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.
Highlights
Forest growth forecasts play an important role in the planning of timber resources and maintaining strategies of sustainable forest management
Significant errors in stand growth forecasts lead to an unreasonable use of forest resources, and they result in unsustainable forestry
Considering the evolution of individual-tree and whole-stand growth paradigms over the past decades, we focus on the “diffusion process” theory of how trees in a stand can respond differently individually and collectively to both their internal and environmental factors, which is based on the Brownian motion model
Summary
Forest growth forecasts play an important role in the planning of timber resources and maintaining strategies of sustainable forest management. Since the data on tree or stand variables are obtained from national forest inventories and experimental plots, they consist of observations through time, so it is natural to define the kinetics of trees and stands by using stochastic differential equations. Mixed-effect parameters stochastic differential equations have been used to define the kinetics of tree height via age [10] and via diameter [11], and tree crown width via age [12]. Many other mean response regression models that adjust the observed data are already available, it is clear that none of them are a panacea for the many problems that confront forest statisticians In this sense, it is important to propose and evaluate the mixed-effect parameters trivariate stochastic differential equation model for tree diameter, potentially available area, and height kinetics by age.
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