I read about sweet potatoes in Polynesia being considered a sign of contact between the Polynesians and the Americas in this article: http://www.pbs.org/wayfinders/polynesian6.html, and it made me wonder, what kind of contact did the Polynesians have with other peoples. I understand that the distances between each island or group of islands were immense, so a lot of trade and other similar must have been quite difficult. So, once any certain island was colonized, were people largely limited to that island and would lose contact with other peoples? Would they be limited to their archipelagos and "island groups"? How much would they know about the world outside their islands? And if there was significant interaction, what kind of interaction would there be: just trade, or political/warfare oriented interactions? Thanks!
I answered a similar question earlier- so feel free to [check it out] (https://www.reddit.com/r/AskHistorians/comments/2z8ncl/how_much_contact_would_polynesian_islands_have/cph4z4v).
So answer somewhat more briefly here-
once any certain island was colonized, were people largely limited to that island and would lose contact with other peoples?
They were not by and large limited to the island that they settled on. After all, islands were usually settled through successive voyages. Near-islands might see many return trips as the island was prepared for settlement (most food crops we associate with the Pacific involve planting/agriculture- the islands are not naturally full of delicious things); more distant islands would likely involve voyages of discovery and then voyages of settlement in which animals and crops would be brought. Eventually- as genealogical links between island chains became more distant, voyaging tailed off between distant points (the example I used in that link was Hawai'i - Tahiti). Worth noting that other expansive island chains- though not Polynesia- such as the Carolines continually saw long distance voyages of trade and ritual until the nineteenth century (though there is still a fair bit that continues today). One reason that contact or long distance voyaging declined between distant polynesian settled island chains was a lack of material motivation. The island chains were self-sufficient- and most islands- and most districts on islands- were self sufficient. We see some goods; especially high quality stone axes, such as those from the quarry at Vitaria on Rurutu being widely distributed between nearby island chains- but as a general rule, those goods likely flowed through smaller trading circuits that gradually saw them carried out throughout what today is French Polynesia.
Would they be limited to their archipelagos and "island groups"?
Generally they stuck to their island groups, though long distance voyaging was not out of the question, so I would hesitate to say 'limited' when really there was just no need. [In another post] (https://www.reddit.com/r/AskHistorians/comments/2pqxzp/when_captain_cook_discovered_hawaii_did_he_bump/cmzesiy) I wrote some about Captain Cook's relationship with a Tahitian navigator named Tupaia who demonstrated extensive knowledge of nearby islands and groups though he had visited few of them. The Polynesian heartland of Samoa-Tonga-Fiji saw extensive voyaging between those three island groups; just as we know extensive voyaging took place between the island groups (except the Marquesas) that make up French Polynesia. Yet, I would say all of those island groups or archipelagos are relatively near- and don't involve quite the same distance to reach the outliers of Aotearoa, Rapa Nui, or Hawai'i, so those three are almost special cases in Polynesia and weren't involved in the same level of sustained inter-archipelago trade/voyaging.
How much would they know about the world outside their islands?
Depends on the islands. The heartland islands of Tonga-Samoa-Fiji had voyages pretty constantly going between one another and had important political and genealogical links to one another- so rulers (and keepers of genealogies) were likely pretty well informed considering the time. Otherwise, as the story of Tupaia illustrates, navigators had pretty extensive knowledge of where- or how to get to islands they had never been to. Often these 'directions' were maintained through chants and stories which were continually passed on. So- how much might a normal person know of other islands and places? As I said in a previous answer, it would likely depend on whether or not they had genealogical links to them and maintained some sort of family connection.
And if there was significant interaction, what kind of interaction would there be: just trade, or political/warfare oriented interactions?
Trade/political (ritualized) interactions were common. Goods, especially high quality ones, moved within and between trading circuits. Food in some instances moved between islands; for example the low islands of the Tuamotu's traded specialized shell hooks and knifes, or large pearls, for crops from high islands like Tahiti that they could not grow on their atolls. Political and warfare interactions were definitely important between Tonga-Samoa-Fiji; Fiji was an important source for raw materials- excellent wood for making ships, red feathers for royalty, things that were not always acquired very peacefully.
Probably the best recent book to recommend on this:
Though check out the links, there are some other good recommendations!