Development of a shortleaf pine individual-tree growth equation using non-linear mixed modeling techniques

Nonlinear mixed-modeling methods were used to estimate parameters in an individual-tree basal area growth model for shortleaf pine (Pinus echinata Mill.). Shortleaf pine individual-tree growth data were available from over 200 permanently established 0.2-acre fixed-radius plots located in naturally-occurring even-aged shortleaf pine forests on the USDA Forest Service Ozark and Ouachita National Forests in western Arkansas and southeastern Oklahoma. The plots were established during the period from 1985 to 1987. Two subsequent re-measurements were used in this study, resulting in a total of three measurements and two growth periods. The equation can be used to predict the annual basal area growth of individual shortleaf pine trees as a function of individual tree basal area, forest stand basal area per acre, stand age, and the ratio of individual tree d.b.h. to quadratic mean stand d.b.h. The mixed-model procedure used random plot-level effects associated with individual tree basal area to account for correlation among individual trees located on the same plot. This resulted in improved fit statistics compared to a similar model fitted using nonlinear ordinary least squares.