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Now, although design-wise Deoxys and the Tangela line are very similar, Deoxys has a lot of additional things that need to be explained. Firstly, Deoxys is far more powerful than Tangela / Tangrowth. I believe this is due to the gem / crystal that is socketed in its chest. In its dex entries, it states that “An alien virus that fell to earth on a meteor underwent a DNA mutation to become this Pokémon”. It seems to be that the meteor (which contained the gem) was the reason Deoxys came to be, and the catalyst for causing the alien virus to mutate. Therefore, the meteor / gem / crystal must contain considerable power.
Deoxys can regenerate much faster than the Tangela line, and it also possesses the psychic type, rather than the grass type that the Tangela line has. However, this is again due to Deoxys’ gem. The reason for Tangela’s and Tangrowth’s grass typing is due to them not having the gem. Without it, their cellular abilities aren’t as strong as Deoxys’, and they can only produce plant cells easily, leading to their vines and grass moves, as well as typing.
Now, as said before, there are two strong theories as to how Tangela / Tangrowth and Deoxys are actually related / connected / the same Pokemon.
Theory One is that Tangela is the result of Deoxys’ arms being cut off and regenerating into Tangela, which then further reproduce to make more Tangela. The reason ancient power is required to evolve to Tangrowth is that it shares enough properties with the meteor / gem Deoxys has to enhance Tangelas power and evolve. I’m not sure whether Tangrowth could use ancient power to develop Deoxys’ gem for itself and become a Deoxys, or if Tangrowth is the furthest it can go.
Theory Two is that when the meteor mentioned in Deoxys’ dex entry hit, it hit a Tangela or Tangrowth, and the alien virus and meteor gem combined with Tangelas DNA which resulted in Deoxys.