Sweet potatoes are native to South America, yet can be found in the pacific Islands and carbon dated back to 1200AD. Does this prove that they had contact with South American tribes?
The short answer: no.
The older belief is that there was a pre-Columbia transport of sweet potatoes from the Americas by visiting Polynesian c. 1000AD. There were also later introductions of new varieties by Europeans, and the new varieties largely replaced the older varieties, and there was hybridisation between the old and new varieties - this complicated research trying to uncover the origins of the Polynesian sweet potato. Genetic studies supported the pre-Columbian introduction of the sweet potato into Polynesia:
Also, there were studies showing American ancestry among Polynesians (from Easter Island):
which suggested the idea that, rather than Polynesians visiting the Americas, some Americans might have settled Easter Island before the Polynesians, bringing sweet potato with them. More recent work failed to detect any such American ancestry:
so this now appears less likely.
However, newer genetic studies show that Polynesian sweet potatoes diverged from American sweet potatoes about 100,000 years ago, long before either Polynesia or the Americas were settled by humans. (The problem of hybridisation of modern populations wasn't an issue - the study used DNA from a sweet potato collected by Joseph Banks from the Society Islands in 1769.) Thus, it appears that sweet potatoes made the voyage from South America unaided by humans.
The sweet potato isn't the only long-distance traveller in the Ipomoea genus. Ipomoea littoralis is found from Polynesia through the Madagascar, and is unknown in the Americas. It appears to share a common ancestor with its close American relative, Ipomoea lactifera. The two species diverged over 1 million years ago. There is also Ipomoea tuboides, a Hawaiian native with close Mexican relatives. Like I. littoralis and I. lactifera, I. tuboides diverged from its relatives over 1 million years ago. I. littoralis and I. tuboides have similar seeds as the sweet potato, and probably spread in the same way - long-distance floating.
For this study, see
This apparent much earlier pre-human arrival of the sweet potato in Polynesia in no way rules out pre-Columbian contact between Polynesians and Americans, just that the Polynesian sweet potato isn't evidence of such contact.