestnut might have. If a chestnut that
was ee, AA was bred to a black that was
EE, aa then every single foal would be
bay. If a chestnut has one black parent, then we can be sure it has at least one
a, and if it has two black parents, then we know it is
aa. Therefore, a chestnut
that had two black parents, when bred to a black which is EE, will produce all
black foals. But chestnuts from bay or chestnut parents could be carrying any of
the "A" genes, and there is no way of knowing. If a chestnut produced
a bay foal when bred to a black, that would be proof that the chestnut had at
least one A.