Polynesians are mostly descended from a population on Taiwan, represented today by Taiwanese aboriginals, and from a Melanesian population similar to New Guinea or the Solomon Islands. They’re about 25% Melanesian autosomally, 6% Melanesian in mtDNA, 65% Melanesian in Y-chromosomes.
Until recently, the dominant model was the slow-boat hypothesis, in which the Taiwanese-derived Lapita culture mixed with Melanesians in New Guinea and the Solomons before sailing out into the deep Pacific. The funny numbers for mtDNA and Y-chromosome were explain by some hand-waving matrifocal cultural bullshit.
Now they’ve looked at ancient DNA from Tonga and Vanuatu. The old samples don’t have any noticeable amount of Melanesian ancestry. So it was like this: the Lapita derived from Taiwan (thru the Philippines), settled Vanuatua and Tonga – then were conquered by some set of Melanesian men, who killed most of the local men and scooped up the women. Probably their sons extended the process, which resulted in a lower percentage of Melanesian ancestry while keeping the Y-chromosomes mostly Melanesian.
After this conquest, the Polynesians expanded further east, and those later settlement (Tahiti, Marquesas, Hawaii, etc) all had that ~25% Melanesian component.
If you want to approach this kind of problem with reasonable priors, read Robert E Howard, not Brian Ferguson.