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Seed eating finches migrated to different habitats, adapted the different feeling methods, by altered beak structure, evolved into different types of finches.
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When new habitats become available, one species may "radiate" out of one location to colonize them. This eventually results in that one species evolving into several different species as they adapt to new conditions. 

Darwin's finches (actually, they are tanagers) are good examples because they include about 14 different species that originated from one species. These evolved into different species as the birds adapted to different feeding habits on the various Galapagos Islands.
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