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In relation to population a sober story of environmental destruction should be paid due attention 

East Polynesia colonization was only in 12th-14th century AD

Janet M. Wilmshurst, Terry L. Hunt, Carl P. Lipo, and Atholl J. Anderson

From the Cover: High-precision radiocarbon dating shows recent and rapid initial human colonization of East Polynesia

PNAS 108 1815 (2011)

In a metaanalysis of 1,434 radiocarbon dates from the region, reliable short-lived samples

*earliest in the Society Islands CE1025-1120, four centuries later than previously assumed; then after 70-265 y, dispersal continued in one major pulse to all

remaining islands A.D. 1190-1290. 

*Previously supported longer chronologies have relied upon radiocarbon-dated materials with large sources of error.