  Neutral models, in which individual agents with equal fitness undergo a
birth-death-mutation process, are very popular in population genetics and
community ecology. Usually these models are applied to populations and
communities with spatial structure, but the analytic results presented so far
are limited to well-mixed or mainland-island scenarios. Here we present a new
technique, based on interface dynamics analysis, and apply it to the neutral
dynamics in one, two and three spatial dimensions. New results are derived for
the correlation length and for the main characteristics of the community, like
total biodiversity and the species abundance distribution above the correlation
length. Our results are supported by extensive numerical simulations, and
provide qualitative and quantitative insights that allow for a rigorous
comparison between model predictions and empirical data.
