'If you had to pick within that core region, Samoa is, on every bit of evidence I know of, the homeland for the Eastern Polynesians,' says Green.
The place names themselves give the game away: Savai'i (Hawaiki) in Samoa, with Tonga ('south') to the south and Tokelau ('north') to the north.
Gradually the early Polynesians improved their canoes. Although their ancestors probably had outriggers and sails from the time they left Taiwan, it was not until about 2000 years ago that they developed double-hulled sailing canoes up to 24m long, almost as big as the European ships that explored the Pacific from AD1520.
In an extraordinary burst of voyaging, they travelled to the Cook Islands, Tahiti, the Marquesas and the extremities of Hawaii and Easter Island, all probably before AD900. Only New Zealand remained unoccupied until AD1200-1300, although visitors may have got here earlier.
The evidence of the kumara shows that Polynesian traders got as far as South America and returned with the gourd and the harpoon as well as the sweet potato. Two American scholars are to publish an article suggesting they also reached California.
Yet this remarkable voyaging era did not last. Limited contacts persisted, such as marriages between chiefly families in Tonga and Samoa. But by the time Europeans arrived, the outliers of Hawaii, Easter Island and New Zealand had all lost contact with the outside world. Sails disappeared from Eastern Polynesia as populations grew and became self-sufficient.
Pottery was abandoned, possibly because earth ovens did not need clay pots, or possibly for social reasons. 'Who made the pots? It was the women,' says Green. 'Who makes wooden vessels? The men.'
On the other hand warfare, which does not show up in the archaeological record of the Lapita period, became dominant as population pressure rose in the isolated societies of New Zealand and Easter Island.
Almost everyone, including me, has pontificated on how terrorism and big government destroyed the social order and its underlying environment on Rapa Nui. Pacific history should be studied a lot more widely than it is.