Wurmple has two evolutionary paths, via Silcoon to Beautifly and via Cascoon to Dustox.
In the original games this is based on Personality Value. There is no sign this is yet in Pokemon Go, so how is is determined in this game?
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There are the a few articles online that come up talking about how to Evolve Wurple to either Silcoon of Cascoon. As it appears, there seems to be no way of dictating what it will evolve to at the moment:
In Pokémon Go, Eevee's evolution into Flareon, Jolteon or Vaporeon could be determined by giving your Eevee the respective nickname.
Unfortunately this is not the case with Wurmple and nicknames have no effect.
At the moment it appears that Wurmples evolve randomly in Pokémon Go which means you need to catch as many as you can to get the evolution you want.
~an extract from The Sun's article
DOES WURMPLE’S EVOLUTION DEPEND ON GENDER?
Looking at Dustox and Beautifly, it’s easy to think that Wurmple’s gender will determine its evolution, but that wasn’t the case in Pokémon Ruby and Sapphire. It’s also not the case in Pokémon Go .
User VarecnaV89 asked whether evolving Wurmple with different gender and they confirmed that they received the same Pokémon.
DOES TIME AFFECT IT?
When Gen 2 came to Pokémon Go, Eevee’s new evolutions, Umbreon and Espeon, could be obtained by evolving Eevee during either the night or day. With Dustox being a moth, many believed the time of day affected Wurmple’s evolution. However, that turned out to be untrue as well, as trainers in this thread determined.
IS IT A NICKNAME TRICK?
Pokémon Go trainers found that evolving Eevee into Flareon, Jolteon or Vaporeon could be determined by its nickname. The nicknames used were the based on the Pokémon anime, so some trainers believed nicknaming their Wurmple after trainers who used them in the anime would do the trick. However, trainers tried naming Wurmple May to get a Silcoon, and Jesse for Cascoon, and that didn’t work.
DOES WURMPLE’S IVs DETERMINE ITS EVOLUTION?
Tyrogue is another Pokémon from the Johto region with an unusual evolution, which could evolve into either Hitmonlee, Hitmontop or Hitmonchan depending on the Tyrogue’s IVs. Naturally, this led trainers to test whether Wurmple’s IVs
User Technovoid200 tested this theory, and thought they were on to> something, but eventually concluded IVs didn’t determine Wurmple’s evolution.
Unfortunately, it looks like Wurmple evolves randomly in Pokémon Go, so be sure to catch as many as you can to get the desired evolution. In the meantime, let us know whether you like Dustox or Beautifly better in the comments section below
Extract Passage from Player One's article