two separate pieces of evidence (appearing in two separate studies) that suggest that the Polynesians of Easter Island mixed with the natives of South America. One study reports two Polynesian skulls that were found in Brazil among the indigenous Botocudo tribe. (Yes, you read that correctly, Brazil!) The other study, shows that the Rapa Nui (Easter Islanders) have 10% South American ancestry, which has been traced back 19-23 generations. I wonder if this explains how the sweet potato made it to south-east Asia. In a related paper by Goncalves et al., we find the following:
New evidence from human and nonhuman material has become available since then. For example, there were archeological findings of Polynesian chicken bones in the Arauco Peninsula, in Chile and evidence has been found in Easter Island of pre-Columbian presence of sweet potato and bottle gourd, both typical of South America. Independent of the plausibility or implausibility of the pre-Columbian arrival of Polynesians to the South American Pacific coast, there still would remain the need to explain how these migrants crossed the Andes and ended up in Minas Gerais, Brazil. We feel that such a scenario is too unlikely to be seriously entertained.
So the sweet potato may have made it to Easter Island at least. The Goncalves et al. paper, which discusses possible explanations for the two skulls, also considers the possibility that they're from Madagascar slaves. (Madagascar was originally settled by Polynesians.)