Quote from Turbophoenix
As for your thylacine example, well they were pretty much extinct on the mainland well before Europeans even discovered Australia, so I honestly don't think humans did much to wipe them out. We definitely helped to kill them off, but they would have died out within a few hundred years anyway. The sea cow is also a similar story - when they were discovered by Europeans it was estimated that there were only 1,500 left.
Just because the Europeans only finished them off doesn't mean humans had nothing to do with them being nearly extinct on the mainland already; the indiginous tribes could also have been hunting them to protect their cattle if they had any. That would also explain why they still survived in Tasmania till the Europeans came; since it's an island there would have been fewer humans.
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