…Actually, there ARE real animals in the series, albeit only during the first and second season due to many of them not having Pokemon equivalents. Some good examples would be the fish in the fish tank in the Cerulean City Gym, and a mongoose illusion made by a Ghastly to scare Jessie's Ekans.

Since the appearance of actual animals have stopped as of the Ruby/Sapphire saga, I'm under the belief that Pokemon are driving "regular" animals into extinction…

If they haven't been already.

In Digimon:

I don't know if they do that the same in Pokemon.