"Welcome to the UK, American robin! Now you will be eaten."

'Scientific name: Turdus migratorius'

...

Sounds like a dilemna a wildlife sanctuary had several years ago. An endangered type of hawk swooped down to kill and eat an endangered type of pigeon.

There's an ongoing problem like this on an island off California. Some non-indigenous pigs introduced a few decades ago have started attracting (endangered) Golden Eagles which also eat the islands native (endangered) foxes. Authorities considered killing off the pigs but then realized that that would likely cause the Eagles to eat yet more foxes.

That's simple. Kill the golden eagles.

I've seen the bison on Catalina Island.. I think they were brought there for a western movie shot in the 20's and just left to fend for themselves.