  We present novel analytical results about ecosystem species diversity that
stem from a proposed coarse grained neutral model based on birth-death
processes. The relevance of the problem lies in the urgency for understanding
and synthesizing both theoretical results of ecological neutral theory and
empirical evidence on species diversity preservation. Neutral model of
biodiversity deals with ecosystems in the same trophic level where per-capita
vital rates are assumed to be species-independent. Close-form analytical
solutions for neutral theory are obtained within a coarse-grained model, where
the only input is the species persistence time distribution. Our results
pertain: the probability distribution function of the number of species in the
ecosystem both in transient and stationary states; the n-points connected time
correlation function; and the survival probability, definned as the
distribution of time-spans to local extinction for a species randomly sampled
from the community. Analytical predictions are also tested on empirical data
from a estuarine fish ecosystem. We find that emerging properties of the
ecosystem are very robust and do not depend on specific details of the model,
with implications on biodiversity and conservation biology.
