Judging from how many ponies, pony sub-species, and similarly equoid creatures there are in the world... Can we surmise that ponies are extremely prone to mutation kinda like the flu?

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OK

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Or they were genetically engineered by a highly advanced species native to this world. I don't know.

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Seeing how their DNA, as completely fucked as it is, can consistently produce a pegasus baby out of an earth pony and a unicorn, I really doubt it. It actually looks remarkably super stable. Again, completely screwy how it works but it does.

6622601 Eh, it depends on how you look at it.

The three tribes of ponies - earth pony, unicorn, and pegasus - are able to interbreed with each other, but with each "tribe" remaining with their distinctive characteristics. That raises some questions as to whether or not they're each different species or not (with no answer that's in accord with what biology tells us; clearly, magic is a factor). But it's simplest enough to say that they are.

Beyond that, it seems more like the various breeds of ponies that we see are an issue of ethnicity rather than species (I like to treat the presence of absence of cutie marks as being definitive for whether or not something is a "pony"). Crystal ponies belong to the same earth/unicorn/pegasus breakdown. So, apparently, do Saddle Arabians (and I'm taking it for granted that the lack of cutie marks we saw on the ambassadors in Magic Duel and again in Equestria Games were animation errors). Presumably the same is true for zebras, even if the only one we've ever seen is Zecora.

That's...really about it. Donkeys are quite obviously not ponies (and except for a play titled "Hinny of the Hills" in Rarity Takes Manehattan, there's no indication that they can interbreed with them). Neither are hippogriffs, even if their rear ends do have a cosmetic resemblance to ponies (but with no cutie marks, tellingly). Sea ponies, at this point, seem to just be transformed hippogriffs (I'm only looking at the show, since the comics have been wrong about too many things for me to treat them as being trustworthy), making that reference Twilight made to a book about "sea pony etiquette" in Shadow Play - Part 2 somewhat awkward (the Sirens do seem like hippocampi, but no one seems to think that they're actual ponies). Kirin aren't ponies at all, and neither are reindeer, from the upcoming Best Gift Ever special.

And of course, alicorns are a group of particular individuals, being ponies that somehow transformed into an ascended state that blends all three tribes (Flurry Heart being an anomaly, in that she was born that way).

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Well my own best guess would be that since their biology is part magic, it can affect which traits their biology expresses during development. If their magic is attuned to sky stuff in the womb, their bodies will activate the wing genomes. If their exposed to a different type of magic they'll suppress the wings and instead express a horn, or suppress both to express less visible traits supporting earth pony magic. For instance if you look at the cakes, it's easy to see discord's magic disruptions causing them and probably a lot of other ponies to have foals expressing unexpected traits.

6622601 Mutation? What mutation?

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Well I think of it as a situation where ponies themselves think there are only a few creatures out there like them. It’s fully possible that other mutations and variants of ponies exist they just don’t show themselves much, or refuse to interact with other cultures or equestrians in particular. There is also the chance that the equestrians themselves played a part in the lack of species variety.

My head canon is the Irish expy in Equis is in a “stay out” relationship with Equestria and is populated by a different subspecies or pony variant, and possibly other supernatural entities or gods who want nothing to do with the Princesses due to harmony magic doing something to the world and them enclosing their realm in a barrier of sorts to keep the old magic in and harmony out. We know that the breezies survived at least, so who is to say others didn’t. The breezies were literally right next door but nobody knew they were still around because they refused to interact with Equestrian ponies.

Keep in mind that though the windigos froze whole regions, it’s implied that entities and in the case of the crystal empire a crystal heart and evil lord/specific bloodline protected it from the windigos. The griffons were also protected somehow, and who knows what other entities roam the realm. Heck for all we know Lavan from G1 was reborn as a good guy and decided to defend an island archipelago with his power from the Windigo onslaught.

