Comparison and selection of growth models using the Schnute model

Abstract

Forestmodellers have long faced the problem of selecting an appropriate mathematical model to describe tree ontogenetic or size-shape empirical relationships for tree species. A common practice is to develop many models (or a model pool) that include different functional forms, and then to select the most appropriate one for a given data set. However, this process may impose subjective restrictions on the functional form. In this process, little attention is paid to the features (e.g. asymptote and inflection point rather than asymptote and nonasymptote) of different functional forms, and to the intrinsic curve of a given data set. In order to find a better way of comparing and selecting the growth models, this paper describes and analyses the characteristics of the Schnute model. This model has both flexibility and versatility that have not been used in forestry. In this study, the Schnute model was applied to different data sets of selected forest species to determine their functional forms. The results indicate that the model shows some desirable properties for the examined data sets, and allows for discerning the different intrinsic curve shapes such as sigmoid, concave and other curve shapes. Since no suitable functional form for a given data set is usually known prior to the comparison of candidate models, it is recommended that the Schnute model be used as the first step to determine an appropriate functional form of the data set under investigation in order to avoid using a functional form a priori.