A Matrix Approach to the Management of Renewable Resources, with Special Reference to Selection Forests-Two Extensions

In an earlier paper in this Journal (Usher 1966) a mathematical model was developed for renewable resources that could be categorized by size classes. The model was developed to answer the question: 'Given the effect of the site factors on the growth of the resource, what then is the structure of the resource that will achieve the maximum sustained yield?' Various parameters of the organisms-the processes of enlargement, the processes of recruitment to the smallest size classes, and the management decision of how to deal with large organisms-were included in a matrix Q, whose dominant latent root determined the exploitation. The latent vector associated with this root gave the structure of the resource that would give a sustained yield. However, in the Appendix to the paper, one problem of the model was stated as: '. . . any latent root greater than unity of the matrix Q determines a structure that is biologically meaningful. It cannot yet be proved that there is only one latent root greater than unity which satisfies the matrix Q.' There was thus no unique soluton to the model, and the forest manager might have been faced with the problem of which of several structures to use.