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

Abstract

. Estimating the sustainable harvesting and the stable diameter distribution of European beech with projection matrix models. Annals of Forest Science, Springer Verlag/EDP Sciences, 2007, 64 (6), pp.593-599. <hal-00884111>Ann. For. Sci. 64 (2007) Abstract -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.sustainability / projection matrix model / European beech / harvesting / stable diameter distribution Résumé -Estimation de la récolte renouvelable et de la distribution stable du diamètre du hêtre par une projection de modèles matriciels. Nous présentons une projection de modèle matriciel pour estimer les taux de récolte renouvelable et les distributions stables de diamètre de trois qualités de hêtre dans la province espagnole de Navarre. La croissance en diamètre sur une période de 10 ans a été prise en compte pour des arbres regroupés en cinq classes de diamètre : (0,10), (10,20), (20,30) et au-delà de 40 cm. Les probabilités ont été calculées en adoptant une approximation par aboutement des courbes de diamètre et les distributions uniformes pour les diamètres dans chaque classe de diamètre. Une condition pour une récolte renouvelable, importante pour atteindre une distribution stable de diamètre, a été introduite. Les résultats obtenus suggèrent, que pour chaque projection et en relation avec la qualité, un taux de récolte se situe dans une variation de 18,8 à 37,5 % pour un recrutement dans une variation de 200 à 840 arbres à l'hectare, peut être supporté sans risque pour une réduction de population. Finalement, des distributions stables de diamètre en relation avec le recrutement ont été obtenues pour chaque qualité. renouvelable / projection de modèle matriciel / hêtre / récolte / distribution stable de diamètre

Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing?

“…For these cases, similar to other matrix models for tree species [25], we attributed the global amount of recruitment R entirely to the last diameter class (r 2 = r 3 = … = r n-1 = 0; r n = ), which had no influence on the stable diameter distribution of the stand, which is established by transition probabilities, the global amount of recruitment and stand basal area [7].…”

“…The above mentioned transition probability formula is a direct application of the one introduced by López et al [7,8] for a Bertalanffy-Richards model. We provide the calculations for Qualities I-III in Table 1.…”

“…The model for recruitment, harvesting and stem migration throughout the dbh classes over time is based on the model proposed by López et al [7,8] for Fagus sylvatica L. and by López et al [9] for Pinus nigra Arn. stands.…”

“…In fact, given the transition probabilities between diameter classes, for each pair (R, G), where G is the stand basal area and R is the global amount of recruitment, the stable diameter distributions of managed uneven-aged Fagus sylvatica L. and Pinus nigra Arn. stands were calculated in [7][8][9]] using a matrix model of stand diameter classes evolution. Those stable diameter distributions are associated with the "sustainable/stable" harvesting strategy [7,8], aimed at reaching in each harvest the proportions of stems/ha in each class corresponding to the stable diameter distribution of the stand, yielding the following "sustainable/stable" harvest rate:…”

“…stands were calculated in [7][8][9]] using a matrix model of stand diameter classes evolution. Those stable diameter distributions are associated with the "sustainable/stable" harvesting strategy [7,8], aimed at reaching in each harvest the proportions of stems/ha in each class corresponding to the stable diameter distribution of the stand, yielding the following "sustainable/stable" harvest rate:…”