The analysis, measurement, and management of species abundance is cent
ral to ecology and conservation biology, but it has proved difficult t
o find a single index that adequately reflects the commonness or rarit
y of species across a range of spatial scales. Here, a scale-independe
nt measure of species abundance is developed, using presence-absence m
aps at varying spatial resolutions. By extrapolating such ''scale-area
'' curves, species abundance can be estimated accurately even at scale
s finer than those used to parameterize the model, a task that had pre
viously been deemed impossible in principle.