Skip to main content
Download PDF
  • Original Article
  • Published:

Estimating growth in beech forests: a study based on long term experiments in Switzerland

Estimation de la croissance dans les hêtraies : une étude basée sur des expérimentations à long terme en Suisse

Annals of Forest Science volume 67, page 307 (2010)Cite this article

Abstract

  • • This contribution presents a dynamic stand growth model for Beech (Fagus sylvatica L.) forests, based on a dataset provided by the Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf. The dataset includes 143 research plots, covering a wide range of growing sites and providing up to 16 interval measurements per research plot.

  • • The objective of this research is to complement the range of existing beech growth models by bridging the gap between the historical yield tables and the single tree growth models. The specific aim is to develop transition functions which will project three state variables (dominant height, basal area and number of trees per hectare) at any particular time, in response to any arbitrary silvicultural treatment.

  • • Two of the transition functions were derived using the generalized algebraic difference approach (GADA), the third one was derived with the algebraic difference approach (ADA). All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The influence of thinnings on basal area growth was included by fitting different transition functions for thinned and unthinned stands.

  • • The overall model provides satisfactory predictions for time intervals up to 20 years. The new model is robust and its relatively simple structure makes it suitable for economic analysis and decision support.

Résumé

  • • Cette contribution présente un modèle dynamique de croissance des peuplements de hêtres (Fagus sylvatica L.), basé sur un ensemble de données fournies par l’Institut Fédéral Suisse de Recherche sur la Forêt, la Neige et le Paysage, WSL à Birmensdorf. L’ensemble des données comprend 143 parcelles de recherche, couvrant un large éventail de sites et fournissant jusqu’à 16 intervalles de mesures par parcelle de recherche.

  • • L’objectif de cette recherche est de compléter la gamme de modèles de croissance du hêtre existants, en jetant un pont entre les tables de production historiques et les modèles de croissance d’arbre. L’objectif spécifique est de développer des fonctions de transition qui projeterons trois variables d’état (hauteur dominante, surface terrière et nombre d’arbres par hectare) à n’importe quel moment déterminé, en réponse à n’importe quel traitement sylvicole arbitraire.

  • • Deux des fonctions de transition ont été calculées en utilisant l’approche différence algébrique généralisée (GADA), la troisième a été dérivée de l’approche différence algébrique (ADA). Toutes les fonctions ont été ajustées en utilisant simultanément une régression itérative sans lien apparent et une méthode basée sur l’invariance de l’âge. L’influence des éclaircies sur la croissance de la surface terrière a été inclue en ajustant différentes fonctions de transition pour les peuplements éclaircis et les peuplements non éclaircis.

  • • Le modèle général fournit des prédictions satisfaisantes pour des intervalles de temps jusqu’à 20 ans. Le nouveau modèle est robuste et sa structure relativement simple fait qu’il est convient pour l’analyse économique et l’aide à la décision.

References

  • Álvarez-González J.G., Castedo-Dorado F., Ruiz González A.D., López Sánchez C.A., and Gadow K.V., 2004. A two-step mortality model for even-aged stands of Pinus radiata D. Don in Galicia (Northwestern Spain). Ann. For. Sci. 61: 439–448.

    Article  Google Scholar 

  • Álvarez-González J.G., Ruiz González A.D., Rodríguez Soalleiro R., and Barrio Anta M., 2005. Ecoregional site index models for Pinus pinaster in Galicia (northwestern Spain). Ann. For. Sci. 62: 115–127.

    Article  Google Scholar 

  • Amateis R.L., 2000. Modeling response to thinning in loblolly pine plantations. South. J. Appl. For. 24: 17–22.

    Google Scholar 

  • Badoux E., 1983. Ertragstafeln Buche. Eidg. Amt. Forstl. Versuchswes., 3rd ed.

  • Bailey R.L. and Clutter J.L., 1974. Base-age invariant polymorphic site curves. For. Sci. 20: 155–159.

    Google Scholar 

  • Barrio Anta M., Castedo Dorado F., Diéguez-Aranda U., Álvarez González, J.G., Parresol B.R., and Rodríguez R., 2006. Development of a basal area growth system for maritime pine in northwestern Spain using the generalized algebraic difference approach. Can. J. For. Res. 36: 1461–1474.

    Article  Google Scholar 

  • Bertalanffy L.V., 1957. Quantitative laws in metabolism and growth. Q. Rev. Biol. 32: 217–231.

    Article  Google Scholar 

  • Bolte A., Czajkowski T., and Kompa T., 2007. The north-eastern distribution range of European beech — a review. Forestry 80: 413–429.

