The stock recovery rate in a Central African rain forest: an index of sustainability based on projection matrix models

The stock recovery rate is used in most natural forests of the Congo Basin to assess logging sustainability. This rate is computed using the so-called Dimako formula. Although this formula has been used for many years now in management plans, its mathematical properties have not been closely reviewed. We show that the Dimako formula corresponds to a Leslie matrix model, and then we propose an extension of it as a Usher matrix model. The stock recovery rate at the end of the first felling cycle for six commercial species in the Central African Republic varied between 21.7% and 99.9%. As felling cycles follow each other, the stock recovery rate converged towards a limit that is the asymptotic stock recovery rate. This limit varies between 27.2% and 158.4% for the same six species. Comparing felling scenarios reveals that increasing the minimum harvest diameter was as efficient at increasing the stock recovery rate at the end of the first felling cycle as decreasing the logging intensity. The results for the other parameters of the felling scenarios varied among species, with changes in the stock recovery rate ranging from 0% to 180% at the end of the first felling cycle, and changes in the asymptotic rate ranging from 0% to 685%.