The species–area relationship (SAR) has been described as one of the few general patterns in ecology. Although there are many types of SAR, here we are concerned solely with the so-called species accumulation curve (SAC). The theoretical basis of this relationship is not well established. Here, we suggest that extreme value theory, also known as the statistics of extremes, provides a theoretical foundation for, as well as functions to fit, empirical species accumulation curves. Among the several procedures in extreme value theory, the appropriate way to deal with the species accumulation curve is the so-called block minima procedure. We first provide a brief description of this approach and the relevant formulas. We then illustrate the application of the block minima approach using data on tree species from a 50 ha plot in Barro Colorado Island, Panama. We conclude by discussing the extent to which the assumptions under which the extreme types theorem occurs are confirmed by the data. Although we recognize limitations to the present application of extreme value theory, we predict that it will provide fertile ground for future work on the theory of SARs and its application in the fields of ecology, biogeography and conservation.

We briefly describe the species-area relationship (SAR) and summarize the different types, including the main dichotomy of island species–area relationship (ISAR) and species accumulation curves (SAC). We discuss the classification of the ISAR as a fundamental ecological law, despite its protean nature. Exploring this protean behaviour, we review the different ways in which ISAR form has been shown to vary between datasets. The final section outlines the structure of the book and provides a summary of the remaining chapters.

We simulate habitat loss and derive species accumulation curves (SAC) and endemics–area relationship curves (EAR) in order to predict expected extinctions. The EAR may have a very different shape depending on the geometry of habitat loss. If area is lost in a spatially random way we may preserve more species than if area is lost in a clustered way, but with a larger extinction debt. If area is lost continuously inwards (‘inward EAR’) then the immediate loss of species can be much greater than if the same area is lost from the core towards its edge (‘outward EAR’). The main reason for these effects is the spatial autocorrelation of species distributions and the definition of endemics. Spatial autocorrelation means that sampling plots that are clustered are occupied by communities with more similar composition. If endemism is defined in relation to the study area, we can observe great species losses at the edge due to the large numbers of ranges that intersect the study area edge, but most of these species persist outside the study area. If instead we examine endemism on a global scale then the pattern of species losses is not influenced by the geometry of habitat loss.