Polynesia and the Americas were connected by ocean voyages and intermarriage before 1250 AD. New work by @alexGioannidis @morestrada and others in @nature doi.org/10.1038/s41586… 
This is a really cool study in what I would describe as "mesogenealogy". The relationships marked by IBD tracts are further than those tracked by genetic genealogy (like @23andme) but much closer than most work on ancient DNA (which mostly isn't genealogical per se)
The study shows the importance of larger and more representative sampling. Focusing on a single small area (like Rapa Nui) was actually getting in the way of finding the broader answer. The deeper pattern goes beyond the recent history of each particular place.
The form and number of contacts between ancestral Polynesian and Native American groups is not clear from the results. The paper mentions that a Kon-Tiki scenario in which ancestral Americans peopled the Marquesas is even possible.
Personally, I think that a larger network of connections operating from the Marquesas, and including many islands and large parts of the North and South American coasts is more likely (also discussed in paper). The results suggest Mexico, Colombia, and Peru were connected
