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

Estimation de la récolte renouvelable et de la distribution stable du diamètre du hêtre par une projection de modèles matriciels

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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.

Résumé

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.

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Authors and Affiliations

  1. Universidad Politécnica de Madrid (UPM), ETSI de Montes, 28040, Madrid, Spain

    Ignacio López, Sigfredo Francisco Ortuño & Ángel Julián Martín

  2. Universidad Pontificia de Comillas, Alberto Aguilera, 23, 28015, Madrid, Spain

    Carmen Fullana

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  1. Ignacio López
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  2. Sigfredo Francisco Ortuño
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  3. Ángel Julián Martín
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  4. Carmen Fullana
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Correspondence to Ignacio López.

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López, I., Ortuño, S.F., Martín, Á.J. et al. Estimating the sustainable harvesting and the stable diameter distribution of European beech with projection matrix models. Ann. For. Sci. 64, 593–599 (2007). https://doi.org/10.1051/forest:2007037

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  • DOI: https://doi.org/10.1051/forest:2007037

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