Do we need to define what is a "natural right"?
The human definition is that it is something I'm entitled to and cannot (meaning should not) be taken from me. If you apply that to animals (as you imply...)
...then it should be illegal to stop a wolf from roaming the city streets, hunting your pets, and that if a person tries to kill said wolf and gets killed by the wolf instead, the wolf should go free... after all, it was self defense.
Or are you saying these things are just the nature of animals and we can't change them... and does that mean we should allow animals to exercise these rights unfettered?