Evaluating management regimes for European beech forests using dynamic programming

  • Juan Torres Rojo Centro de Investigación y Docencia Económicas, A.C. Lomas de Santa Fé, México D.F.
  • Klaus von Gadow Retired. Dept of Forest and Wood Science, University of Stellenbosch, South Africa, and Burckhardt Institut, Georg-August-Universität Büsgenweg. Göttingen.
  • Frantisek Vilcko Burckhardt Institut, Georg-August-Universität, Göttingen.

Abstract

Aim of study: This contribution describes a systematic search method for identifying optimum thinning regimes for beech forests (Fagus sylvatica L.) by using a combination of optimization heuristics and a simple whole stand growth prediction model. 

Area of study: Data to build the model come from standard and management forest inventories as well as yield tables from the Northern and Western part of Germany and from southern and central Denmark.

Material and Methods: Growth projections are made from equations to project basal area and top height.  The remaining stand variables are recovered from additional equations fitted from forest inventory data or acquired from other authors.  Mortality is estimated through an algorithm based on the maximum density line. The optimization routine uses a two-state dynamic programming model. Thinning type is defined by the NG index, which describes the ratio of the proportion of removed trees and basal area with respect to the same proportion  before thinning. 

Main results: Growth equations fitted from inventory data show high goodness of fit with R2 values larger than 0.85 and high significance levels for the parameter estimates. The mortality algorithm converges quickly providing mortality estimates within the expected range.

Research Highlights: The combination of a simple growth and yield model within a Dynamic Programming framework in conjunction with NG values as indicators of thinning type yield good estimates of practical thinning schedules compared to thinning recommendations provided by diverse authors.

Keywords: beech (Fagus sylvatica L.); NG ratio; thinning optimization; growth and yield simulation; mortality.

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References

Altherr E, 1971. Alternatives to producing large dimensional beech logs. Report for the 15th meeting of the Forestry Union of Baden-Württemberg. Germany. Forstverein:123-127.

Álvarez-González, JG, Zingg, A. and Gadow, KV, 2009: Estimating Growth in Beech Forests - a study based on longterm experiments in Switzerland. Annals of Forest Science. 67: 307. http://dx.doi.org/10.1051/forest/2009113

Amidon EL, Akin GS, 1968. Dynamic programming to determine optimal levels of growing stock. Forest Science 14: 287-291.

Arimizu T, 1959. Dynamic programming in forestry. J of Japan Forest Society 41: 448-458.

Baur F, 1881. About thinnings and thinning trials. In (Ganhofer, A. ed.): Das forstliche Versuchswesen (Vol. 1). Commission der B. Schmid'schen Buchhandlung (A. Manz).

Brodie JD, Adams DM, Kao C, 1978. Analysis of economic impacts on thinning and rotation for Douglas-fir using dynamic programming. Forest Science 24: 513-522.

Brodie JD, Haight RG, 1985. Optimization of silvicultural investment for several types of stand projection system. Canadian J of Forestry Research 15: 188-191. http://dx.doi.org/10.1139/x85-034

Brodie JD, Kao C, 1979. Optimizing thinning in Douglas fir with three-descriptor dynamic programming to account for accelerated diameter growth. Forest Science 25: 665-672.

Chen CM, Rose DW, Leary RA, 1980. Derivation of optimal stand density over time-a discrete stage, continuous state dynamic programming solution. Forest Science 26: 217-227.

Dittmar O, Knapp E, Lembcke G, 1986. GDR Yield Table for beech 1983 (in German). IFE-Berichte.

Döbbeler H, Spelmann H, 2002. Methodological approach to simulate and evaluate silvicultural treatments under climate change. Forstw. Cbl. 121, Supplement 1: 52-69.

Eberhard J, 1902. Tables for estimating site quality and yields based on mean height for Fir, Spruce, Pine, Beech and Oak (In German). Selbstverl. d. Ver. Eidgenössische Anstalt für das forstliche Versuchswesen Birmensdorf, 1983: Ertragstafeln 3 Auflage.

Franz F, Bachler J, Deckelmann B, Kennel E, Kennel R, Schmidt A, Wotschikowski U, 1973. Forest Inventory in Bavaria 1970/71 – Methods of Assessment and Analysis (in German). Forstl. Forschungsanstalt München, Forschungsbericht Nr. 11.

Freist H, 1962. Investigations about the response of beech to thinning and use of this information for practical management (In German) Forstwiss. Forschungen Nr. 17. Paul Parey, Berlin, Germany.

Gadow K, 1992. A growth and yield model for predicting the development of stand parameters (in German). In: Festschrift zum 65 (Preuhsler T, Röhle H, Utschig H.v, Bachmann M., Eds.). Geburtstag von Prof. Franz; Lehrstuhl f. Waldwachstumskunde, Universität München, Germany: 75-83.

