Modelo não linear misto para descrever o afilamento do tronco de Araucaria angustifolia no sul do Brasil

Abstract

This study was develop aiming to apply the approach of nonlinear mixed models to describe the taper of stem of Araucaria angustifolia (Bertol.) Kuntze of planted forests in southern Brazil. A total of 340 trees were cubed in five locations: Caçador (SC), Três Barras (SC), Chapecó (SC), São Francisco de Paula (RS) e Canela (RS). Group of 2/3 trees in each local were sample and used to fit stem taper models and the other 1/3 to validation. Models of Kozak's variable-form (1988, 1994 e 2004) were tested and modified to explain the variation of taper the stem within and between trees with %NLINMIX in SAS of parameter estimates with fixed and random effects. The variance and covariance matrix used to determine the parameters with random effects were unstructured and based in method expansion around zero. The specific calibration in the tree for estimating parameters with random effects was calculed using measurements of relative diameters by approach of Bayesian estimator. The modified nonlinear mixed model of Kozak (1994) show a reduction 17,5% in values of AIC and BIC when included the random effect in three coefficients compared to the model without. The calibration of the random effects in tree was possible with the mensuration diameter at 6.3 m from the ground with smaller deviation to determine relative diameters and volumes. Taper of stem in araucaria described by the modified nonlinear mixed model of Kozak (1994) showed flexibility and efficiency for defining wood assortments.