Developing stem taper and stem volume equations using nonlinear mixed effect modeling approach for crimean pine stands [Pinus nigra Arnold. Subsp. Pallasiana (Lamb.) Holmboe] in Tarsus forest enterprise

In addition to the total volume predictions of individual trees, the detailed volume predictions for timber assortments, i. e. mine poles, sawlogs, firewoods and industrial wood, can be acquired by the compatible taper and volume equations. In this regard, the compatible taper and volume equations are important to accurately and comprehensively obtain individual tree wood volume predictions in various tree species and sites. The compatible taper and volume equations were developed by using Max and Burkhart (1976), Parresol et al. (1987) and Jiang et al. (2005) equations for Crimean Pine [Pinus nigra Arnold. subsp. pallasiana (Lamb.) Holmboe] trees located in Buladan and Cehennemdere Planning Units, Tarsus Forest Enterprise, Mersin Forest District Directorate, and these models' fitting results were compared. Based on some statistical indices, Jiang et al. (2005)'s equation with 98.43% of the coefficient of determination produced the most satisfactory predictive results than other equation. Also, single entry volume equation with 91.8 % of the coefficient of determination and double entry volume equation with 98.1 % of the coefficient of determination were developed in this study. Nonlinear mixed effect modeling procedure was applied to Jiang et al. (2005)'s equation and these modeling procedure including simultaneously fixed and random parameters produced in more predictive results (SSE: 8484.27, MSE: 3.4929) than ones which were obtained by nonlinear regression (SSE: 10888.80, MSE: 4.4828). In addition to nonlinear regression, the use of nonlinear mixed effect modeling that were proposed for solving serially correlated data could be improved the predictions of Jiang et al. (2005)'s tree taper equation. Also, calibration response of nonlinear mixed effect model were analyzed by using 48 sample trees which were not used in predicting the parameters of equation and calibration practice enhanced tree taper predictions. In Turkey, The development of the compatible taper and volume equations to obtain the detailed volume predictions for other Crimean pine's distribution areas will provide important contributions to these forest managements.