Asymptotic distribution of stage-grouped population models

Zetlaoui Mélanie, Picard Nicolas, Bar-Hen Avner. 2006. Asymptotic distribution of stage-grouped population models. Mathematical Biosciences, 200 (1) : 76-89.

Résumé : Matrix models are often used to predict the dynamics of size-structured or age-structured populations. The asymptotic behaviour of such models is defined by their malthusian growth rate [lambda], and by their stationary distribution w that gives the asymptotic proportion of individuals in each stage. As the coefficients of the transition matrix are estimated from a sample of observations, [lambda] and w can be considered as random variables whose law depends on the distribution of the observations. The goal of this study is to specify the asymptotic law of [lambda] and w when using the maximum likelihood estimators of the coefficients of the transition matrix. We prove that [lambda] and w are asymptotically normal, and the expressions of the asymptotic variance of [lambda] and of the asymptotic covariance matrix of w are given. The convergence speed of [lambda] and w towards their asymptotic law is studied using simulations. The results are applied to a real case study that consists of a Usher model for a tropical rain forest in French Guiana. They permit to assess the number of trees to measure to get a given precision on the estimated asymptotic diameter distribution, which is an important information on tropical forest management.

Mots-clés Agrovoc : modèle mathématique, dynamique des populations, forêt tropicale humide, aménagement forestier

Classification Agris : U10 - Informatique, mathématiques et statistiques
K10 - Production forestière

Champ stratégique Cirad : Axe 6 (2005-2013) - Agriculture, environnement, nature et sociétés

Auteurs et affiliations

• Zetlaoui Mélanie, INA-PG (FRA)
• Picard Nicolas, CIRAD-FORET-UPR Dynamique forestière (FRA)
• Bar-Hen Avner, INA-PG (FRA)

Source : Cirad - Agritrop (https://agritrop.cirad.fr/532080/)

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