Does the self-similar species distribution model lead to unrealistic predictions?

J. Harte et al. demonstrated that the power law form of the species-area relationship may be derived from a bisected, self-similar landscape and a community-level probability rule. Harte's self-similarity model has been widely applied in modeling species distributions. However, R. D. Maddux showed that this self-similarity model generates biologically unrealistic predictions. We resolve the Harte-Maddux debate by demonstrating that the problems identified by Maddux result from an assumption that the probability of occurrence of a species at one scale is independent of its probability of occurrence at the next. We refer to this as a "non-heritage assumption." By altering this assumption to one in which each species in the community has an occupancy status that is partially inherited across scales (a scale-heritage assumption), the predictions of the self-similarity model are neither mathematically inconsistent nor biologically unrealistic. Harte's self-similarity model remains an important framework for modeling species distributions. Our results illustrate the importance of considering patterns of species co-occurrence, and the way in which species occupancy patterns change with scale, when modeling species distributions.