I've toiled for hours trying to solve this. I have no doubts that I'm not the first, but I think I may have cracked just how the traits of a pony are determined. Maybe. Bare with me here. Also, warning: the following post will have a lot of genetic terminology. If you need clarification on anything, feel free to ask.

For the sake of being fair, let's say that there are four traits (or phenotypes): Alicorn, Unicorn, Pegasus, and Earth. The reason we won't be using Strength, Flight, and Magic is because the ability to use these things differs from pony to pony. Let us assume, because no normal two ponies have ever produced an alicorn, that alicorns are comprised of completely different allele forms than the other types, which they obtain after transformation or birth (let's say "A¹A² A³A³" - which you will understand the order for soon). Let us also assume - again because two normal ponies cannot produce an alicorn - that co-dominance does not happen. That is, a pegasus can't show the strength of an earth pony, and a unicorn couldn't either. However, we should not assume that there is no incomplete dominance. In fact, we should assume that there is!

Y'see, if we compare Fluttershy or Derpy to Rainbow Dash or Spitfire, it's clear that the former pair can't fly quite as well. For the gene that codes to produce a pegasus (or at least the genes of a pegasus), this must mean that it can show incomplete dominance. It is on this train of logic that I began working.

The main relationship that I began with was Derpy and Dinky. We don't know if they are mother and daughter or sisters (but I doubt that many would deny it as extremely likely), but what we CAN determine is that they most definitely have different genotypes and that Derpy has the code for "Pp" somewhere. Using this, and factoring in that "p" must be either the trait for unicorns or Earth ponies, we know that one of the parents - whether Derpy or someone else - also has the gene "Pp". If the "p" were "e," producing a Dinky is made impossible. Therefore, it must be "u," meaning that the trait for unicorns is recessive to the dominant trait of pegasi.

Now that's all nice and fun, but what about Earth ponies? How do they fit in? Well, this is where we step into polygenic trait territory. We need to have two genes to determine a pony's phenotype. This is also where we step more into the realm of guessing and assuming. Let's look at Equestria for a moment: several of the major cities are made up of a majority of Earth ponies. Two are primarily Pegasi towns (Las Pegasus and Cloudsdale). Only one is populated mostly by unicorns: Canterlot. I'm sure you can see where I'm going with this. It isn't exactly fair to assume that Earth ponies just tend to breed more or that they simply got a headstart of some kind. The most likely reason would be that, simply put, the Earth gene trumps the others. This would make a heterozygous first gene look like "Ee," where "e" is replaced with "u" again because it is the recessive trait of the three.

After a bit of assuming some things that are likely true (not absolute, but pretty likely), we have our gene set-up: EuPu. Because it contains E, that pony appears as an Earth pony. Remember that even if a pony has "PP" in its second gene, just one "E" will be enough to show the Earth trait. Furthermore, this set-up means that only with an output of "uu uu" will there be a unicorn. No wonder there's only one unicorn city!

If you couldn't tell by now, I've based this set up on the way our eye color is dictated, with eight different possible allele combinations. I'll list them now.
The genotypes of Earth ponies are as follows: EE PP, EE Pu, EE uu, Eu PP, Eu Pu, Eu uu.
The genotypes of Pegasi are as follows: uu PP, uu Pu.
And as said before, the only genotype to display magic is uu uu.

That more-or-less wraps up what I've theorized the genetic properties to be, but I'd like to close off with the Cake twins. I always thought Mrs. Cake unloyal, and I still kinda do (Pound Cake looks NOTHING like Mr. Cake), but my genetic properties can (potentially) clear Mrs. Cake's name. It's hard to explain in words, so I'll just say that doing a Punnett Square of "EuPu" x "EuPu" produces a small probability that a Pegasus and a unicorn could have been produced: 18.75% chance of a Pegasus and 6.25% of a unicorn. Like I said, small probability, but it's there.

Thanks to whoever read this far. If I made an error somewhere, by all means let me know. Hope you got something out of all this.

I would pose that Alicorns are, by all evidence, completely unrelated to genetics. Rather, they are the result of intense magical forces converging on a single locus. A powerful magical mutation, in other words, that enables all three alelles to be expressed simultaneously, as co-dominant traits, rather than as successive dominance traits.

Evidence of this would include the fact that, in order to get a natural-born alicorn, it took an alicorn mother, a father from a line with *insanely* powerful magic galloping through it, *and* the probable influence of being within the aura field of a world-controlling magical artifact for the majority of gestation. Otherwise, it takes the magical equivalent of being Bruce Banner to become an alicorn.

6227805
I don't see anything wrong, per se.
I do feel there's a LOT more to pony genetics though yielding traits that could be EuPu x EuPu = creates a unicorn with slightly less Eu causing a uu imbalance which might lead to a mentally capable unicorn with barely enough magic to levitate or a Pegasus that can't fly.

My genetics are a bit weak and using my phone didn't help, but all I'm saying is because there are three races by default just race alone offers maybe, just a guess, 27-32 possible trait combinations just with tribe and magic usage.
That doesn't include coat and eye color!

I'd like to go over this more with you!
Especially to figure out Alicorn genetics!

6227809

all three alelles to be expressed simultaneously, as co-dominant traits, rather than as successive dominance traits.

Yes, co-dominance is what I was meaning to express with the "A" code. The superscripts indicate that, though the traits share the same symbol, they are different and thus yield different phenotypes. But yes, I get what you were saying. I think. Sounds kinda mean of me to say, but I hope in some ways that Flurry Heart is sterile. If she's not, Equestria's likely to become a land of alicorns. Then again, there's the possibility that she may have some hidden traits of unicorn in her from her father. But even then, that'll mean she has to stand by as her kid dies. Damned if she does, damned if she doesn't, I guess.

6227831
Feel free to message me. I'm not quite sure what you mean here. It seems that you have a different genetic theory. Is that it? Because if we're just going by mine, then there will inevitably be less phenotypes than genotypes. That's just how genetics work. If all you're trying to say is that incomplete dominance is a thing, yes, I would agree.

6227906
I think he's suggesting genetic combinations that could basically turn into pony genetic disorders where tribal trait expression doesn't work out right.

In other words, how we get Snips and Snails, or Scootaloo, or Pipsqueak.

If we start getting into this, I might actually have a hypothetical situation that would get my Mom into this. She's something of an amateur geneticist, though her practice focuses on guinea pigs.

6228021
The more stuff we have to go off of the better, so go for it. I can't say that I entirely agree with the whole defect and disorder things caused directly by the gene. Weak wings caused by "Pu" and lower strength caused by "Eu" would make sense, but I'd think that traits like short height, long bodies, crossed eyes, and other abnormalities are caused by other factors: possibly different genes altogether.

And Scootaloo's wings I count among the wings that are weak, but that's just me. It could by all means be a defect of some sort. Additionally, I think that Pound Cake DEFINITELY ended up with a "PP" gene. One can only imagine how pissed off Scoots would be if she saw him flying around.

Oh, I meant specifically the "wimpy Earth ponies, dumb/amagickal unicorns/flightless or poor-flying pegasi" type.

Bulk Biceps, for example.

6228608
So we were both thinking the same thing, right? Am I reading the situation correctly?

Also, I'm at the moment trying to formulate a fan theory on who Pinkie's real dad is and how she may - just possibly - be related to Fluttershy. Still got a bit of figuring to go.

6229503
Yep, we were.

Though I'm inclined to say that it's fine for Pinkie's Dad to be who we expect. We all know Granny Pie was really Loki.

6229749

We all know Granny Pie was really Loki.

Well, I can't argue with that. I really do believe that she's adopted though.