We present an explanation for the widely reported power-law species-area relationship (SAR), which relates the area occupied by a biome to the number of species that it supports. We argue that power-law SARs are a robust consequence of a skewed species abundance distribution resembling a lognormal with higher rarity, together with the observation that individuals of a given species tend to cluster. We show that the precise form of the SAR transcends the specific details of organism interactions, enabling us to characterize its broad trends across taxa.clustering ͉ lognormal T here are an estimated 5-10 million nonmicrobial species on earth (1). This estimate is based on the extrapolation of sampled data rather than on a thorough count. Understanding the spatial distribution of biodiversity is of practical importance, providing information regarding the probability of species extinction due to loss of habitat (2) and the design of reserves that can protect the greatest amount of biological diversity (3, 4). In addition, the spatial distribution of species is an important factor governing a wide range of key biological phenomena, including competition (5), division of niche space (6), and the effect of disturbances (7).One of the main tools for extrapolation is the species-area relationship (SAR), relating area, A, to the number of species it supports, S. Several functional forms have been demonstrated for the SAR (8-10), but the power-law form, in which the number of species is a constant power of the area S ϭ cA z , is most commonly cited (10, 11). This form is reported (3) for climates ranging from temperate to tropical and for such different organisms as plants, birds, insects, mammals, and fish; this functional dependence also was recently extended to bacteria (12) and microbial eukaryotes (13). The exponent z has been reported to depend on habitat, scale, and taxa (3), with values in the range 0.1-0.4 for plants and birds in island groups [the most frequent values being in the range 0.2-0.4 (14)], values near unity for intercontinental scales, and a value as small as 0.05 for microbes (12). The widely reported occurrence of this functional form is indicative of a very robust mechanism, transcending the specific details of organism interactions. Explanations for the occurrence of this power-law SAR focusing on abundance distributions (15, 16), the allocation of individuals (17-23), or population dynamics (24-26) have been proposed. Nonetheless, there remains no consensus as to the common occurrence of the power-law SAR itself nor the systematics of the SAR exponents z. Modern theoretical work assuming self-similarity (27) permits neither a calculation of the SAR exponent nor its variation across taxa. Thus, the key questions (11) are (i) why is the power-law relationship so commonly reported? and (ii) what factors account for the observed distribution of exponent values?In this paper, we show that the SAR of an ecosystem depends primarily on the distribution of mean minimum distances between conspecific indiv...