Asymptotic distribution of stage-grouped population models.
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.
Zetlaoui
M
M
Institut National Agronomique Paris-Grignon 16, rue Claude Bernard-75231 Paris Cedex 05, France.
Picard
N
N
Cirad-forêt/plantations, Campus international de Baillarguet-TA 10/C 34398, Montpellier Cedex 5, France.
Bar-Hen
A
A
Institut National Agronomique Paris-Grignon 16, rue Claude Bernard-75231 Paris Cedex 05, France. Electronic address: avner@inapg.fr.
D000465:Algorithms; D000704:Analysis of Variance; D003198:Computer Simulation; D017753:Ecosystem; D005616:French Guiana; D016013:Likelihood Functions; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics; D014197:Trees / Q000254:growth & development*