Using optimization for fitting individual-tree growth models for uneven-aged stands

A convenient model type for simulating the dynamics of uneven-aged and uneven-sized stands of Finland is individual-tree model. This is because the stand structures are complex due to the presence of several tree species and irregular size distributions of trees. The required minimum set of models in this approach consists of species-specific individual-tree diameter increment models, individual-tree survival models, and ingrowth models. The development of these models needs data in which the diameter and survival of each tree of the sample plots is known for at least two time points. For this, the trees need to be numbered, which is tedious in uneven-aged forests due to the great number of small trees and the continuous ingrowth process. This study proposes a modelling approach that fits the above models but requires only the diameter distributions of the plots in the beginning and at the end of the measurement interval. The method uses non-linear optimization to derive such values for model parameters that, when the models are applied to the initial diameter distribution, the simulated stand development results in a diameter distribution which agrees with the measured ending distribution. The study showed that the method produces similar models and model parameters as regression analysis. Since the method is less demanding in terms of modelling data, it brings new data sets available for modelling the dynamics of uneven-aged stands and reduces the cost of collecting new data. The models fitted by the proposed optimization method were rather similar to the models developed earlier for Finnish uneven-aged forests.