A Matrix Model for Forest Management

A model for the management of renewable resources is developed, a variant of a model previously given by Usher [1966] which posed one question-is the manager faced with one or several solutions? The mathematical development here shows that there is only one solution of the model that is biologically meaningful. This is associated with the only latent root of the matrix which is greater than unity. This dominant latent root has a latent vector such that all the elements can be chosen as positive. The result is based on a study of the derivative of the model, and from this a rapid method of solving the model is described. Data for a Scots pine forest are given.