title: Dynamics of neutral biodiversity.
abstract: Hubbell's neutral model has become a major paradigm in ecology. Whereas the steady-state structure is well understood, results about the dynamical aspects of the model are scarce. Here we derive dynamical equations for the Simpson diversity index. Both mean and variance of the diversity are proven to satisfy stable linear system dynamics. We show that in the stationary limit we indeed recover previous results, and we supplement this with numerical simulations to validate the dynamical part of our analytical computations. These findings are especially relevant for experiments in microbial ecology, where the Simpson diversity index can be accurately measured as a function of time.
authors.affiliation: INRA, UR50, Laboratoire de Biotechnologie de l'Environnement, Avenue des Etangs, Narbonne, France.
authors.forename: Dimitri
authors.initials: D
authors.lastname: Vanpeteghem
authors.forename: Olivier
authors.initials: O
authors.lastname: Zemb
authors.forename: Bart
authors.initials: B
authors.lastname: Haegeman
mesh_terms: D044822:Biodiversity; D003198:Computer Simulation; D017753:Ecosystem; D008954:Models, Biological; D013269:Stochastic Processes