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Even-aged or uneven-aged modelling approach? A case for Pinus brutia



The past management of Pinus brutia forests in Lebanon has led to diverse stand structures that cannot be easily classified as even-aged (EA) or uneven-aged (UA). Most stands are between these stand types, and they may be called as “semi-even-aged”. This is a very common characteristic throughout the Mediterranean conifer forests and makes the choice between the EA and UA approaches problematic, in both management and modelling. However, previous research has devoted little attention to the performance of growth and yield models when applied to transitional stand structures.


The aim of this study was to find the best modelling approach and to recommend equations for simulating the dynamics of the semi-even-aged P. brutia stands of Lebanon on an individual-tree basis.


Fifty sample plots were measured in Lebanon. Individual-tree growth models were fitted to the whole dataset using either UA or EA modelling approach. Models were also fitted using two sub-samples containing the most EA and the most UA plots. The performance and accuracy of the two modelling approaches were evaluated in all three datasets.


The article provides the first complete growth model for uneven-aged P. brutia stands. The EA sub-models presented better statistical fitting. However, the UA sub-models enabled more accurate predictions of wood production and were almost as good as the EA sub-models when predicting stand dynamics of the EA plots. The EA approach provided poor predictions, and the errors were high when it was applied to UA stands.


In structurally complex stands, the UA modelling approach is to be preferred since it predicts the whole stand dynamics more accurately and enables simulations of a broader range of silvicultural treatments.

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  • Assaf N (2010) A growth and yield model for even-aged Pinus brutia Ten. stands in Lebanon. M.Sc.Thesis, University of Lleida, Spain

    Google Scholar 

  • Boydak M (2004) Silvicultural characteristics and natural regeneration of Pinus brutia Ten.—a review. Plant Ecol 171:153–163

    Article  Google Scholar 

  • Buongiorno J, Dahir S, Lu HC, Lin CR (2004) Tree size diversity and economic returns in uneven-aged forest stands. For Sci 40:83–103

    Google Scholar 

  • Clutter JL, Forston JC, Piennar LV, Brister GH, Bailey RL (1983) Timber management—a quantitative approach. Willey, New York, 333 p

    Google Scholar 

  • de-Miguel S, Pukkala T, Shater Z, Assaf N, Kraid B, Palahí M (2010) Models for simulating the development of even-aged Pinus brutia stands in Middle East. Forest Systems 19:449–457

    Google Scholar 

  • de-Miguel S, Shater Z, Kraid B, Mehtätalo L, Pukkala T (2011) Modelling the taper of Pinus brutia in Syria (in press)

  • Fischer R, Lorenz M, Köhl M, Becher G, Granke O, Christou A (2008) The condition of forests in Europe: 2008 executive report. United Nations Economic Commission for Europe, Convention on Longrange Transboundary Air Pollution, International Co-operative Programme on Assessment and Monitoring of Air Pollution Effects on Forests (ICP Forests). 23 p.

  • Fontaine M, Aerts R, Özkan K, Mert A, Gülsoy S, Süel H, Waelkens M, Muys B (2007) Elevation and exposition rather than soil types determine communities and site suitability in Mediterranean mountain forests of southern Anatolia, Turkey. For Ecol Manage 247:18–25

    Article  Google Scholar 

  • Fyllas NM, Dimitrakopoulos PG, Troumbis AY (2008) Regeneration dynamics of a mixed Mediterranean pine forest in the absence of fire. For Ecol Manage 256:1552–1559

    Article  Google Scholar 

  • Gauch HG, Hwang JTG, Fick GW (2003) Model evaluation by comparison of model-based predictions and measured values. Agron J 95:1442–1446

    Article  Google Scholar 

  • Gezer A (1985) The sylviculture of Pinus brutia in Turkey. In: CIHEAM, le pin d’Alep et le pin brutia dans la sylviculture méditerranéenne. Options Méditerranéennes, Série Etudes, Paris, 86:55-66.

  • González, JM (2005) Introducción a la selvicultura general. Ed. Universidad de León. León. 309 pp. ISBN: 84-9773-223-5.

