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melanesian paternal line
east asian maternal line
Four thousand years ago there were no polynesians. The islands of polynesia, roughly speaking those islands in a longitudinal line from Hawaii, down through Tonga and Samoa to New Zealand and across the Pacific to Easter Island, had no human inhabitants.
There is a consensus among linguists that the languages of Polynesia can be traced back to the aboriginal people of present day Taiwan. That is to the people living in Taiwan from 8,000 years ago, before the migration of Han Chinese in the seventeenth century. They share ancestry with the people of Malaysia and the Phillipines, and their eyes do not have the epicanthic folds associated with 'Chinese'. Asian, but not Chinese Asian.
The archeological evidence is that present day polynesian culture had its origins in Melanesia. The islands of Melanesia, from New Guinea to the Solomons, Vanuatu, Fiji, and New Caledonia were inhabited perhaps as long as 30,000 years ago. Melanesian physical features include dark (black) skin, flat (bridgeless) nose, everted lips, woolly hair
Polynesians are phenotypically distinct from both Asians and Melanesians. They were generally postively described by early European explorers as having "much cause to praise their creator" (Mendana), "..of the larger size of European, all excellently made.." (Beaglehole), "I never saw men better made" (Bougainville). Today, Polynesian males perform well in contact sports. Indeed, it is said that Tonga has the greatest' proportion of professional sportsmen of any race in the world. The photo above is of Roger Tuivasa-Sheck a Samoan born professional rugby league player.
Studies of limited size (such as that of Kayser et al, 2008) suggest that Polynesians almost all have an Asian great...great-grandmother (94% in Kayser's sample of 47 have East Asian mitochondrial DNA) but 67% have Y chromosomes derived from a Melanesian great..great-grandfather.
However, breedings between Melanesian men and Malay women today do not produce polynesian babies. So, why are there polynesians?
The standard answer is 'natural selection acting on accumulated mutations or other copying errors'. But 4,000 years is nowhere near enough time for this version of 'gradualism' to produce this degree of change. If true, this answer requires that Polynesians have beneficial mutations compared to Melanesians (for example) which could perhaps be true. However, what is implausible is that early polynesians on different islands had the same mutations, or that they had different mutations with the same effect.
Another orthodox answer is to point to the different environment of, say, Samoa, compared to either Papua New Guinea or Malaysia. But, if a Melanesian and a Malay do their breeeding in Samoa, have their baby there, and then continue to live there, the baby will not look like a Samoan.
One possible theory of origins is that for a period, beginning some 4,000 years ago, there was a tendency for groups of young Melanesian warriors to head into Asia, capturing slaves including women. Those who then chose to sail into the Pacific bred with the women.
This natural experiment in evolutionary development has a number of features
The suggestion is that a polynesian is distinguished not by his or her genes, but by which genes are available for expresson when and for how long, that is by the changing genome topology over a lifespan (see www.genometopology.com).