    Article  Google Scholar 

  • Castedo-Dorado F., Diéguez-Aranda U., and Álvarez-González J.G., 2007a. A growth model for Pinus radiata D. Don stands in north-western Spain. Ann. For. Sci. 64: 453–465.

    Article  Google Scholar 

  • Castedo-Dorado F., Diéguez-Aranda U., Barrio Anta M., and Álvarez-González J.G., 2007b. Modelling stand basal area growth for radiata pine plantations in Northwestern Spain using the GADA. Ann. For. Sci. 64: 609–619.

    Article  Google Scholar 

  • Cieszewski C.J., 2002. Comparing fixed- and variable-base-age site equations having single versus multiple asymptotes. For. Sci. 48: 7–23.

    Google Scholar 

  • Cieszewski C.J., 2003. Developing a well-behaved dynamic site equation using a modified Hossfeld IV function Y3 = (axm)/ (c + xm_1), a simplified mixed-model and scant subalpine fir data. For. Sci. 49: 539–554.

    Google Scholar 

  • Cieszewski C.J. and Bailey R.L., 2000. Generalized algebraic difference approach: theory based derivation of dynamic site equations with polymorphism and variable asymptotes. For. Sci. 46: 116–126.

    Google Scholar 

  • Cieszewski C.J., Harrison M., and Martin S.W, 2000. Practical methods for estimating non-biased parameters in self-referencing growth and yield models. University of Georgia, PMRC-TR 2000-7.

  • Clutter J.L. and Jones E.P., 1980. Prediction of growth after thinning in oldfield slash pine plantations, USDA For. Serv. Pap. SE-217.

  • Clutter J.L., Fortson J.C., Pienaar L.V., Brister G.H., and Bailey R.L., 1983. Timber management — A quantitative approach, John Wiley & Sons, 333 p.

  • Diéguez-Aranda U., Castedo-Dorado F., Álvarez González J.G., and Rodríguez-Soalleiro R., 2005. Modelling mortality of Scots pine (Pinus sylvestris L.) plantations in the northwest of Spain. Eur. J. For. Res. 124: 143–153.

    Google Scholar 

  • Diéguez-Aranda U., Castedo F., Álvarez González J.G., and Rojo A., 2006. Dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain). Ecol. Model. 191: 225–242.

    Article  Google Scholar 

  • Gadow K.V., 2006. Forsteinrichtung — Adaptive Steuerung und Mehrpfadprinzip. Universitätsdrucke Göttingen.

  • Gadow K.V. and Pukkala T., 2008. Designing Green Landscapes. Managing Forest Ecosystems Vol. 15, Springer Verlag, Dordrecht.

    Book  Google Scholar 

  • García O., 1988. Growth modelling — a (re)view. N. Z. J. For. Sci. 33 (3): 14–17.

    Google Scholar 

  • García O., 1994. The State-Space Approach in Growth Modeling. Can. J. For. Res. 24: 1894–1903.

    Article  Google Scholar 

  • Gregoire T.G., Schabenberger O., and Barrett J.P., 1995. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Can. J. For. Res. 25: 137–156.

    Article  Google Scholar 

  • Hallenbarter D., Hasenauer H., and Zingg A., 2005. Validierung des Waldwachstumsmodells MOSES für Schweizer Wälder. Schweiz. Z. Forstwes. 156, 5: 149–156.

    Article  Google Scholar 

  • Hasenauer H., Burkhart H.E., and Amateis R.L., 1997. Basal area development in thinned and unthinned loblolly pine plantations. Can. J. For. Res. 27: 265–271.

    Article  Google Scholar 

  • Huang S., Yang Y., and Wang Y., 2003. A critical look at procedures for validating growth and yield models. In: Amaro A., Reed D. and Soares P. (Eds.). Modelling forest systems. CAB International, Wallingford, UK, pp. 271–293.

    Google Scholar 

  • Hynynen J., 1995. Predicting the growth response to thinning for Scots pine stands using individual-tree growth models. Silva Fenn. 29: 225–247.

    Google Scholar 

  • Knoebel B.R., Burkhart H.E., and Beck D.E., 1986. A growth and yield model for thinned stands of yellow-poplar. For. Sci. Monogr. 27.

  • Korf V., 1939. Pøíspìvek k matematické definici vzrùstového zákona lesních porostù. Lesnická práce 18: 339–356.

    Google Scholar 

  • Kozak A. and Kozak R., 2003. Does cross validation provide additional information in the evaluation of regression models? Can J. For. Res. 33: 976–987.

    Article  Google Scholar 

  • Lindstrom M. and Bates D., 1990. Nonlinear mixed effects models for repeated measures data. Biometrics 46: 673–687.

    Article  PubMed  CAS  Google Scholar 

  • Monserud R.A., 1984. Height growth and site-index curves for inland Douglas-fir based on stem analysis data and forest habitat type. For. Sci. 30: 943–965.