  • Groot A (2002) Is uneven-aged silviculture applicable to peatland black spruce (Picea mariana) in Ontario, Canada? Forestry 75:437–442

    Article  Google Scholar 

  • Jactel H, Nicoll BC, Branco M, González-Olabarria JR, Grodzki W, Gangstrom B, Moreira F, Netherer S, Orazio C, Piou D, Santos H, Schelhaas MJ, Tojic K, Vodde F (2009) The influences of forest stand management on biotic and abiotic risks of damage. Ann For Sci 66

  • Kobayashi K, Salam MU (2000) Comparing simulated and measured values using mean squared deviation and its components. Agron J 92:345–352

    Google Scholar 

  • Oliver CD, Larson BC (1996) Forest stand dynamics. Update edition. Wiley, New York, p 540

    Google Scholar 

  • Palahí M, Pukkala T, Kasimiadis D, Poirazidis K, Papageorgiou AC (2008) Modelling site quality and individual-tree growth in pure and mixed Pinus brutia stands in north-east Greece. Ann For Sci 65:501

    Article  Google Scholar 

  • Peng C (2000) Growth and yield models for uneven-aged stands: past, present and future. For Ecol Manage 132:259–279

    Article  Google Scholar 

  • Peschel W (1938) Die mathematischen methoden zur herleitung der wachstumsgesetze von baum und bestand und die ergebnisse ihrer anwendung. Tharandter Forstliches Jahrburch 89:169–247

    Google Scholar 

  • Piñeiro G, Perelman S, Guerschman JP, Paruelo JM (2008) How to evaluate models: observed vs. predicted or predicted vs. observed? Ecol Model 216:316–322

    Article  Google Scholar 

  • R Development Core Team (2011) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL

  • Render B, Stair RM (1992) Introduction to management science. Allyn and Bacon, Boston, 856 pp

    Google Scholar 

  • Shater Z, de-Miguel S, Kraid B, Pukkala T, Palahí M (2011) A growth and yield model for even-aged Pinus brutia stands in Syria. Ann For Sci 68:149–157

    Article  Google Scholar 

  • Skovsgaard JP, Vanclay JK (2008) Forest site productivity: a review of the evolution of dendrometric concepts for even-aged stands. Forestry 81:13–31

    Article  Google Scholar 

  • Smith DM, Larson BC, Kelty MJ, Ashton P (1996) The practice of silviculture: applied forest ecology, 9th ed. Wiley, New York

  • Sterba H (2004) Equilibrium curves and growth models to deal with forests in transition to uneven-aged structure – application in two sample stands. Silva Fennica 38:413–423

    Google Scholar 

  • Stoffels A, Van Soest J (1953) The main problems in sample plots. Ned Boschb Tijdschr 25:190–199

    Google Scholar 

  • Tomé M. (1989) Modelação do crescimiento da árvore individual em povoamentos de Eucalyptus globulus Labill. (1ª Rotação). Região Centro de Portugal. PhD thesis, ISA, Lisbon.

  • Vanclay JK (1994) Modelling forest growth and yield: applications to mixed tropical forests. CAB International, UK, 312 p

    Google Scholar 

  • Vanclay JK (2003) Growth modelling and yield prediction for sustainable forest management. The Malaysian Forester 66(1):58–69

    Google Scholar 

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This study has been supported by the Spanish Agency for International Development Cooperation (Agencia Española de Cooperación Internacional para el Desarrollo, AECID) and Fundación Biodiversidad. The authors wish to thank the Government of Lebanon (Ministry of Agriculture) for the precious collaboration.

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Correspondence to Sergio de-Miguel.

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Handling Editor:

Eric Rigolot

Contribution of the co-authors

Sergio de-Miguel: design of sampling methods, running data analysis, writing the paper, supervising the work, and coordinating the research project.

Timo Pukkala: design of sampling, running data analysis, writing the paper, and supervising the work.

Nabil Assaf: design of sampling methods, data collection, and supervising the work.

José Antonio Bonet: writing the paper, and supervising the work.

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de-Miguel, S., Pukkala, T., Assaf, N. et al. Even-aged or uneven-aged modelling approach? A case for Pinus brutia . Annals of Forest Science 69, 455–465 (2012).

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  • Stand dynamics
  • Forest management
  • Semi-even-aged stands
  • Growth model
  • Simulation
  • Model evaluation