In Latin America, there's ceviche, that originally Peruvian dish of raw fish "cooked" (well, whitened and stiffened) from being marinated in lime juice. In the islands of the South Pacific, people often make a dish called ika ota by marinating raw fish with lime juice and coconut milk. Remnants of an ancient South Pacific Rim cuisine?
Afraid not. The Polynesian dishisn't necessarily "cooked." The lime juice is optional, because it wasn't part of the original recipe. Citrus fruits were unknown in Polynesia until Europeans introduced them in the 18th century.
In fact, though Hawaii is a paradise of tropical fruit today, there were no fruits at all there when the first Hawaiians arrived--nothing but coconuts. And things pretty much stayed that way. During the Middle Ages, only the banana and a fragrant but not very sweet fruit known as 'ohi'a-'ai or mountain apple (Syzygium malaccense) made their way to Hawaii. (Hawaiians also call the tomato 'ohi'a.)
Otherwise, all the fruits Hawaii is known for have arrived in the last 200 years. Pineapple and passion fruit came from Brazil, the mango from India, the papaya from Central America. The guava, and even poha, an odd tomato-like fruit (otherwise known as Cape gooseberry) that a lot of people imagine to be native to Hawaii, were both domesticated in Peru. Poha's scientific name is Physalis peruviana.
And as for the Peruvian ceviche, it might not be a terribly ancient dish itself. The name seems to be Spanish (derived from "cebo," fish bait--evidently an unflattering comparison to what fishermen call chum). And before the Europeans arrived, there were no citrus fruits in Peru either.