  One of the first successes of neutral ecology was to predict
realistically-broad distributions of rare and abundant species. However, it has
remained an outstanding theoretical challenge to describe how this distribution
of abundances changes with spatial scale, and this gap has hampered attempts to
use observed species abundances as a way to quantify what non-neutral processes
are needed to fully explain observed patterns. To address this, we introduce a
new formulation of spatial neutral biodiversity theory and derive analytical
predictions for the way abundance distributions change with scale. For tropical
forest data where neutrality has been extensively tested before now, we apply
this approach and identify an incompatibility between neutral fits at regional
and local scales. We use this approach derive a sharp quantification of what
remains to be explained by non-neutral processes at the local scale, setting a
quantitative target for more general models for the maintenance of
biodiversity.
