[Arkinhallow]

In early horses, it's thought that bay or bay dun (EE/AA) was the predominant colour. The agouti gene mutated, resulting in the "a" allele which did not restrict black pigment to the points of the horse. The "a" allele can be considered recessive black, like it is in dogs, because an Ee/aa or EE/aa horse will be all black. The extension gene mutated to create "e", recessive red, which shows over recessive black, as it prevents black pigment from being made (so ee/aa, ee/AA or ee/Aa will all be recessive red). It's commonly thought that chestnut and black are the base colours and that bay is a modifier of those base coats, and indeed when explaining the genes it's often easier to understand them this way - it's how I've explained it here. Technically, though, bay is the original base colour, and both solid black and solid red are mutations of it.

Agouti is also called "wild-type" in many animals, including cats, dogs, mice and rabbits.

──────────────────────────────── Agouti Gene ────────────────────────────────

Agouti is responsible for bay and wild bay, and is theorised to be responsible for seal/brown. While extension controls the production of black pigment, agouti controls the distribution of it. There are four theorised alleles for the agouti gene: non-bay (or recessive black) "a"; bay "A"; seal brown "At"; and wild bay "A+". Of these, only non-bay and bay have been confirmed and can be consistently tested for. A test was created for seal brown but it had inconsistent results and it is no longer available. It's unclear if seal brown is entirely the result of the action of the agouti gene, or whether there are other genes involved. Wild bay has not been thoroughly researched and does not have a test. Seal brown and wild bay horses both genetically test as "A" agouti bays, so they are demonstrably agouti horses, but they do not have their own proven and testable alleles. Like chestnut and black horses, agouti horses have dark grey/black skin.

The "A" bay allele restricts black to the points: the muzzle, lower legs, mane and tail, and inner ears. Bays have a large range of colouring, and their "red" areas may be many shades of brown or red. There are many names for shades of bays: mahogany bay; blood bay; cherry bay; golden bay; and light bay, to name a few. All bay horses have at least one copy of dominant black (Ee or EE). Recessive red horses (ee) can have the bay allele, but they do not have black points because they can't produce black pigment.

The "a" non-bay allele does not restrict black to the points, so it causes a black-based horse. Because of this, it can also be called recessive black (different from dominant black "E" on the E locus!). All black-based horses are homozygous for non-bay. Recessive red (ee) overrides non-bay/recessive black, because recessive reds cannot produce any black pigment. Therefore ee/aa horses will always be red, not black.

So, the testable alleles for the agouti gene are:

"A" allele = dominant bay
"a" allele = recessive black/non-bay

And the theorised (presently disproven) alleles are:

"At" allele = seal brown
"A+" allele = wild bay

Because agouti and extension interact and influence the expression of eachother, they are pretty much always written together, and genotypes at their most basic always list these two genes. The expression of all other genes is dependent on whether the horse is bay-based, black-based, or red-based, so extension and agouti are the most important genes for indicating what colour a horse will be.

The genotypes for bay horses are written like this:

(assuming one copy of dominant black E is present)
AA = bay coat (two copies of agouti)
Aa = bay coat (one copy of agouti, one of recessive black)
aa = black coat (two copies of recessive black)

If we combine extension and agouti to make a complete genotype:

EE/AA = bay coat (two copies of black; two of agouti)
Ee/AA = bay coat (one copy of black, one of red; two of agouti)
ee/AA = red coat (two copies of red; two of agouti - black pigment cannot be produced due to recessive red allele)

EE/Aa = bay coat (two copies of black; one of agouti, one of recessive black)
Ee/Aa = bay coat (one copy of black, one of red; one of agouti, one of recessive black)
ee/Aa = red coat (two copies of red; one of agouti, one of recessive black)

EE/aa = black coat (two copies of black; two of recessive black)
Ee/aa = black coat (one copy of black, one of red; two of recessive black)
ee/aa = red coat (two copies of red; two of recessive black)

As you can tell just by looking at the resulting coats, bay occurs the most often, and black the least, with chestnut in between. This is why true black horses are not as common as bay or chestnut.

───────────────────────────────── On Seal ─────────────────────────────────

A number of theories have come up and been disproven so far regarding seal brown.
- It had been theorised that it was the result of pangare on black-based horses, but that was disproven by a 2001 study that showed no brown horses were homozygous "aa" - that is, none of them were black-based, they were all bay-based.
- It was at one point thought to be the result of the TYRP1 gene, also called the "b" locus. The "b" locus is where chocolate brown is located in dogs and cats. This was also disproven in 2001 by sequencing of the gene.
- A dominant black allele "Ed" or "Eb" was also theorised, and it was suggested that seal brown occurred in these dominant black horses, however this, too, has been disproven with sequencing of the Extension gene.

