I have probably blogged this before, but if I have, it still bears repeating. The data come from a 2014 article in Current Biology that was recently blogged about by Bernard.
The autosomal genetics of the indigenous people of Polynesian Easter Island show three contributions: the largest is typical of other Polynesians. The best available evidence is that Easter Island was colonized by 30 to 100 people around 1200 CE.
Recent studies have also cast considerable light on the mechanism by which the Polynesian blend came to have a mix of about 25% Papuan and about 75% indigenous Taiwanese Austronesian genetics. This probably involved a conquest of a previously purely Austronesian Lapita population in Tonga and Vanuatu by Papuan men, probably around 500 CE, after which the resulting mixed Polynesian population expanded further into Oceania.
Two other components of Easter Islander DNA are largely absent from Polynesians, one South American, and one European.
A very homogeneous 6% of the autosomal genes of indigenous Easter Islanders are Native American. This component results from an admixture date ca. 1310 CE to 1420 CE based upon Native American DNA segment lengths and the homogeneity of the contribution. This is clearly pre-Columbian and pre-Easter Island's first contact with Europeans.
Two other strong pieces of physical evidence corroborate this genetic evidence of pre-European contact between Easter Island Polynesians and South America. On one hand, the kumara (a sweet potato native to South America), which showed up in the Polynesian diet at about the right time with a name linguistically similar to its name in South American languages. In the other direction:
[C]hicken bones were also found in Chile in pre-Columbian sites before the arrival of Europeans. Mitochondrial DNA of these Chilean remains belong to the same lines as the remains of the Oceania Lapita culture, which seems to show that the Polynesians reached America before the Europeans.
A European genetic contribution is also present in proportions that vary greatly from person to person and is made up of longer segments, which averages about 16% of autosomal Easter Islander DNA. The estimated age of this contribution is 1850 CE to 1870 CE, based upon the same methods used to determine the age of the Native American contribution. The first European contact with Easter Island was on Easter Sunday in 1722 (at which point there was a population of about 4,000), and there was major Peruvian contact in the 1860s. European diseases and other factors reduced the indigenous population of Easter Island to 110 people.
Notably, this still can't explain Paleo-Asian genetic contributions found in low percentages in a few recently contacted central South American jungle tribes, which differ from the Polynesian genetic component and also appears to be more ancient, if this is really a signal at all and not an unnoticed experimental or analysis error.
The Easter Island-South American connection seems to have had only a minimal impact on the South Americans in the long run, although it did have a discernible genetic impact on the Easter Islanders and a discernible dietary impact on all of Polynesia.