Self‐similarity in species–area relationship and in species abundance distribution

Abstract

In an influential paper, Harte et al. highlighted the scaling or ‘self‐similar’ character of the power law species–area relationship (SAR), and used this feature to derive a species abundance distribution (SAD) and an endemics–area relationship. Here I show that their analysis was incorrect and leads to unrealistic results. I develop a different approach and obtain different results, both for SAD and for endemism. In particular, I show that the power law SAR is naturally associated with the power law statistical distribution, which is the only self‐similar distribution and closely matches empirical SADs. The results in this paper shed light on some of the main issues that have been discussed with regard to SARs: their relationship with the lognormal and with the neutral theory, the relative importance of sampling effects vs other mechanisms, and the deviations from a power law. The equations that I develop are simple and easy to apply to field studies.