The map of Equis is limited to protect modern equestrians from the reality of how big the world really is, and possibly to keep them from trying to go places that they can’t, likely due to peace treaties and more. So the reason we don’t see other species much in the series is they don’t want to deal with equestrians, and equestrians for the most part don’t know they exist or don’t care. Chances are that not only do other mutations or subspecies or relatives of ponies exist, but whole species that are not pony exist too.

Like cat people. They exist.

Again, equestrians just don’t know about them or talk to them, in fact I’d wager that they don’t visit many non pony regions at all. The ponies from say Prance or Saddle Arabia might know other species or mutations exist, but keep quiet either due to royal declaration or just preffering not to mention it to outsiders.

I mean the reality of a freaking Graboid (tatzleworm) existing was kept secret from the entire populace, think on that.

Glen Gorewood

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Can we surmise that ponies are extremely prone to mutation kinda like the flu?

Now that would make a wonderful writing prompt.

What if there were PonySharks?
PonyBears?
PonyCrocs?

What if way back in the past, there were no higher level animals?
Some advanced pony race used their DNA as a foundation to make higher level animals.
What if these advanced pony like beings made Xenoponphs.
Super cute facehuggers that jump on people's faces and put Xenoponph embryos in people's stomachs.
When Xenoponph's shyly break out of the person's stomach, everyone is like,"OMFG, look how cute it is! I want to hug it and pet it..."
Also the wound caused by the eruption of the Xenoponph larva slowly heals itself so it's not fatal.

That would be a cool story to write.

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In my headcanon all these sub-species are result of magical mutations, mainly induced by Discord just fo lulz.

I find it interesting that the three main pony races are mutually exclusive. If an Earth Pony and a Pegasus has a child together you know its going to be either a Pegasus or an Earth Pony (Or possibly a Unicorn). It's never a hybrid between the two. If it was about genetics you'd expect the foals to have characteristics of both races. You kind of have to invoke magic here. The magic of the three different races are simply mutually exclusive, with Alicorns being the exception. The rarity of Alicorns, their power level and the mythology surrounding them proves just how unusual it is that a pony has magic from more than one race/tribe.

The Crystal Ponies are split into the 3 main races suggesting that the Crystal trait is not mutually exclusive with the other three. A pony can be both a Pegasi and a Crystal Pony, but it can't be both Pegasi and Unicorn. This suggest that "Crystalism" is either a condition that the other races can gain. (The mane6 turning crystal supports this theory.) Or a forth pony race/tribe that can create hybrids with the other three. If that's the case then it might be hard to spot the difference between a pure Crystal Pony and a Crystal/Earth Pony hybrid.

Having only seen one Zebra it's hard to say if canonically it's another tribe/race of ponies or a separate species. If Zebras are a pony tribe then you'd expect the foal of a Zebra and a Pegasus to be either a Zebra or a Pegasus, because the pony races are mutually exclusive. If the foal ended up as a Zony, Pegazebra or something like that then Zebra genes/magic do not block the Pegasii traits like Unicorn genes/magic would.

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I kind of have to state the opposite. The three pony races are amazingly stable, being able to interbreed with each other without mixing the racial traits. That is pretty amazing from a genetic perspective and more or less requires invocation of magic to explain it.

If the other pony-like species (Zebras, Hippogriffs, Donkeys etc.) are not descended from ponies then that's that.
But if the pony like races are mutated or hybrid ponies then I agree with you. Ponies are remarkably able to adapt and mutate.

There might be a bit of both. For example Ponies and Griffins being unrelated species but Hippogriffs being the hybrid between the two.

That's as far as I can extrapolate, I think. At least from canon sources. I might have more when I finish season 8. There's plenty more from fanfiction but it works slightly different in every universe. Zonies are a thing in some and not in others. Hippogriffs is their own species in some and the hybrid between Ponies and Griffins in one.

The surprising thing is that changelings are the one species that makes sense.

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Trying to apply an understanding of human biological sciences to understanding the complexities of Equestrian biological variances is an exercise in frustration and futility. Besides, that is the thing about fiction, if you want it to happen, then it can happen, irregardless of how far removed it may be from any realization in science.