Why did some "beak" types survive on the new island ( with large seeds) when they could not survive on the original island?

I believe that the reason as to why some beak types survive on the new island when they could not survive on the original island is because they are adapted to grip larger seeds better than the smaller seeds. The characteristics of beaks that interfered with feeding success on the original island are the shape, size, type of edge, and ability to handle it. Adaptation help organisms to survive in their ecological niches, the adaptive traits may be structural, behavioral or physiological. 

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A, if i am wrong correct me