Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

Abstract

(1) Background: This paper deals with unevenly aged, whole-stand models from mixed-effect parameters diffusion processes and Voronoi diagram points of view and concentrates on the mixed-species stands in Lithuania. We focus on the Voronoi diagram of potentially available areas to tree positions as the measure of the competition effect of individual trees and the tree diameter at breast height to relate their evolution through time. (2) Methods: We consider a bivariate hybrid mixed-effect parameters stochastic differential equation for the parameterization of the diameter and available polygon area at age to ensure a proper description of the link between them during the age (time) span of a forest stand. In this study, the Voronoi diagram was used as a mathematical tool for the quantitative characterization of inter-tree competition. (3) Results: The newly derived model considers bivariate correlated observations, tree diameter, and polygon area arising from a particular stand and enables defining equations for calculating diameter, polygon-area, and stand-density predictions and forecasts. (4) Conclusions: From a statistical point of view, the newly developed models produced acceptable statistical measures of predictions and forecasts. All the results were implemented in the Maple computer algebra system.