Self-similarity and the species-area relationship

Self-similar distributions of species across a landscape have been proposed as one potential cause of the well-known species-area relationship. The best known of these proposals is in the form of a probability rule for species occurrence. The application of this rule to the number of species occurring in primary well-shaped rectangles within the landscape gives rise to a discrete power law for species-area relationships. However, this result requires a specific scheme for bisecting the landscape to generate the rectangles. Some additional, more general consequences of the probability rule are presented here. These include the result that the number of species in a well-shaped rectangle depends on its location, not just on its area. In addition, a self-similar landscape contains well-shaped rectangles that are, in fact, not self-similar. The probability rule in general produces testable predictions about how and where species are distributed that are independent of the power law.