I have no idea how those Polynesians supposedly sailed across open ocean to South America. If they could do it, you'd think they also would have built structures in Chile that we could find remnants of today. According to that article Polynesians were in Chile in the Middle Ages....recent enough that you'd think we could find traces of their settlements there, if they had any.
Start with Heyerdahl and his voyage on the Kon Tiki, to prove that P. came from South Am. He made the trip but sadly turns out he was wrong.http://en.wikipedia.org/wiki/Thor_Heyerdahl
From "Daughters of Eve" ch.7 pg.103-104
"The first Europeans to reach Ploynesia saw canoes over 30 meters long, and smaller version still used today. The double hull prevents capsizing in the same way as an outrigger on a catamaran. The vessels had a prow at each end, and so it could be tacked across the wind and then reversed without turning round. These were the vessels that carried the Polynesians into the Pacific......complimentary and equally crucial navigational skills.....fairly straightforward to travel along a line of latitude by keeping an eye on rising and setting stars...."
I can elaborate if you have specific questions. So, there matching DNA markers found in Vanuatu and Chile but it is very rare, maybe Poly. only wanted to settle uninhabited lands. We know the sweet potato is native to the Andes.
Did early Poly.'s give women in exchange for s.potato?
Purely speculation on my part.