Middle Earth does not have a single tree of common descent, but multiple acts of special creation, each of which then speciates further.
Souls are directly created by Eru for all sentient races (elves, men, dwarves, ents) and sent directly from outside creation.
I reached the bit about the dancing bears.
Rabbits and chickens were not native to Beleriand. (Another point for the European theory.)
Elves do not eat mushrooms, apparently.