Fitting three parameter growth curves using a nonlinear mixed effects modelling approach

Abstract

A nonlinear mixed modelling approach was applied to model individual tree diameter increment using three nonlinear growth functions for Eucalyptus tree plantations. The objective of the study is to develop a stem radial increment model for two clones of Eucalyptus tree, and compare their growth potential. Three nonlinear growth curves (Gompertz, logistic and asymptotic regression) were fitted to stem radius data. Estimations of parameters were made using the approximate likelihood functions. The estimators obtained from these approximate likelihood function are a combination of least squares estimators for nonlinear mixed effects models and maximum likelihood estimators from linear mixed effects models. The asymptotic regression model with three random effects appears well suited to represent the random effect covariance structure. The heterogeneous variance model that varies with tree age is found to be suitable model that characterize the within tree error variability. Clone has a significant effect on the asymptote of the asymptotic regression curve. The analysis suggests that GU clone on the average has a larger stem radial measurement than the GC clone during the entire juvenile stage.