Mixed-effects height-diameter models for Drimys winteri in the south (41-43° S) of Chile

Drimys winteri is an abundant tree species in the natural forests of Chile, growing as secondary forest of high ecological and economical importance between 41 degrees and 43 degrees S. The height-diameter relationship is key for estimating volume, biomass and for understanding ecological features of tree species. However, there is a lack of research about allometric relationships for this species. We aim at modeling the height-diameter relationship of D. winteri by nonlinear mixed-effects models. We used an extensive sample of trees between Llanquihue and Chiloe Provinces in southern Chile. We analyzed several models, and afterwards, assessed to which parameters allocate the random effects. Finally, we modeled these random effects as a function of stand-level variables (e.g., density, basal area). The proposed model has a biologically consistent behavior, its parameters are efficiently estimated because we considered the hierarchical structure of the data and took into account the effect of competition (represented by density and diameter of the mean basal area tree) and site quality (represented by the mean annual increment in dominant height) of the forests where the trees are growing. Our findings showed that the height-diameter allometry of D. winteri varies depending on competition and site productivity, two key variables for silvicultural management.