The Biology of Elves and Men.

[Nurvingiel]

In Biology class, we learned that the definition of a species is:

One that can interbreed to produce viable, fertile offspring, and who have similar physical characteristics.

In this case, wouldn't Elves and Men be the same species?

Example: Donkeys and horses are considered to be seperate species because their offspring, mules and hinnies, can't have children.

Luthien and Beren had children who were in turn able to produce fertile children for generations. (A dry, scientific run-down of an amazing love story, I know, but love is for Arts majors. )

Elves and Men also have decently similar physical characteristics, in that they have two legs, two eyes, hair, etc.

Are they the same species, or, as defined in Middle-earth, the same race?

If they are not, why not?