Stochastic Simulation of Self-Thinning

Abstract

Understanding the principles of self-thinning forest ecosystems is essential for taking modern management techniques into practice. The spatial distribution of the surviving trees in a stand is influenced by a variety of factors, including tree mortality. In young forests, competition has a major role in determining spatial mortality; in older forests, random changes in the environment have a major role. The dynamics of the number of living and dead trees in the forests of central Lithuania will be addressed in this study. The Gompertz type mixed effect parameters univariate stochastic differential equations of the tree diameter, height, and occupied area combined with the normal copula function are used to derive new models for the number per ha of living and dead trees. The mean values of the dead tree size variables had much lower trajectories, which is especially apparent in mature stands, as demonstrated by the study of the individual tree size variables (height and diameter). The results are illustrated using experimental field studies carried out in Lithuania, in the municipality of Kazlu Ruda. The following information was gathered using 48 permanent test plots placed in mixed-species, uneven-aged stands: age, diameter at breast height (58,829 trees), tree position (58,829 trees), and height (10,796 trees). All results were implemented using the symbolic algebra system Maple.