The Blue Lagoon by H. De Vere Stacpoole

The woods here had been less affected by the cyclone than those upon the other side of the island, but there had been destruction enough. To reach the place he wanted, Dick had to climb over felled trees and fight his way through a tangle of vines that had once hung overhead.

The banana trees had not suffered at all; as if by some special dispensation of Providence even the great bunches of fruit had been scarcely injured, and he proceeded to climb and cut them. He cut two bunches, and with one across his shoulder came back down through the trees.