The conclusion for this particular observation would be that one of the finches has food sources on both islands, thus lives on both of them, while the other finch has food sources only one of the islands, thus lives on that island. The food sources about which the finches, or any other organisms, have specialized, determines where they can be found. If there is sufficient amount of the food source to support a population, then the species can and will probably live there, but if there isn't then the species can not, and will not live there.
