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The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch (Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak's (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D0.2, D0.5, and D0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position. [ABSTRACT FROM AUTHOR]

Stem form is the shape of the trunk, differs among tree species and mainly affected by stand density factor. Accurate taper equations are crucial for estimating the stem diameter, form and tree volume, which is conducive to timber utilization and sustainable forest management and planning. Larch (Larix principis-rupprechtii Mayr.) is a valuable afforestation species under large-scale development in North China, but no study on the effect of density on its stem taper has been reported yet. The dataset included 396 analytical trees from 132 standard plots of larch plantation in Saihanba, Hebei Province. Based on 12 different forms of models, we explored the optimal basic equation for plantations and the effects of the stand density, basal area, canopy density and different forms of stand density on the prediction accuracy of the variableexponent models. The variable-exponent taper equation that includes Sd (stand density) was constructed by using nonlinear regression, a nonlinear mixed effect model and the nonlinear quantile regression method. The results indicate that the Kozak's 2004 variable-exponent taper equation was the best basic model for describing changes in the stem form of larch plantations, and the density factor in the form of Sd improved the prediction accuracy of the basic model. Among the three regression methods, the quantile regression method had the highest fitting accuracy, followed by the nonlinear mixed effect model. When the quantile was 0.5, the nonlinear quantile regression model exhibited the best performance which provides a scientific basis for the rational management of larch plantations. [ABSTRACT FROM AUTHOR]

The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch ( Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak's (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D 0.2 , D 0.5 , and D 0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Wang, Zhang, Zhang and Huang.)

Stem form is the shape of the trunk, differs among tree species and mainly affected by stand density factor. Accurate taper equations are crucial for estimating the stem diameter, form and tree volume, which is conducive to timber utilization and sustainable forest management and planning. Larch ( Larix principis-rupprechtii Mayr.) is a valuable afforestation species under large-scale development in North China, but no study on the effect of density on its stem taper has been reported yet. The dataset included 396 analytical trees from 132 standard plots of larch plantation in Saihanba, Hebei Province. Based on 12 different forms of models, we explored the optimal basic equation for plantations and the effects of the stand density, basal area, canopy density and different forms of stand density on the prediction accuracy of the variable-exponent models. The variable-exponent taper equation that includes Sd (stand density) was constructed by using nonlinear regression, a nonlinear mixed effect model and the nonlinear quantile regression method. The results indicate that the Kozak's 2004 variable-exponent taper equation was the best basic model for describing changes in the stem form of larch plantations, and the density factor in the form of S d improved the prediction accuracy of the basic model. Among the three regression methods, the quantile regression method had the highest fitting accuracy, followed by the nonlinear mixed effect model. When the quantile was 0.5, the nonlinear quantile regression model exhibited the best performance which provides a scientific basis for the rational management of larch plantations., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Xu, Wang, Liu, Zhang, Zhang and Huang.)