The assembly of an ecosystem such as a tropical forest depends crucially on the species interaction network, and the deduction of its rules is a formidably complex problem. In spite of this, many recent studies using Hubbell's neutral theory of biodiversity and biogeography have demonstrated that the resulting emergent macroscopic behaviour of the ecosystem at or near a stationary state shows a surprising simplicity reminiscent of many physical systems. Indeed the symmetry postulate, that the effective birth and death rates are species-independent within a single trophic level, allows one to make analytical predictions for various static distributions such as the relative species abundance, beta-diversity and the species-area relationship. In contrast, there have only been a few studies of the dynamics and stability of tropical rain forests. Here we consider the dynamical behaviour of a community, and benchmark it against the exact predictions of a neutral model near or at stationarity. In addition to providing a description of the relative species abundance, our analysis leads to a quantitative understanding of the species turnover distribution and extinction times, and a measure of the temporal scales of neutral evolution. Our model gives a very good description of the large quantity of data collected in Barro Colorado Island in Panama in the period 1990-2000 with just three ecologically relevant parameters and predicts the dynamics of extinction of the existing species.