Let me preface this with saying that everything discussed here is only theory and nothing was ever confirmed by admins.

/!\ Updates are added at the end of this post. Some things in the initial post have since been disproved or confirmed but still are written. 

What do we know for sure?

• Horses with variations appear different from 'regular-marking' horses.
• According to wiki on the variation page : 'Variations are based on hidden genes that can not be revealed'  and also 'Marking variations occur in the foundation store and pass through breeding'. We can add that variations are inheritable, as the wiki page says 'It is possible for a horse to pass on its marking variation. This occurs at a fairly low rate with a higher chance of the mares marking passing than a stallions variation. This means foals may either have the variation from their sire or dam or the default variation for the gene'. If not inherited, they can only come from foundation (or admin-made/admin-modified horses).
• Variations happen on the following genes: To (tobiano), Sa1 (sabino), Fr (overo), Rn (roan), Rb (rabicano), SW# (splash white), ma (manchado), da (dapple), D/nd1 (dun), Lp (leopard). 
• There is several variations for a same gene (Tobiano 2, Sabino 3, Leopard 6, etc...). Note that the number is given according to the name of the layer used to render the image of the horse in-game (for example: https://eqcetera.s3.us-west-2[...]markings/overo3.png will be considered as an Overo 3 variation). Exceptions: Skewed Roan which is a Roan 3 but mostly called skewed roan and Skewed Dun. Skewed Dun is a Dun 2 2 (layer dun2_2) if the dun gene is D but it can also be Dun 1 2 (layer dun_2) if the dun gene is dn1. Regular Dun D is layer dun2 and regular dun nd1 is layer dun.

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My current theory (which is not the absolute truth and please, feel free to discuss why it might not be right):

Variations genes are independent of marking/base genes, meaning that even plain horses can carry variations genes. Breeding a plain horse carrying a variation gene can, with the right pairing, give a foal that will display a variation. A single variation gene can only modify a specific gene or a specific list of gene (example to come below) and can only modify it/them in a specific way (example below). It is possible for a horse to carry more than 1 variation gene at a time.

Premises: let's imagine a plain liver chestnut thoroughbred stallion bought in foundation called 'A'. Let's take a sabino overo liver chestnut thoroughbred mare, called 'B', which comes from a long line of thoroughbreds bred way before the implementation of variations in game.

• Example #1, Variation genes are independent of marking/base genes:
  (Personnal confidence: 9/10)
  
  'A' and 'B' are bred and upon age up their foal displays a Sabino 4 pattern.
  Explanation: 'B' cannot be a variation carrier because its line has been in the game long before the implementation of the variation genes in game. Variations genes have been introduced via foundation horses, 'B' has no foundation horses in her recent lineage, she cannot have hidden variation genes. 'A', despite being a plain horse, produced a variation foal. He's a foundation, he can carry hidden genes.
  
  In-game examples to support this part of the theory:
  - Brown Dun foudation Morgan produces a Roan 3 foal out of a long-standing line (shortened to LSL from now on) Roan Mustang.
  - Red Chesnut foundation TB produces an Overo 5 foal out of a LSL Smoky Black Overo TB.
  - Brown Bay foundation Arabian produces a Tobiano 4 foal out of a LSL Sabino Tobiano Varnish Roan Crossbreed.
  
  Note: It is most likely possible that a foundation overo horse carries a hidden variation gene for say Overo while not displaying the variation itself.
  
  
  
• Example #2, variation genes can only modify a specific gene or specific list of genes. Plus, variation genes can modify marking genes in a specific way.
  (Personnal confidence: 7/10)
  
  'A' and 'B' are bred again and again but the only foals coming out of this pair are either regular plain/overo/sabino or sabino 4.
  Explanation: We saw earlier that 'B' cannot be a carrier so it only leaves 'A' to be carrying a variation 4 that is specific to sabino*. Foals will never be Sabino 2/3/5/6.
  
  In-game examples to support this:
  (It's not specifically game examples that actually 'support' this but most frequently, a parent displaying a given variation will have foals with that same variation, on the same gene.)
  - Sabino 4 Shetland produces a Sabino 4 foal out of a Calico Shetland.
  - Tobiano 4 TWH produces a Tobiano 4 foal out of a plain TWH.
  - Tobiano 4 APH produces a Tobiano 4 foal out of a plain Friesian.
  - Roan 3 Appy produces a Roan 3 foal out of a plain Andalusian.
  - Splash White 2 Appy produces a Splash White 2 foal out a LSL Snowcap Rabicano Appy.
  
