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The Common Brushtail Possum was introduced to New Zealand by European settlers in an attempt to establish a fur industry.
They soon escaped into the wild where they have thrived as an invasive species with great numbers: around 60 million individuals estimated. There are no native predators of the possum in New Zealand. There have been numerous attempts to eradicate them because of the damage they do to native trees and wildlife, as well as acting as a carrier of bovine tuberculosis. For New Zealand, the introduction of possums has resulted in as much of an ecological disaster as the introduction of rabbits has been in Australia.
http://en.wikipedia.org/wiki/Possum