An equirectangular projection of Polynesia, created from the same data as Worldmap wdb combined.svg. Inkscape was used to add colour, clip the land, and add in migration arrows.
Own work. Migration arrows are supported by the following sources.

From Taiwan through Melanesia to Polynesia, and earlier migration to Australia and New Guinea:
Yoshan Moodley, Bodo Linz, Yoshio Yamaoka, Helen M. Windsor, Sebastien Breurec, Jeng-Yih Wu, Ayas Maady, Steffie Bernhöft, Jean-Michel Thiberge, Suparat Phuanukoonnon, Gangolf Jobb, Peter Siba, David Y. Graham, Barry J. Marshall, and Mark Achtman (2009). The Peopling of the Pacific from a Bacterial Perspective, Science 23 January 2009: 323 (5913), 527-530. doi:10.1126/science.1166083
Colonisation of East Polynesia, and dispersal to more remote islands (including Hawaii, Easter Island, and New Zealand):
Janet M. Wilmshurst, Terry L. Hunt, Carl P. Lipo, and Atholl J. Anderson (2011). High-precision radiocarbon dating shows recent and rapid initial human colonization of East Polynesia, Proceedings of the National Academy of Sciences of the United States of America, February 1, 2011, vol. 108 no. 5, 1815-1820. doi:10.1073/pnas.1015876108
David Hall (Gringer ), translated:--MacedonianBoy