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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.

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For plant populations, carrying capacity is the maximum number or biomass of a species that can be sustained under finite site resources on a long-term basis. This study was aimed at estimating the carrying capacity in planted stands of loblolly pine. Maximum stand basal area (BA) that can be sustained over a long period of time can be regarded as a measure of carrying capacity. To quantify and project stand BA carrying capacity, one approach is to use the estimate from a fitted cumulative BA-age equation; another approach is to obtain BA estimates implied by maximum size-density relationships (MSDRs), denoted implied maximum stand BA. The efficacy of three diameter-based MSDR measures: Reineke's self-thinning rule, competition-density rule and Nilson's sparsity index, were evaluated. Estimates from these three MSDR measures were compared with estimates from the Chapman-Richards (C-R) equation fitted to the maximum stand BA observed on plots from spacing trials. The spacing trials, established in two physiographic regions (Piedmont and Coastal Plain) in the southeastern United States, and at two