Comparison of Parametric and Nonparametric Methods for Estimating Size–Density Relationships in Old-Growth Japanese Cedar (Cryptomeria japonica D. Don) Plantations

Abstract

Accurately quantifying the size–density relationships is important to predict stand development, estimate stand carrying capacity and prescribe silvicultural treatments. Parametric methods, such as segmented regression, were proposed to estimate the complicated trajectory of size–density relationships. However, applying nonparametric methods to assess stand development has not been explicitly examined. In this study, we compared parametric and nonparametric methods for estimating size–density relationships for Japanese cedar plantations in Taiwan. Specifically, we compared the efficacy of two segmented regression models with the penalized spline and random forest for regression methods. We also examined various stages in stand development for old-growth Japanese cedar stands. Data collected from 237 Japanese cedar permanent plots were used in model fitting and validation. Results indicated that the parametric and nonparametric methods used in this study can provide reliable estimates of the size–density relationship for Japanese cedar. Higher accuracy was achieved before the stands diverged from the self-thinning line. The penalized spline approach behaved consistently well regardless of datasets or stages in stand development, while the predictability of the random forest algorithm slightly decreased when the validation data was fitted. The results of this study provide insights on the use of methods to quantify the size–density relationships as well as enhance the understanding of long-term stand development.