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Based on the island variations and the curved beak, I think it's loosely based on the Hawaiian honeycreepers. They all diversified from an ancestral finch that arrived on the islands and evolved to suit different habitats. Very colorful, cool birds.
This kind of thing happens in archipelagos around the world. Fun fact: the famous Darwin finches in the Galapagos are not real finches. They probably evolved from a member of the tanager family.