In Chap. 1, we discuss some of the statistical patterns that seem to be ubiquitous
in ecosystems. Evidences for these patterns are collected both in study of living
ecosystem and in quantitative study of the Fossil Record.
In Chap. 2, we introduce the most important models that tried to give an explanation
for the observed patterns. The important concept of neutrality will be
also discussed.
In Chap. 3, we present a stochastic neutral model of the populations in a singletrophic
level ecosystems. A continuous version of this model is analytically
solvable; we compare the analytical solution with numerical simulations and
with experimental data coming from studies of tropical forests.
In Chap. 4, we address the problem of calculating the species lifetime distribution
function for the \u201cstandard\u201d formulation of the ecological neutral theory
[4, 13]. Depending on the parameters range and on the initial condition, the
solution has several different asymptotic behaviors We study them and make a
comparison with evidences of the fossil record. In a realistic parameter range,
we obtain the correct scaling.
In Chap. 5, we discuss the possible ecological implications of the result of
Chap. 4. In particular, we try to \u201cscale up\u201d the predictions of the neutral theory
on a long timescale. We predict in the same framework the lifetimes of species
and genera and the distribution of species among genera. Finally, we outline final conclusions and perspectives
