Statistical inference for density-dependent Markovian forestry models

Stéphan Clémençon (1) , Mélanie Zetlaoui (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 MET@RISK - Méthodologies d'Analyse de Risque Alimentaire

A stochastic forestry model with a density-dependence structure is studied. The population evolves in discrete-time through stage-structured processes, in a way that its temporal evolution is described by a stochastic Markov chain. For adequate scalings of the transition rates, it is shown to converge to the deterministic matrix model, known as the Usher model, as a parameter n, interpreted as the population size roughly speaking, becomes large. From the perspective of the analysis of forestry data and predict the forestry population evolution, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relation of the model to the available data of a tropical rain forest in French Guiana is investigated and numerical applications are carried out.

Mots clés: Population dynamics; Matrix model; Markov chain; Density dependence; Large population approximation; Maximum likelihood estimation

Domaines: Probabilités [math.PR]; Théorie [stat.TH]; Statistiques [math.ST]; Biodiversité et Ecologie

Stéphan Clémençon, Mélanie Zetlaoui. Statistical inference for density-dependent Markovian forestry models. 2010. ⟨hal-00484540⟩