The Bivariate Gompertz Diffusion Model for Tree Diameter and Height Distribution

Abstract

With this research we present a new method for describing the bivariate diameter and height distribution of trees growing in a pure, uneven-aged forest. We use a stochastic differential equation framework to derive a bivariate age-dependent probability density function of tree diameter and height when the tree diameter and height follow a bivariate stochastic Gompertz shape growth process. We also adopt the two-dimensional transition probability function methodology for growth modeling of forest stands. The bivariate stochastic Gompertz model is fit to diameter and height observations for 1,575 pine trees in the Dubrava district of Lithuania. A considerable advantage of the bivariate stochastic Gompertz growth model is that the model parameters are easily interpretable. All results are implemented in the symbolic algebra system MAPLE.