Not necessarily, if you take the hindu system for reincarnation, it is said that "human" souls are developed from "animal" souls (Humans are supposed to have primordial chakras left over from our lives as animals down towards the legs as well, but they are unimportant/much less energized than the ones along the spine)
Of course this same system also says that there is a chance for souls to "revert" to less sophisticated lives. I.E.: if you are degenerate enough you could be reborn as an animal.
But I am hardly an expert, just opinions and educated guesses…