Estimating the sustainable harvesting and the stable diameter distribution of European beech with projection matrix models

We present a projection matrix model to estimate the sustainable harvest rates and the stable diameter distributions of three qualities of European beech in the Spanish province of Navarre. Considering a period of 10 years and the diameter growth, trees were grouped into five classes: (0,10), (10,20), (20,30), (30,40) and over 40 cm. The transition probabilities were calculated assuming an approximation by splines to the diameter growth curves and uniform distributions for the diameters in each class. A condition for sustainable harvesting, leading to reach in each harvest the stable diameter distribution, was introduced. The results obtained suggest that, for each projection and depending on the quality, harvest rates in the range 18.8–37.5% for recruitments in the range 200–840 stems/ha, may be sustained without risk of a population reduction. Finally, the stable diameter distributions in relation to the recruitment were also obtained for each quality.