There is an interesting article in American Scientist about Easter Island (Rapa Nui). Easter Island has been used as a morality tale, most famously by Jared Diamond who has used Easter Island as a warning about what happens to societies that destroy themselves by overexploiting their resources. New evidence points not to overexploitation, but to the introduction of rats by the Polynesian colonists, and later contact with Europeans, new diseases, conflict with European invaders and enslavement as the sources of the population collapse.
The first settlers arrived from other Polynesian islands around 1200 A.D. Their numbers grew quickly, perhaps at about three percent annually, which would be similar to the rapid growth shown to have taken place elsewhere in the Pacific. On Pitcairn Island, for example, the population increased by about 3.4 percent per year following the appearance of the Bounty mutineers in 1790. For Rapa Nui, three percent annual growth would mean that a colonizing population of 50 would have grown to more than a thousand in about a century. The rat population would have exploded even more quickly, and the combination of humans cutting down trees and rats eating the seeds would have led to rapid deforestation. Thus, in my view, there was no extended period during which the human population lived in some sort of idyllic balance with the fragile environment…
The human population probably reached a maximum of about 3,000, perhaps a bit higher, around 1350 A.D. and remained fairly stable until the arrival of Europeans. The environmental limitations of Rapa Nui would have kept the population from growing much larger. By the time Roggeveen arrived in 1722, most of the island’s trees were gone, but deforestation did not trigger societal collapse, as Diamond and others have argued.
The article by Terry Hunt is here.