Analysis of Longitudinal Forest Data on Individual-Tree and Whole-Stand Attributes Using a Stochastic Differential Equation Model

Abstract

This paper focuses on individual-tree and whole-stand growth models for uneven-aged and mixed-species stands in Lithuania. All the growth models were derived using a single trivariate diffusion process defined by a mixed-effect parameters trivariate stochastic differential equation describing the tree diameter, potentially available area, and height. The mixed-effect parameters of the newly developed trivariate transition probability density function were estimated using an approximate maximum likelihood procedure. Using the relationship between the multivariate probability density and univariate marginal (conditional) densities, the growth equations were derived to predict or forecast the individual-tree and whole-stand variables, such as diameter, potentially available area, height, basal area, and stand density. All the results are illustrated using an observed dataset from 53 permanent experimental plots remeasured from 1 to 7 times. The computed statistical measures showed high predictive and forecast accuracy compared with validation data that were not used to find parameter estimates. All the results were implemented in the Maple computer algebra system.