Geometrical effect of island shape on the species richness

We introduce a new immigration model which merges two aspects of island length. One aspect is determination of colonizer's chance of reaching recipient island, and the other is constraint on the statistical self-affinity (anisotropy) of island shapes. This immigration model derives the famous power law on species-area (SA) relation, which shows that the number of species on the anisotropic island is constrained by not only the size of the island area but also the shape of the island. From this viewpoint, we analyze an SA curve of the land snail fauna in Ryukyu arc, Japan. Moreover, we show that species of the most previous studies have immigrated along the island chain due to the stepping-stone dispersal.