Gadow K, Heydecke H, 2000. Growth and thinning in a mixed beech forest (in German). Forst und Holz 56(3): 86-88.

Grundner F, 1904. Investigations in a beech high forest about growth and volume yields (in German), Springer, Berlin, Germany.

Hessenmöller D, 2001. Models for simulating growth and thinnings in a beech ecosystem near Göttingen/Germany (in German). Doctoral thesis, Georg-August-Universität-Göttingen. Logos Verlag, Berlin, Germany. 163 S.

Hoffmann F, 1995. FAGUS, a model for growth and development of beech. Ecol. Model. 83 (3): 327-348. http://dx.doi.org/10.1016/0304-3800(94)00101-8

Kassier HW, 1993. Dynamics of Diameter and Height Distributions in Commercial Timber Plantations, Doctoral thesis, Faculty of Forestry, Univ. of Stellenbosch, South Africa.

Kilkki, P, Väisänen U, 1970. Determination of the optimum cutting policy for the forest stand by means of dynamic programming. Acta Forestalia Fennica 102: 22 pp.

Klädtke J, 2002. On the growth of beech trees with large crowns and consequences for silviculture (in German). Forstarchiv 73, S. 211:217.

Nagel J, Albert M, Schmidt M, 2002. BWINPro 6.1 – a growth model for silvicultural decisions (in German). Forst und Holz 57(15/16): 486-493.

Paredes VGL, Brodie JD, 1987. Efficient specification and solution of the even-aged rotation and thinning problem. Forest Science 33: 14-29.

Paulsen JC, 1795. Practical guide to Forest Management (In German). Detmold, Germany.

Pretzsch H, Kahn M, 1998. Design and Development of Growth Models for mixed forests in Bavaria. Final report Project W28 part 2. Design and Development of the Growth Model SILVA 2.2 – Methodological Base (in German). Lehrstuhl für Waldwachstumskunde der Ludwig-Maximilians-Universität München, Freising, Germany, 279 S.

Ritters K, Brodie JD, Hann DW, 1982. Dynamic programming for optimization of timber production and grazing in ponderosa pine. Forest Science 28: 517-526.

Schober R, 1972. The European beech 1971 (in German). J. D. Sauerländer's Verlag, Frankfurt am Main, 333 pp.

Schober R. 1987. Yield Tables of important tree species (in German). Sauerländer's Verlag.

Schwappach A, 1890. Growth and Yield of normal spruce stands (in German) J. Springer, Berlin, Germany. 100 S.

Schwappach A, 1911. The European beech (In German). Neumann Verlag, Neudamm.

Skovsgaard JP, Mosing UM, 1996. beech Yields in Eastern Jutland (in Danish). Danish Forest and Landscape Research Institute.

Sloboda B, 1971. First order differential equations for depicting growth processes (in German) Mitt. Bad. – Württemb. Forstl. Vers. u. Forsch. Anstalt. Heft. 32.

Souter RA, 1986. Dynamic stand structure in thinned stands of naturally regenerated loblolly pine in the Georgia Piedmont. Doctoral thesis. University of Georgia. Athens, USA.

Staupendahl K, 1999. Stand level modeling of thinnings in pure beech stands based on the stem number – basal area ratio (in German). Deutscher Verband forstlicher Forschungsanstalten. Sektion Ertragskunde. S. 112-125.

Trincado G, Gadow Kv, 1996. Estimating assortments in standing hardwood trees (in German). Centralblatt für das gesamte Forstwesen 1, 27-38

Wiedemann E, 1931. The European beech (in German). Mitteilung aus Forstwirtschaft und Forstwissenschaft, 96 S.

Wilhelm GJ, Letter H-A, Eder W, 1999. Concept of a near-natural production of high value timber of large dimensions (in German). AFZ/Der Wald 54: 232-240.

Wimmenauer E, 1914. Investigations about assortment yields in beech forests based on assessments by the research station of Baden (in German). Mitteilungen aus dem forstlichen Versuchswesen Badens, 140 pp.

Yoda K, Kira T, Ogawa H, Hozami K, 1963. Self thinning in overcrowded pure stands under cultivated and natural conditions. J. Biol.Osaka City Univ. 14:107–129.

Zhang, CY, Petráš, R., Zhao, XH and Gadow, Kv, 2009: Estimating Beech Growth and Survival - a study based on longterm experiments in Slovakia. AFJZ, German Journal of Forest Research. 180 (3/4): 45-55.

Published
2014-12-01
How to Cite
Rojo, J. T., von Gadow, K., & Vilcko, F. (2014). Evaluating management regimes for European beech forests using dynamic programming. Forest Systems, 23(3), 470-482. https://doi.org/10.5424/fs/2014233-05296
Section
Research Articles