MODELAGEM DE EFEITOS MISTOS PARA AFILAMENTO EM FUSTES DE Tectona grandis L.f.

Abstract

Teak plantations in Brazil have notorious importance in the forestry sector, with prospects of short- and medium-term financial returns. However, this species lacks studies regarding stem shape and tapering, to serve as a subsidy to forest companies ensuring the best multiproducts use of forest stands. Thus, the present research had the objective to evaluate and compare different strategies to describe the stem shape of Tectona grandis, applying the mixed modeling for diameters and volume estimations along the stems of Tectona grandis. The research was carried out in plantations of T. grandis, of 5- to 25-years old, located in Brasnorte, State of Mato Grosso. The volume of 509 trees was determined by the relative height method, which was stratified into three shape classes and five diameter classes. In order to evaluate the accuracy of the diameter estimations along the stems, seven taper models were adjusted by the ordinary least squares method, of which four were non-segmented, one segmented and two of variable form. After the selection of the best model fitted, non-linear mixed-effects modeling was applied to evaluate the accuracy and precision of the diameters and volumes estimations, respectively. Two strategies were tested: (1) considering the tree as a random effect in the application of the mixed modeling; (2) applying mixed modeling at multilevels, in a total of 18 variation levels (3 shape classes and 6 diameter classes). In addition, three scenarios were evaluated, testing the combination of 1, 2 or 3 random coefficients. The adjustments were performed using the nls and nlme functions of the R software. Six statistics were used to evaluate the accuracy of the taper models: standard error of estimation in percentage (Syx%), coefficient of determination (R²), Akaike’s information criterion (AIC), bias (V), quadratic error (MSE) and absolute bias (MD), as well as residual graph and autocorrelation analysis. Mixed effect modeling improved accuracy and precision of diameters and volumes estimations. Strategy 1 eliminated autocorrelation and residual heteroscedasticity. For the two strategies evaluated, as the number of mixed coefficients increased, the accuracy and precision of diameters and volumes estimations increased as well.