Developing and Comparing Individual Tree Growth Models of Major Coniferous Species in South Korea Based on Stem Analysis Data

Abstract

Tree growth in Korean red pine (Pinus densiflora, hereafter Pd), Korean white pine (Pinus koraiensis, hereafter Pk), and Japanese larch (Larix kaempferi, hereafter Lk) was modeled using Logistic, Korf, Gompertz, Chapman-Richards, and Weibull equations and stem analysis data from sample trees: 38 trees for Pd, 46 trees for Pk, and 45 trees for Lk. The models were fitted to the total increment of tree size variables, diameter at breast height (DBH), height, basal area, and stem volume, as a function of age. After selecting the best-fit growth function, the current annual increment (CAI) and mean annual increment (MAI) were compared for each variable by species. The optimal growth functions were Chapman-Richards for DBH and stem volume, Korf for height, and Gompertz for basal area. The parameter estimates in the final models were all significant (p < 0.01) with best-fit statistics and unbiased residual plots. When plotted with observed values, the growth patterns of each variable were represented properly. The predicted growth curves over age were concave with respect to the Y-axis in DBH and height but lightly convex in basal area, and explicitly convex in stem volume, whereas an asymptote of sigmoid curve in stem volume was not apparent until 100 years. Age with the maximum MAI among variables was arranged similarly to CAI; the age with maximum MAI was earliest for DBH and latest for volume. The maximum growth was achieved earliest in Lk, followed by Pk and Pd. The developed models were able to predict tree size variables and serve as a reference to understand growth characteristics by species.

Tree size distribution as the stationary limit of an evolutionary master equation

“…Both our measurement data on the Populus plantations (demonstrating an increasing standard deviation with mean size increment; see Fig. 2d) and the data available in the literature 11,13,[42][43][44][45][46][47][48][49] supports the assumption that the growth rate ( µ(x) ) of deciduous trees monotonically increases with the tree diameter. Even without a reset process, this increase cannot go on indefinitely, therefore for large trees, it has to saturate.…”

“…The first process is a monotonic growth, which was assumed to increase with tree size and saturate in the limit of large diameters. For analytical simplicity and in agreement with supporting information from literature 11,42,43,45,46,49 , we chose a simple sub-linear function for the above (Eq. 15).…”

Developing the Additive Systems of Stand Basal Area Model for Broad-Leaved Mixed Forests

“…When applied to the P. davidiana × B. platyphylla broad-leaved mixed forests, the Richards model (M6) and the Korf model (M1) were optimal for predicting the SBA of P. davidiana and B. platyphylla, respectively (Table 2). These results show that optimal models for predicting tree species-level basal area differ among different species due to differences in biological characteristics [65]. When compared to the Schumacher model, the Richards model exhibited improved mathematical properties and biological significance [33].…”

“…The SBA model can be expressed both theoretically and empirically [98], with the former being highly logical and containing parameters with biological significance [38]. Recent studies [2,21,30] have constructed individual tree-level [65] and stand-level [33,38] basal area prediction models for various stand types based on theoretical models developed by Korf, Schumacher, and Richards. Therefore, the present study adopted different forms of theoretical models (Table 7) to construct an SBA prediction model for a P. davidiana × B. platyphylla mixed broadleaved forest.…”

A Statistical Dependence Framework Based on a Multivariate Normal Copula Function and Stochastic Differential Equations for Multivariate Data in Forestry

“…The relationships among the growth processes of individual tree size components (for example, diameter) and other tree size components (for example, potentially available area, height, etc.) are very important tools for modeling stand productivity and increments because these models are very useful in formulating forest management plans [49,50]. The newly developed methodology of linking stochastic differential equations and the normal copula function makes it possible to formalize the evolution of individual components of tree size with respect to other components of tree size by using nonlinear relationships.…”