Modelling primary branch growth based on a multilevel nonlinear mixed-effects model: a Pinus koraiensis plantation case study in north-east China

On the basis of a multilevel nonlinear mixed-effects model approach, branch diameter and length growth models were developed for a Pinus koraiensis plantation in north-east China. The models developed were able to better capture the residual variation successfully by partitioning the residual variance into plot-, tree- and branch-level variations via random parameter modeling at the three levels. In addition to random effects, various time series correlation structures were evaluated to account for residual autocorrelation, and the AR(1) and ARMA(1,1) structures were selected for the branch diameter and length growth models, respectively. Model validation results using an independent data set confirmed that multilevel mixed models with an appropriate correlation structure produced more accurate and precise branch-specified diameter and length predictions. Overall, the models were suitable in describing the trends and inherent variability of crown profile and good enough to be included in growth simulation systems for Pinus koraiensis plantations.