A community-le el fractal property produces power-law species-area relationships

Power-law relationships appear to characterize many patterns observed in ecology, from the level of individuals to the level of ecosystems (Calder 1984, Gaston and Blackburn 2000). These power laws often hold over scale ranges sufficiently large to justify the search for a unifying theoretical framework explaining the relationship between these patterns. A promising avenue for discovering such a framework is the exploration of the fractal properties from which these power laws derive and their implications for other ecological characteristics. In this vein, Harte and Kinzig (1997) and Harte et al. (1999a) studied the fractal property behind a powerlaw species-area relationship and its implications for other species distribution characteristics. In a recent paper published in Oikos, Lennon et al. (2002) claim that in order to derive a power-law species-area relationship from fractals in the distribution of species, Harte et al. (1999a) assumed that individual species distributions are fractal and that all species patterns have the same fractal dimension D. Inspired by empirical evidence that indicates that fractal dimension tends to vary between species, they then show that in this more realistic case of varying D, the species-area relationship does not follow a power law. Hence Lennon et al. (2002) conclude that, despite Harte et al. (1999a) derivation of the power-law species-area relationship from fractals, a fractal distribution of species is not what produces power-law species-area relationships in nature. We show here the misleading error in Lennon et al.’s (2002) critique. Harte et al. (1999a) did not derive the power-law species-area relationship from fractals at the ‘species-level’, but rather from a ‘community-level’ fractal property that can hold without the presence of ‘species-level’ fractals. Furthermore, this communitylevel fractal property holds in any region where the power-law species-area relationship holds (Harte and Kinzig 1997). Hence this community-level fractal property must be what produces power-law species-area relationships in nature – it is equivalent to it. Lennon et al. are correct that if the species-level fractal property holds for each species in a community, a power-law species-area relationship will result only if the fractal dimension is constant across species. This result was found previously in Harte et al. (2001), where the overall degree of compatibility between the communitylevel and species-level fractal properties was derived. However, as Harte et al. (2001) showed, the community-level fractal property and hence the power-law species-area relationship can exist either if the fractal dimension is constant across species, or if some individual species distributions are not fractal on their own. This does not rule out the possibility that species-level fractals are important in nature. Below we provide a detailed analysis of these issues.