A Mathematical Model for an Energy Forest

A mathematical model for a forest consisting of a single species of trees with a steady state distribution of age is suggested. The forest is self-sustained in the sense that trees put out seeds from which new trees will grow. Therefore, there will be trees of different year classes. The rules for tree cutting are obtained to maximize the physical yield from the forest. The rule of cutting is given by function u(τ) of the age τ of the tree which tells which fraction of all trees of age τ of the forest must be felled during unit time. Function u(τ) is obtained by using a slightly generalized optimal control theory which reduces the problem to a fairly simple nonlinear programming problem. The cost of harvesting may be included in the objective functional. All biological characteristics of a forest are contained in two functions of the age of a tree. These functions would be obtained through a process of identification. The model is intended to be a part of a large forest-economy system, therefore mathematical simplicity has been a goal.