Matrix Modeling in Uneven-aged forest Management Planning

A matrix growth model suitable for analysis of uneven-aged forest management is developed based on recursive equations represented on matrix form. The equations consist of transition probabilities forming part of application of Markov chain theory, which describe growth between diameter classes, ingrowth to the smallest diameter class, and mortality in the larger classes. The model is exemplified with the use of growth and yield data for beech (Fagus silvatica L.). The growth model is based on a diameter class structure where the width is equal to 5 cm. The time interval between interventions is equal to 5 years. Diameter growth according to a treatment regime for even-aged stands is assumed. The system of recursive equations is solved by use of linear programming allowing analysis of economic optimal treatment. Possible stand structures are analysed using constraints in linear programming of the maximum harvest by diameter classes. Formulation of harvesting constraints is based on analysis of the production in a normal forest structure. The economic characteristics in the steady-state are analysed and the model structure is suitable for economic analysis of conversion from even-aged to uneven-aged forest management characterizing near-natural forest management. It is concluded that the model is suitable for analyses of stand structure, growth and yield, including economic yield, and analyses of different harvesting regimes applied in uneven-aged forest management.