Application of Sigmoid Models for Growth Investigations of Forest Trees

Abstract

Radial growth of the trees and its relationships with other factors is one of the most important research areas of forestry for a long time. For measuring intra-annual growth there are several widely used methods: one of them is measuring the girth of trees regularly, preferably on weekly basis. However, the weekly measured growth data may have bias due to the actual precipitation, temperature or other environmental conditions. This bias can be reduced and using adequate growth functions the discrete growth data can be transformed into a continuous curve. In our investigations the widely used logistic, Gompertz and Richards sigmoid growth models were compared on intra-annual girth data of beech trees. To choose the best model two statistical criteria, the Akaike weight and the modified coefficient of determination were examined. Based on these investigations and the view of applicability, Gompertz model was chosen for later applications. However, we came to the conclusion that all three models can be applied to the annual growth curve with sufficient accuracy. The modified form of the Gompertz function gives three basic curve parameters that can be used in further investigations. These are the time lag, the maximum specific growth rate and the upper asymptotic value of the curve. Based on the fitted growth curves several other completely objective curve parameters can be defined. For example, the intersection of the tangent drawn in the inflection point and the upper asymptote, the distance between upper intersection point and the time lag, the time and value of the inflection point etc. and even different ratios of these parameters can be identified. The main advantages of these parameters are that they can be created uniformly and objectively from the fitted growth curves. This paper demonstrates the application opportunities of the curve parameters in a particular study of tree growth.