Nonlinear mixed modeling of basal area growth for shortleaf pine.

Mixed model estimation methods were used to fit individual-tree basal area growth models to tree and stand-level measurements available from permanent plots established in naturally regenerated shortleaf pine (Pinus echinata Mill.) even-aged stands in western Arkansas and eastern Oklahoma in the USA. As a part of the development of a comprehensive distance-independent individual-tree shortleaf pine growth and yield model, several individual-tree annual basal area growth models were fitted to the data with the objective of selecting the model that has superior fit to the data as well as attributes suitable for practical application in shortleaf pine stand simulator useful as an aid in forest management decision-making. The distance-independent individual-tree model of Lynch et al. [Lynch, T.B., Hitch, K.L., Huebschmann, M.M., Murphy, P.A., 1999. An individual-tree growth and yield prediction system for even-aged natural shortleaf pine forests. South. J. Appl. For. 23, 203-211] for annual basal area growth was improved to incorporate random-effects for plots in a potential-modifier framework with stand-level and tree-level explanatory variables. The fitted mixed-effects models were found to fit the data and to predict annual basal area growth better than the previous model forms fitted using ordinary least-squares. There was also some evidence of heterogeneous errors, the effects of which could be corrected by using a variance function in the estimation process. The revised parameter estimates from the selected mixed model could be utilized in a growth and yield simulator that also takes appropriate dbh-height and mortality functions into account.