Well to begin, the theory of island biogeography is built off of three principles including population, ecology, and genetics. This explains to how immigration and extinction are regulated on islands.
So to answer your question the number of species are going to be far smaller on a small island versus a large island. Why? Because the smaller the island the less diversity of species on the island.
Also more species of animals are going to be located on an island closer to the mainland than further away. This gives species more opportunity to "travel" inbetween the mainland and the island. Less species will be likely if an island is more remote.
A great example would be the Galapogos island, which is a larger island closer to the mainland which has a great variety of species.