Little consensus has emerged regarding how proximate and ultimate drivers such as productivity, disturbance and temperature may affect species richness and other aspects of biodiversity. Part of the confusion is that most studies examine species richness at a single spatial scale and ignore how the underlying components of species richness can vary with spatial scale. We provide an approach for the measurement of biodiversity that decomposes changes in species rarefaction curves into proximate components attributed to: (a) the species abundance distribution, (b) density of individuals and (c) the spatial arrangement of individuals. We decompose species richness by comparing spatial and nonspatial sample- and individual-based species rarefaction curves that differentially capture the influence of these components to estimate the relative importance of each in driving patterns of species richness change. We tested the validity of our method on simulated data, and we demonstrate it on empirical data on plant species richness in invaded and uninvaded woodlands. We integrated these methods into a new r package (mobr). The metrics that mobr provides will allow ecologists to move beyond comparisons of species richness in response to ecological drivers at a single spatial scale toward a dissection of the proximate components that determine species richness across scales.