# Modeling species distributions by breaking the assumption of self-similarity

15 August 2009Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte’s bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.