How the Polynesians spread

A new genetic study helps confirm the way the Polynesians spread through the Pacific:

The analysis suggests canoes set sail from the shores of Samoa—more than 2000 kilometers north of New Zealand—around 800 CE. The explorers arrived first on Rarotonga, the largest island in a chain now called the Cook Islands. Successive explorers moved in all directions, island hopping over the course of centuries and eventually reaching all the way to Rapa Nui, 6500 kilometers from Samoa and 3700 kilometers off the coast of Chile, by 1210 C.E.

The seems to have narrowed down the timeline considerably:

Archaeologists already had hints of how this great exploration took place. Studying the styles of stone tools and carvings, as well as languages, of the people on the various islands had suggested the original ancestors traced back to Samoa and that the expansion ended halfway across the ocean in Rapa Nui, or Easter Island. But they disagreed on whether it happened in a few centuries, beginning around 900 C.E., or started much earlier and lasted 1 millennium or more.

What's this about Native American ancestry?:

And because the genetic evidence allowed the researchers to reconstruct the order in which the islands were settled, they could spot connections between islands that might not seem intuitive based on the geography. For example, they argue that three island cultures known for carving massive stone statues—Rapa Nui, Raivavae, and the North and South Marquesas—shared a common founder population in the Tuamotu Islands, even though they are thousands of kilometers apart and geographically closer to other parts of the Pacific.

Those three islands also hold the earliest genetic traces of Native American ancestry among Polynesians. That suggests ancient Polynesians first contacted the Americas around 1100 C.E., when the seafarers were beginning their last, and longest, expeditions. “That’s something no one could have predicted through archaeology or oral history,” Moreno Estrada says.

Oh, here's another article explaining that part:

Researchers, published in Nature, sampled genes of modern peoples living across the Pacific and along the South American coast and the results suggest that voyages between eastern Polynesia and the Americas happened around the year 1200, resulting in a mixture of those populations in the remote South Marquesas archipelago. It remains a mystery whether Polynesians, Native Americans, or both peoples undertook the long journeys that would have led them together. The findings could mean that South Americans, hailing from what’s now coastal Ecuador or Columbia, ventured to East Polynesia. Alternatively, Polynesians could have arrived in the Marquesas alone having already mixed with those South American people—but only if they’d first sailed to the American continent to meet them.

Alexander Ioannidis, who studies genomics and population genetics at Stanford University, co-authored the new study in Nature. “The genes show that the Native Americans who contributed came from the coastal regions of Ecuador and Columbia,” he says. “What they can’t show, and we don’t know, is where exactly it first took place—on a Polynesian island or the coast of the Americas.”

 So, some Native Americans might have made it to, say, Rapa Nui, kon tiki style.  I thought that had been discredited - but it was more the idea that all of Polynesia came from the East, rather than the West.