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The finches that survived have a beak that's 1.12 mm bigger than they normally did. Because those finches that survived have larger beaks than the ones who didn't. 

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This proves that natural selection helps with survival instincts. They were able to survive with the longer beak with more than 50% of their population not there.

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When the plant life went down from almost 20 seeds per square meter to 0 to 3, the long beak finches survived.

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When the rainfall went down in 1988 from 600 mm to 0 mm of rainfall only the large beak finches survived.

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This proves that natural selection is helping the finch with the longer beak would be able to get more food. In 1976 they were able to survive with 751 finches on the island, and and 2 years later in 1978 there was only 90 finches left on the island proving that they were able to stay alive with the longer beaks.

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This proves it was natural selection because the finches with the longer beaks have better survivability because they can get more food and water with 98%of their population gone.