This study aims to evaluate the robustness of parametric and nonparametric procedures using alternative definitions of validation data for loblolly pine. Specifically, four data division strategies were implemented: random selection of one-third of the trees in the data set, selection of the smallest one-third of the trees by diameter at breast height (DBH), selection of the middle third of the trees by DBH, and selection of the largest third of the trees by DBH. Results indicate that tree taper was predicted reasonably well by both procedures when the smallest, medium-sized, or randomly selected trees were withheld for validation. However, when the largest trees were withheld for validation, diameters predicted by the nonparametric random forest algorithm were considerably less accurate than those predicted by the parametric models, especially for diameters near the tree top. When extrapolation is anticipated, a carefully designed data-partitioning strategy should provide some protection against poor results for given prediction objectives.Study Implications: Parametric tree-stem taper models have been widely applied in forestry. Recently, nonparametric methods with computationally intensive algorithms were proposed for estimating tree taper, but reliability of the methods has not been explicitly examined. In practice, models are commonly applied to predict unknown populations, which may vary from the observations used in model development. This study provides insights for natural resource and forest managers to select appropriate validation procedures when developing models for predicting tree-stem taper and examining robustness of parametric and nonparametric fitting of tree-stem taper under varying levels of interpolation/extrapolation from fitting to validation of data.

Accurately quantifying stem taper is essential to predict diameter at any given height along the stem and to estimate tree volume for various sections of the stem. With increased computing power, semi- and nonparamatric methods have been proposed as alternative approaches for modelling tree taper. The main objective of this study was to assess the accuracy of stem taper predicted for four pine and four hardwood species by semi- and nonparametric models. Specifically, generalized additive models (GAM), random forests (RF) and regression-enhanced random forests (RERF) were compared with two widely-used parametric models: variable-exponent function (VAR) and segmented polynomial regression model (SEG). Test datasets selected from four different data splitting methods were used to examine the prediction accuracy of the models. Results showed that all examined models can be used to quantify stem taper and volume for all species when prediction is limited to be within the range of tree sizes used in model building. The nonparametric RF algorithm generally produced higher bias and lower precision than the semiparametric (GAM and RERF) and parametric models (VAR and SEG). For all species, GAM, VAR and SEG provided more robust predictions of stem taper than RF and RERF algorithms, especially when small or large trees were withheld for model testing. The data splitting strategies used in this work provide an efficient ‘stress test’ to evaluate model performance when collecting an independent test dataset is not feasible. The findings of this work provide additional insights for forest practitioners and resource managers to select appropriate methods in stem taper modelling.

Heartwood, sapwood, and bark constitute the main components of the tree stem. The stem is the main component of the tree and plays an important role in supporting the tree and transporting nutrients and water. Therefore, quantifying the profiles of heartwood, sapwood, and bark is fundamental to understanding the different components of the tree stem. A seemingly unrelated mixed-effect model system was developed based on 179 destructively sampled trees for 31 permanent sample plots in Korean larch plantation in Northeast China. The heartwood radius and sapwood width were estimated and calibrated only by the observed bark thickness or by all response variables considering the correlations of submodel random effects. The results indicated that the model system achieved good fitting performance and prediction. In addition, after including one to ten bark thickness points and all response variables of sampling below the 2 m height of the tree, the estimated best linear predictor (EBLUP) for local calibration improved the prediction performance, indicating that the heartwood radius and sapwood width could be effectively calibrated by bark thickness while keeping intact the complete inner structure inside the stem. The results provided important information for forest managers and ecologists when selecting appropriate approaches for quantifying the profiles of heartwood, sapwood, and bark.