Recent theoretical approaches to community structure and dynamics reveal that
many large-scale features of community structure (such as species-rank
distributions and species-area relations) can be explained by a so-called
neutral model. Using this approach, species are taken to be equivalent and
trophic relations are not taken into account explicitly. Here we provide a
general analytic solution to the local community model of Hubbell's neutral
theory of biodiversity by recasting it as an urn model i.e.a Markovian
description of states and their transitions. Both stationary and time-dependent
distributions are analysed. The stationary distribution -- also called the
zero-sum multinomial -- is given in closed form. An approximate form for the
time-dependence is obtained by using an expansion of the master equation. The
temporal evolution of the approximate distribution is shown to be a good
representation for the true temporal evolution for a large range of parameter
values.Comment: 10 pages, 2 figure