  
  
• Example 3, horses can carry several variation genes**:
  (Personnal confidence: 9/10)
  
  Lemme introduce you 'C', a foundation Irish Cob mare with a Splash White 2 variation and 'D' a LSL Roan Overo Irish Cob stallion. 'C' and 'D' are bred and seemingly out of the blue, an Overo 5 foal is born.
  Explanation: 'D' is from a LSL and cannot be a carrier. We know 'C' has a variation gene for Splash White because she shows the variation so it makes sense that she can also carry a variation gene for Overo.
  
  In-game examples to support this:
  - Roan 3 foundation Irish Cob produces a Splash White 2 foal out of a LSL Roan Overo Splash Irish Cob.
  - Sabino 3, regular Tobiano and Overo TB produces an Overo 6 foal out of foundation Roan 3 TB.
  
  
  

Special cases that cast a doubt on some parts of the theory:
* I believe the variation gene that modifies Sabino can actually modify Tobiano as well. Both are KIT genes but at the same time Roan only has 3 forms (regular, 2 and skewed).
In-game example:
- Tobiano 3 foundation TB produces a Sabino 3, regular Tobiano and Overo foal out of a LSL Sabino Overo TB.

Thing is, I also have the following horse that suggest that Overo can be modified by the same variation gene than Sabino and Tobiano:
- Overo 3 horse.
What's interesting with this one is that the sire is a regular Overo *but* his own sire and granddam are both Overo 4. His dam on the other end is a foundation Tobiano 3. Maybe one of the parents (likely the dam) carries Overo 3 or like I said earlier, Overo can be modified by the same gene than Sabino/Tobiano, which seems fair as Tovero variations are a thing.

**Since there is no way to test the variation genes and everything is just theory, it is entirely possible that there is simply variation genes like Variation 2, Variation 3, Variation 4, Variation 5, Variation 6 that can modify any marking gene. In this case, point 2 is also invalid.

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07/11 Update:

Tovero variation seems controlled by the Frame variation gene. I did a few searches and here are the results:

Search: Fr variation 2 + To/any variation 1 (regular KIT gene)
Full results:
- Tovero 2, regular Sabino Shetland
- Tovero 2, regular Sabino APH
- Tovero 2 IC
- Tovero 2 APH
- another Tovero 2, regular Sabino APH

Search: Fr variation 1 (regular Overo) + To/any variation 2
Full results:
- Regular Tovero APH
- Regular Tovero TB
- Regular Tovero ASB
- Regular Tovero TWH


So far, I think the variation genes are the following:

Dun: 1 single variation gene 'Skewed' which modifies D or nd1.
Frame/Overo: 5 variation genes (2/3/4/5/6) which will also give the tovero variations if a horse has tobiano as well.
KIT: 5 variation genes (2/3/4/5/6) which modify Tobiano/Sabino/Roan*.
Lp: 5 variation genes (2/3/4/5/6) which modify every combination of leopard patterns (leopard, blanket, varnish roan, etc...).
SW#: 5 variation genes (2/3/4/5/6) which modify Splash White.
Manchado: 1 variation gene which modifies manchado.
Dapple:  1 variation gene 'Reverse' which gives the rare Reverse Dapple.


* Searching for Rn/n horses with a variation 4/5/6 will give a lot of skewed roan results.

08/06/22 Update

Because variation genes are still gene, they must have 2 alleles as well. This mean that a horse can carry 2 variations alleles. For example, E is the Extension gene (black coat) and Ee are the representation of the 2 alleles.

A horse could, for example, be KIT(2)KIT(5) and pass one of the variation gene. Reminder that because a horse possesses the gene doesn't mean that the foal *will* express the variation.

09/06/22 Update

It seems that Overo and To/Rn/Sa1 are actually affected by the same variation gene! I have this mare who is a daughter of an admin-modified stallion. By that, I mean that the stallion who had no variation genes, because he's from a LSL, received a designated variation gene (Tovero 3). This daughter of his doesn't show a tovero variation but appears in the search results when looking for a Tobiano variation 3. I adressed in the initial post that Tovero variation seems controlled by the Overo gene rather than Tobiano. Her sabino isn't modified either (layer is sabino.png). The only possibility left is that To/Rn/Sa1/Fr are affected by the same variation gene.

New variation gene rable would be the following:

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This marks the end of my rambling about variations. Feel free to add more and link horses with interesting breeding results!

You can join us at the Variation Experimentation Society club to help solve this mystery here!