The management of forests may be motivated from production economic and environmental perspectives. The dynamically changing properties of trees affect environmental objectives and values of trees as raw material in the construction sector and in the energy sector. In order to optimize the management of forests, it is necessary to have access to reliable functions that predict how trees develop over time. One central property of a tree is the basal area, the area of the stem segment 1.3 meters above ground. In this paper, a general dynamic function for the basal area of individual trees has been developed from a production theoretically motivated autonomous differential equation. A closed form solution is derived and analyzed. Several examples of recent application of this function in Iran and Sweden are reported.

Economically optimal management of a continuous cover forest is considered here. Initially, there is a large number of trees of different sizes and the forest may contain several species. We want to optimize the harvest decisions over time, using continuous cover forestry, which is denoted by CCF. We maximize our objective function, the expected present value, with consideration of stochastic prices, timber quality variations and dynamically changing spatial competition. The problem is solved using an adaptive control function. The parameters of the control function are optimized via the first order optimum conditions based on a multivariate polynomial approximation of the objective function. The second order maximum conditions are investigated and used to determine relevant parameter ranges. The procedure is described and optimal results are derived for a general function multi-species CCF forest. Concrete examples from Germany, with beech, and from Sweden, with Norwegian spruce, are used to illustrate the methodology and typical numerical results. It is important to make market adapted harvest decisions. If the stochastic price variations are not considered when the harvest decisions are taken, the expected present value is reduced by 23%.