Self-similarity in the distribution and abundance of species

Human population growth and the subsequent increase in global resource use are exerting a tremendous pressure on the Earth's ecological systems. An improved understanding of how ecological assemblages are spatially distributed within and across habitats is at the center of our ability to quantify the risks posed to ecosystems by human activities.; The postulate of self-similarity provides an overarching theoretical framework for a unified understanding of patterns among the range, abundance and distribution of species. By casting power-law scaling relationships such as the species-area relationship (SAR) and the range-area relationship (RAR) in the form of self-similarity scaling relationships, a host of analytical predictions fundamental to ecology can be derived. Among these predictions are an endemics-area relationship, a range-abundance relationship, a community- and species-level abundance distribution, a commonality formula, and the dependence of species richness on patch shape.; Theoretical predictions stemming from the postulate of self-similarity were tested using plant census data collected from a Northern Californian serpentine biome. Several aspects of the theory were in good agreement with the data: (1) the predicted abundance of each species, (2) the predicted slopes of plots of log(range size) versus log(abundance), and (3) greater species richness on long skinny patches than on square patches of equal area. Aspects of the theory in poor agreement with the data include the endemics-area relationship, the community- and species-level abundance distribution, and the commonality formula. Possible causes of divergences from the theory are discussed.; The theory developed in this thesis was applied to quantify the risk of species extinction following global climate change for different climate change scenarios, biome shapes and taxonomic groups. Biomes that taper in area towards the poles will suffer greater species loss than those that do not. If climate warming is more intense at the poles than at the equator, mobile species loss will be greater than if climate warming was uniform with latitude. If climate warming is uniform across a biome, sessile species loss will be greater. Finally, species loss will be magnified for sessile species and habitats characterized by a large SAR exponent z.