Just stumbled upon a recent genetics study that has given some evidence for Amerindian genetic influence on Easter Islanders predating European contact. Here's a news link from the time of its presentation 2011:
http://www.telegraph...ican-roots.html
And here is the full journal article published last year:
http://rstb.royalsoc...7/1590/812.full
Basically they tested two sets of samples, one which had been collected in 1971 and frozen, and another collected in 2008. They restricted the sampling to people with documented lineages to avoid picking up markers from modern mixing. Thus they can be almost certain that the Amerindian genetic contribution predates the slave trade of the 19th century, and that it probably predates all European contact (given the possibility that a European vessel might bring some Amerindians along with it).
They performed three types of tests: mtDNA, Y-DNA, and HLA. For both sets of samples they found mtDNA to be exclusively Polynesian, while the Y-DNA was mostly Polynesian with a few samples having European haplotypes. But the HLA revealed traces of Amerindian ancestry. The first set revealed alleles exclusive to Amerindians, and most concentrated in the northern Peru/Ecuador/Colombia region (fitting with the idea of Inca contact). The second set revealed different alleles than the first, but which were still exclusive to Amerindians. But these are most concentrated in the southern reaches of the continent, in Chile/Argentina/Southern Brazil. So this might suggest that contact occurred at multiple times with different groups.
The authors also noted a study from 2007 which found that chicken remains, dated to 1300-1400 and found in Southern Chile, carried mtDNA typical of Polynesian chickens. So it seems there is a growing body of evidence for contact between Polynesia and South America, including food (chicken, sweet potato) and human genetics.