Model building of tree height, volume, their increments and stem profile with stochastic differential equations

Abstract

Tree height, volume and stem profile modelling is most often performed using non-linear fixed or mixed effects regression models based on ordinary differential equations or the solutions thereof. More sophisticated models as e.g. stochastic differential equations (SDEs) can in many cases provide a better description of the variations, which could be useful in various aspects of modelling. Models defined through stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems of a tree: height, volume and stem profile. This class of models is becoming more and more important and is a standard tool to model financial and population growth dynamics. The SDEs method can model height, volume, their increments and stem profile curves for trees growing under different site conditions. However, this method is highly non-trivial statistical problem where an analytical likelihood function can rarely be found. In the present paper, we use the Gompertz, the Verhulst and the Vasicek forms of SDEs with multiplicative or additive noise. It also represents a general framework that can be utilized to other SDEs form