Linear mixed-effects models and calibration applied to volume models in two rotations of Eucalyptus grandis plantations

This work presents applications of the linear mixed-effects model calibration to predict individual tree volumes of Eucalyptus grandis W. Hill ex Maiden plantations on first and second rotations located in different farms of the same region in São Paulo, Brazil. We started with the Schumacher and Hall equation in its linearized form to develop our mixed-effects model. Some parameters were considered as random among the different farms, and the calibration was made at the farm level using a small number of sample trees. The approach was developed for univariate models of the first rotation, which were calibrated with first- and second-rotation trees, and for bivariate models of the two rotations, which were calibrated with first-rotation trees. The results showed that the calibrated mixed model provides more reliable predictions than the fixed part of the model alone; however, the benefit is only moderate due to the rather small variation of the stem form between farms and rotations. The results indicate that the approach can reduce the measurement requirements on second-rotation crops.