There's an island far from anywhere, Gough Island. With the human population out of control nearly everywhere Gough Island has become a critical breeding ground for many bird species. However visiting ships in the past brought mice to the island. With no competitors the mice are now everywhere, grown huge, and have taken to attacking bird chicks. There's a video on You tube (warning, it is disturbing) showing how they can kill a chick in just a few short nights:



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It really shows how we can really screw up an environment with something as simple as a few mice.  There is a plan to clean the island of mice.  Sadly removing all wild pigs in the US really isn't possible.

BTW - The comments for the video can be quite ignorant.