Yes, they are a major problem out there, nearly wiping out a lot of the local wildlife.
It's much the same in New Zealand with introduced species. Out walking in the countryside, the sound of birdsong is virtually absent. Many, many years ago rabbits were introduced. When they got out of hand, some bright spark decided to introduce stoats/weasels to get rid of the rabbits. They decided that the local bird life, who had never seen a stoat, were an easier option.
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