As it stands, seal brown is thought to be polygenic or the result of the action of another gene on Agouti. On Chicken Smoothie, for simplicity's sake, seal brown is usually still considered to be on the "At" allele and is usually considered distinct from bay genetically, as is wild bay.

──────────────────────────────── On Wild Bay ────────────────────────────────

There is extremely little information regarding wild bay out there. Multiple sources agree that it has been theorised to be the most dominant type of bay, however I cannot find any actual source of a study or research into this - it's like these sites all took that information from each other without ever looking for a source to that claim. Conversely, at least one source I found said that "there had been reports" wild bays had been born to bay parents, which would disprove the theory that wild bay is the most dominant bay type anyway (although this claim in itself once again has no source that I can find). Very little research appears to have been done or published on wild bay. There is no conclusive research that suggests that it is more dominant than normal bay, or even that it is on its own allele at all.
From my own observation, wild bay seems to be most commonly shown on young horses, and my understanding is that bays grow in their black points as they age, so it seems likely that these "wild bays" are actually just normal bays whose full colour has not grown in (for example: yearling, adult). That said, this source shows an obviously elderly horse who is (debatably, given the extent of the black points) wild bay despite being of advanced age, so it seems it may be possible for adult horses to still be wild bays. That is largely speculation on my part, though. In summary there is very little information to find on wild bays, and virtually nothing reliably sourced, so it remains largely a mystery. As with seal, on CS it is still usually considered to be on its own allele, A+.

Sources: (for the above three sections)

wikipedia.org "Bay (horse)"
animalgenetics.us "Agouti (Bay/Black)"
vgl.ucdavis.edu "Agouti (Bay/Black)"
etalon diagnostics "More about Agouti"
bapsh.co.uk "Agouti Locus and Bay, Black, & Seal-Brown"
wikipedia.org "Seal brown (horse)"
morgancolors.com"The Base Colours"
horse.jenniferhoffman.net "Agouti Bay"

Sources I do not recommend:

theequinest.com: Information was out of date and reference images have no sources. Frankly, I don't trust that the images are what they say they are.
horse-genetics.com: Information is heavily out-dated and makes a lot of assumptions. Contrary to what is stated, only one test was ever created for "At" seal brown and it has now been pulled for inaccuracies and inconsistency. There is no further proof that seal brown is on the proposed "At" seal brown allele of agouti.

─────────────────────────────── Inheritance on CS ───────────────────────────────

As I've mentioned previously, on CS seal brown is usually still considered to be on the "At" allele and wild bay is usually put on the A+ allele, rather than them both having the "A" allele (which is what current real life testing allows for).

Because the information and research on seal brown and wild bay is so lacking, how inheritance works is confusing and many artists have different ideas of how inheritance works for agouti horses. I myself have always considered "A" bay to be the most dominant (due to the demonstrable lack of wild bays as the dominant bay colour in real life, which leads me to believe it cannot be more dominant), followed by seal "At", then wild bay "A+" and then non-bay/recessive black "a". Others subscribe to the theory that wild bay is the most dominant. Until more research is done into agouti, there will remain no "right" way to do inheritance of agouti alleles (especially as At and A+ are not even confirmed to exist in the first place).

The system of inheritance I personally use is this:

A > At > A+ > a

and I will be using this going forward. So, considering this, what happens when seal and bay are both present? Or seal and wild bay? Bay always out-competes seal and wild bay:

AA or Aa = bay coat (two copies of bay, or one copy of bay and one of recessive black)
AAt = bay coat (one copy bay, one copy seal)
AA+ = bay coat (one copy bay, one copy wild bay)

Seal out-competes wild bay:

AtAt or Ata = seal coat (two copies seal, or one copy seal and one copy of recessive black)
AtA+ = seal coat (one copy seal, one copy wild bay)

And wild bay only out-competes recessive black/non-bay:

A+A+ or A+a = wild bay (two copies wild bay, or one copy wild bay and one recessive black)

────────────────────────────── References and Overlap ──────────────────────────────

Bays
Browns/Seals
Wild Bays

Image sources:

sources

Further reading and references

This article goes over information about seal brown that was thought to be correct after the test for seal brown came out. At this time, it is outdated and no longer accurate or relevant due to the test being pulled from the market.
A study suggesting the presence of a dominant black "Ed" allele. This was subsequently proven to be incorrect.
On wild bays
On seal brown and pangare

Foal references