Modelling of tree diameter growth using growth functions parameterised by least squares and Bayesian methods

Abstract

The purpose of this paper is to present a new growth and yield function (denoted as KM-function), which was empirically derived from the cumulative density function of the Kumaraswamy probability distribution. KM-function is theoretically well disposed for the prediction of future growth; however, the function also has other theoretical features that make it useful also for retrospective estimation of the past growth frequently used in biological analyses of growth in the initial life stages. In order to demonstrate the practical applicability of the KM-function for growth reconstruction, an investigation of the accuracy of five-year retrospective projections of the real tree diameters obtained by stem analyses of 35 beech trees was done. Bias and accuracy of the new function were compared with bias and accuracy of some well-known growth functions on the same database. Compared functions were parameterised in two ways: by the method of nonlinear least squares and Bayesian methods. Empirical validation of the KM-function confirmed its good theoretical properties when it was used for retrospective estimation of the tree diameter growth. The valuable knowledge of this research is also a finding that the incorporation of a great deal of a priori known facts about the growth of trees and stands in natural conditions of Slovakia into Bayesian parameter estimation led to a decrease in the bias and magnitude of reconstruction errors.