Hotspot identification is a crucial strategy for setting conservation priorities. Since both the total number of species and the number of endemic species tend to increase with area, prioritizing sites according to their overall species richness or endemic species richness can produce rankings that simply mirror the sizes of the sites. Thus, it is important to control for the dependence of species number on site area. For this reason, some authors have proposed that the species–area relationship (SAR) and/or the endemics–area relationship (EAR) should be modelled and then the sites located above the fitted curve(s) (i.e. those having positive residuals) designated as hotspots. However, (1) there may be large uncertainties about which model provides the best fit to the SARs/EARs, (2) the use of residuals may lead to sites being identified as hotspots when they only have very few species and (3) there is no guarantee that the sites selected as hotspots by the SAR really include a large fraction of the overall diversity. Thus, it is important to evaluate the ability of the hotspots designated by these procedures to really conserve total and endemic species diversity; the best strategy may in fact be to use a combination of approaches.

Although the species–area relationship (SAR) is commonly presumed to be either a power law or to follow the logarithmic relationship, a large number of other mathematical expressions have been proposed to describe the relationship. These models can be divided into four general categories, distinguishing between asymptotic and non-asymptotic, and between convex upward and sigmoid models (in arithmetic space). The choice of regression model should not be determined by best fit alone; rather, the choice should relate to the purpose of fitting mathematical models to SAR data: either descriptive, explicative or predictive. Therefore, we should choose models that are likely to result from expected ecological patterns. We argue that neither (accumulative) sample-area SARs (saSARs) nor island SARs (ISARs) have upper asymptotes and ISARs may be sigmoid if the smallest islands (finest scales) are included. Amongst the 30 different models we review here, few are non-asymptotic. Both the power model and logarithmic model return convex non-asymptotic curves, whereas the second persistence (P2) model and the quadratic logarithmic model consistently return sigmoid curves without asymptotes. We add the Tjørve-hybrid to this shortlist, as it can be useful when neither the power nor the logarithmic model provides a good fit to saSAR data.