Self-similarity, the power law form of the species-area relationship, and a probability rule: a reply to Maddux.

We reply here to the comment by Maddux (2004, in this issue), which discusses a fractal probability rule (PR) for the spatial distribution of species proposed by Harte and Kinzig (1997) and Harte et al. (1999b) as a means of deriving the characteristics of species distributions that exhibit power law species-area relationships. In his comment, Maddux derives certain properties of spatial distributions that follow this PR, including the dependence of the species richness in a patch on the location of that patch, and argues that these properties are biologically unlikely. He also argues that the PR leads to a power law relationship between species richness and area only for a discrete set of patch sizes and that it does not constrain the speciesarea relationship for areas that fall between these discrete sizes. On the basis of these arguments, Maddux concludes that the PR is not an adequate method for relating the power law species-area relationship (PLSAR) to an underlying fractal or self-similarity condition. We agree with Maddux that the PR leads to distributions with unrealistic properties when it is used to simulate landscapes and that the PR leads to a discrete, rather than