In today's column, Polly Toynbee writes:
Think of Easter Island and the history of its destruction, recounted by Jared Diamond in his book Collapse. The Easter Islanders became so obsessed with their own status symbols, the moai - the mighty stone statues for which their island is famous - that in erecting them they destroyed every tree that made life on the island sustainable, competing clan against clan in statue-building. They starved when there was no wood left to build canoes for fishing.
When Thor Heyerdahl visited in the mid-1950's, there was still a tree on Easter Island living, a toromiro, so not every tree was destroyed, according to, er, Jared Diamond. In addition, it is clear that there was a substantial drop in population on Easter Island, but life did not stop being sustainable -- as of 2002, there were 2,269 Rapanui (the native Polynesian inhabitants) living on the island (source).