Evolution of the bivariate tree diameter and height distributions via the stand age: von Bertalanffy bivariate diffusion process approach

Abstract

This paper focuses on the tree diameter and height distribution modeling and prediction technique, which better reflects the tree size dynamics in a stand. The evolution of the tree diameter and height structure in a forest stand is modeled using the bivariate fixed- and mixed-effect parameters Bertalanffy-type stochastic differential equation, resulting in a new biologically plausible class of bivariate lognormal probability density functions of the tree size components for response to the average stand age. The newly developed bivariate lognormal shape probability density function of the tree diameter and height at a given stand age can be used to describe the evolution of the mean diameter, height, stem volume, and stand volume per hectare in a stand in the forward and backward directions. Fixed and random effects are estimated by the maximum likelihood procedure using the Scots pine trees dataset in Lithuania.