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Experimental design for spatial sampling applied to the study of tropical forest regeneration

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Abstract:

For practical reasons, estimating seed production in tropical forest is only possible by sampling. Classical sampling designs (random or systematic) give poor estimations of seed abundance. The spatial disposition of the trees, combined with nonuniform seed dispersal, leads to a highly heterogeneous spatial distribution of the seeds. We propose a random stratified sampling design based on a model that takes account of seed dispersal processes and the location of the trees. We assume a gamma distribution for dispersal distances. The overall seed dispersal area is divided into adjacent quadrats. In each quadrat, the number of seeds follows a Poisson distribution with the mean derived from the model. We estimate model parameters from the results of a previous study and give the variance of the Horvitz–Thompson estimator of population total for stratified and random sampling designs. A simulation study is used to find the optimal number of strata, and the performance of the sampling design is evaluated. For each model, we compared the variance of the estimator of population total obtained with the stratified sampling design with that obtained with the random sampling design with the same sample size. The stratified sampling design is, on average, 25 times as precise as the random sampling design.

L'estimation de la production de graines d'un groupe de semenciers spatialement agrégés en forêts tropicales n'est faisable qu'à partir d'un échantillonnage. Les plans d'échantillonnage classique (aléatoire ou systématique) donnent de mauvaises estimations de l'abondance des graines. La disposition spatiale des semenciers conjuguée à un mode de dispersion des graines non uniforme induit une répartition très hétérogène des graines dans l'aire de dispersion globale des semenciers. Nous proposons un échantillonnage stratifié basé sur un modèle qui prend en compte la forme de la dispersion des graines et la position des semenciers. Nous supposons une distribution gamma pour les distances de dispersion. L'aire de dispersion globale est découpée en quadrats adjacents dans lesquels la variable d'intérêt est un comptage suivant une loi de Poisson dont la moyenne est issue du modèle. Nous estimons les paramètres du modèle indépendamment des données et donnons les variances de l'estimateur de Horvitz–Thompson pour un plan stratifié et un plan aléatoire. Nous illustrons la méthode par des simulations qui nous permettent à la fois de construire la stratification sans définir a priori le nombre de strates et de comparer les performances des estimateurs. Conditionnellement au modèle, l'échantillonnage stratifié permet d'augmenter en moyenne 25 fois la précision de l'estimateur pour une même taille d'échantillonnage.

Document Type: Research Article

Publication date: May 1, 2005

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  • Published since 1971, this monthly journal features articles, reviews, notes and commentaries on all aspects of forest science, including biometrics and mensuration, conservation, disturbance, ecology, economics, entomology, fire, genetics, management, operations, pathology, physiology, policy, remote sensing, social science, soil, silviculture, wildlife and wood science, contributed by internationally respected scientists. It also publishes special issues dedicated to a topic of current interest.
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