Spatially constrained rarefaction: incorporating the autocorrelated structure of biological communities into sample-based rarefaction

Rarefaction is a widely applied technique for comparing the species richness of samples that differ in area, volume or sampling effort. Despite widespread adoption of sample-based rarefaction curves, serious concerns persist. In this paper, we address the issue of the spatial arrangement of sampling units when computing sample-based rarefaction curves. If the spatial arrangement is neglected when building rarefaction curves, a direct comparison of species richness estimates obtained for areas that differ in their spatial extent is not possible, even if they were sampled with a similar intensity. We demonstrate a major effect of the spatial extent of the samples on species richness estimates through the use of data from a temperate forest. We show that the use of Spatially Constrained Rarefaction (SCR) results in species richness estimates that are directly comparable for areas that differ in spatial extent. As expected, standard rarefaction curves tend to overestimate species richness because they ignore the spatial autocorrelation of species composition among sampling units. This spatial autocorrelation is captured by the SCR, thus providing a useful technique for characterizing the spatial structure of biodiversity patterns. Further work is necessary to determine how species richness estimates and the shape of the SCR are affected by the method of spatial constraint and sampling unit density and distribution.