Neutral models in ecology : species abundance and extinction dynamics

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 “standard” 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 “scale up” 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.