Ah! It varies from creature to creature so... I know that I have a few that don't evolve at all, like my Emolga, and some that need stones, like my Sunflora. If you show me everyone you have I could tell you if and about what power levels they should evolve at? I've put a lot of research into it because some you want to encourage not to evolve because they stop learning after they do.

Get stronger, yes, learn new abilities, no.