You know, I think I’ve been asked this before, ages ago; hold on a bit…
…wait, hang on.
That was YOU! YOU’VE asked me this before!
Ah, whatever; it was nearly four years ago, I’m sure I have different and even more wildly speculative things to say about it now.
So, my standard line on this is that I think (most) stone-evolved forms are actually vestigial – that is, once upon a time, all Pikachu (for example) naturally had the ability to evolve into Raichu at a certain stage of their development, but they shed that ability because it became maladaptive in a changing environment. Maybe Pikachu and Raichu filled slightly different ecological niches, and Raichu’s particular niche vanished due to changing environmental conditions; perhaps Raichu’s lower energy efficiency became a liability because certain food sources disappeared from their habitat. Basically, there was some reason other than straight-up combat prowess that made Pikachu a better-suited form to the conditions they lived in. This is a thing that evolution will do sometimes that seems counterintuitive to us – an adaptation that we might consider “powerful” will turn out to be too costly, relative to its usefulness (like flight in a lot of bird species from New Zealand, where I come from; if you have no natural predators, you don’t need to fly, and flying is hard bloody work). So what happens in the case of these Pokémon is that they technically still “have” their evolved forms in their genetic code, but they’ve lost all the triggers that would have caused them to activate those forms at a particular stage of their life cycle. Something about the energy of the stone reactivates the vestigial transformation. This makes a lot of sense to me because these forms are practically nonexistent in the wild (at least, in the games; the anime has some exceptions but there’s usually an explanation), and are clearly unnecessary to the survival of an individual, a community, or the species as a whole.
And that’s my standard line on this; the problem is I just talked to Jim the Editor about it and he thinks I’m coming at this from the wrong direction. He thinks we’re supposed to understand the stones as providing the energy for a jump forward – that is, they give a Pokémon a major energy boost and also provide them with direction to channel that boost in the form of the elemental force/essence/whatever within the stone. And like a lot of things, I think this is probably closer to the answer Game Freak would give you if you pressed them on it, but actually makes less sense to me. We’re basically thinking of the stones as mutagenic here, in that they accelerate the normal process of evolution (here meaning Darwinian evolution, not that weird bull$#!t that Pokémon do), but I’m concerned that if that were the case then we shouldn’t expect all individuals to be affected in the same way. There should be an element of randomness in what happens upon exposure, with all Pikachu gaining somewhat different sets of new abilities and physical traits when they evolve into Raichu. It’s also not clear in this case why the stones only affect a handful of Pokémon species. Again though, I think this is probably closer to what Game Freak have in their heads, because aesthetically it makes more sense; evolution for them is about attainment, progress, motion towards perfection, but in my interpretation it instead becomes about regression, in a way, which I think is something they wouldn’t particularly like.
Anyway, like I said the last time this came up, the Dawn Stone evolutions would in this case just be the vestiges of what was once a split evolution based on gender, where (almost) all male Kirlia once became Gallade, and (almost) all female Snorunt once become Froslass, but at some point it became more beneficial to have male Gardevoir and female Glalie instead. Why there seems to be a particular type of stone connected with these gender-specific evolutions is beyond me, though (and it does seem clear that Game Freak intended for this to be a specific property of the Dawn Stone; it’s only associated with these two Pokémon, and it’s the only stone type hasn’t gained any more evolutions since generation IV). This kind of idea happens to be easiest to accept if you also believe my unarguably bat$#!t ideas about what Pokémon gender is – i.e. that Pokémon gender, and the mechanisms that determine reproductive compatibility among Pokémon, are primarily psychological phenomena, and Pokémon don’t actually have biologically differentiated sexes (’cause then you don’t need Gardevoir with male reproductive organs to be a new thing that appeared out of nowhere).
As for the Moon Stones… well, the Pokémon they evolve are kind of a grab-bag; Clefairy, obviously, is closely associated with the moon, outer space, the cosmos, etc, and I think Jigglypuff and Munna fit because they’re both linked with sleep, and therefore with night. I’m not sure about Skitty. Now, for Nidorino and Nidorina, I think the most likely explanation (and I feel like I can’t be the first person to come up with this, but it doesn’t seem to be widely agreed) is probably because they’re actually supposed to be rabbits, and rabbits are lunar animals in East Asian myth and folklore. Where Europe and North America see a “man in the moon,” most of East Asia sees a rabbit, often with a mortar and pestle (Poison-type connection there? Eh; that’s a stretch even for me). When you look at it that way, it’s actually kind of odd that they never got any other lunar powers, like access to Moonlight or Moonblast.