    Google Scholar 

  • Nagel J., Albert M., and Schmidt M., 2002. Das waldbauliche Prognose- und Entscheidungsmodell BWINPro 6.1. Forst Holz 57 (15/16): 486–493.

    Google Scholar 

  • Nord-Larsen T. and Johannsen V.K., 2007. A state-space approach to stand growth modelling of European beech. Ann. For. Sci. 64: 365–374.

    Article  Google Scholar 

  • Paulsen J.C., 1795. Praktische Anweisung zum Forstwesen, Detmold.

  • Pienaar L.V. and Shiver B.D., 1984. An analysis and models of basal area growth in 45-year-old unthinned and thinned slash pine plantation plots. For. Sci. 30: 933–942.

    Google Scholar 

  • Pienaar L.V., Shiver B.D., and Grider G.E., 1985. Predicting basal area growth in thinned slash pine plantations. For. Sci. 31: 731–741.

    Google Scholar 

  • Pretzsch H., Biber P., Ïurský J., Gadow K.V., Hasenauer H., Kändler G., Kenk G., Kublin E., Nagel J., Pukkala T., Skovsgaard J.P., Sodtke R., and Sterba, H., 2002. Recommendations for standardized documentation and further development of forest growth simulators. Forstw. Cbl. 121 (3): 138–151.

    Article  Google Scholar 

  • Rennolls K. and Peace A., 1986. Flow models of mortality and yield for unthinned forest stands. Forestry 59: 47–58.

    Article  Google Scholar 

  • Reynolds M.R., 1984. Estimating the error in model predictions. For. Sci. 30: 454–468.

    Google Scholar 

  • SAEFL/WSL, 2005. Forest Report 2005 — Facts and Figures about the Condition of Swiss Forests. Swiss Agency for the Environment, Forest and Landscape and Swiss Federal Research Institute, Berne/Birmensdorf.

    Google Scholar 

  • SAS Institute Inc., 2004. SAS/ETS1 9.1.2. User’s Guide. SAS Institute Inc., Cary, NC.

    Google Scholar 

  • Schmid S., Zingg A., Biber, P., and Bugmann H., 2006. Evaluation of the forest growth model SILVA along an elevational gradient in Switzerland. Eur. J. For. Res. 125: 43–55.

    Google Scholar 

  • Sharma M., Smith M., Burkhart H.E., and Amateis R.L., 2006. Modeling the impact of thinning on height development of dominant and codominant trees, Ann. For. Sci. 63: 349–354.

    Article  Google Scholar 

  • Sterba H. and Monserud, R.A., 1997. Applicability of the forest stand growth simulator Prognaus for the Austrian part of the Bohemian Massif. Ecol. Model. 98: 23–34.

    Article  Google Scholar 

  • Vanclay J.K., 1995. Growth models for tropical forests: a synthesis of models and methods. For. Sci. 41: 7–42.

    Google Scholar 

  • Woollons R.C., 1998. Even-aged stand mortality estimation through a two-step regression process, For. Ecol. Manage. 105: 189–195.

    Article  Google Scholar 

  • Yang Y., Monserud R.A., and Huang, S., 2004. An evaluation of diagnostic tests and their roles in validating forest biometrics models. Can. J. For. Res. 34: 619–629.

    Article  Google Scholar 

  • Zarnoch S.J., Feduccia D.P., Baldwin V.C., and Dell T.R., 1991. Growth and yield predictions for thinned and unthinned slash pine plantations on cutover sites in the West Gulf region. USDA Forest Service Res. Pap. SO-264.

Download references

Author information

Authors and Affiliations

  1. Unidad de Gestión Forestal Sostenible, Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela, Lugo, Spain

    Juan Gabriel Álvarez-González

  2. Snow and Landscape Research WSL, Swiss Federal Institute for Forest, Birmensdorf, Switzerland

    Andreas Zingg

  3. Faculty of Forest Sciences and Forest Ecology, Burckhardt-Institute, Georg-August-University Göttingen, Göttingen, Germany

    Klaus V. Gadow

Authors
  1. Juan Gabriel Álvarez-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Zingg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Klaus V. Gadow
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Gabriel Álvarez-González.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Álvarez-González, J.G., Zingg, A. & Gadow, K.V. Estimating growth in beech forests: a study based on long term experiments in Switzerland. Ann. For. Sci. 67, 307 (2010). https://0-doi-org.brum.beds.ac.uk/10.1051/forest/2009113

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://0-doi-org.brum.beds.ac.uk/10.1051/forest/2009113

Keywords

Mots-clés

Annals of Forest Science

ISSN: 1297-966X