There weren't unlimited resources. Each of the Pacific islands (except to some extent the large ones like Hawaii, which was settled late) got to carrying capac

There weren't unlimited resources. Each of the Pacific islands (except to some extent the large ones like Hawaii, which was settled late) got to carrying capacity pretty quickly after settlement, and populations were balanced through some variety of ritual warfare, cannibalism, infanticide, and starvation. Plus, it doesn't take everyone doing it. It only takes a couple families in a couple boats, each generation, to hop across the whole ocean.