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A state-space approach to stand growth modelling of European beech

Une approche étatespace de la modélisation de la croissance des peuplements de hêtre

Annals of Forest Science volume 64, pages 365–374 (2007)Cite this article

Abstract

Static models of forest growth, such as yield tables or cumulative growth functions, generally fail to recognize that forest stands are dynamic systems, subject to changes in growth dynamics due to silvicultural interventions or natural dynamics. Based on experimental data, covering a wide range of initial spacings and thinning practises, we developed a dynamic stand growth model of European beech in Denmark. The model entailed three equations for predicting dominant height growth, basal area growth, and mortality. The signs of the parameter estimates generally corroborated the anticipated growth paths of dominant height and basal area. Although statistical tests indicated significant systematic deviations between observed and predicted values, the deviations were small and of little practical importance. Cross validation procedures indicated that the model may be applied across a wide range of growth conditions and thinning practises without significant loss of precision.

Résumé

Les modèles statiques de croissance des peuplements forestiers, tels que les tables de production ou les fonctions cumulatives de croissance, ne reconnaissent pas que les peuplements forestiers sont des systèmes dynamiques, soumis à des changements de dynamiques de croissance dus aux interventions sylvicoles ou à des dynamiques naturelles. Sur la base de données expérimentales, couvrant un large éventail d’espacements initiaux et de pratiques d’éclaircie, nous avons développé un modéle dynamique de croissance de peuplement pour le hêtre au Danemark. Le modèle comporte trois équations pour prédire la croissance de la hauteur dominante, la croissance de la surface terrière et la mortalité. Les signes des paramètres estimés ont confirmè en général la trajectoire prévue de la croissance de la hauteur dominante et de la surface terrière. Bien que les tests statistiques aient indiqué des déviations systématiques significatives entre valeurs observées et valeurs prédites, les déviations ont été faibles et de peu d’importance pratique. Des procédures de validation croisées ont indiqué que le modèle peut être appliqué dans un large éventail de conditions de croissance et de pratiques sylvicoles sans perte significative de précision.

References

  1. Bailey R.L., Clutter J.L., Base-age invariant polymorphic site curves, For. Sci. 20 (1974) 155–159.

    Google Scholar 

  2. Bertalanffy L.v., Quantative laws in metabolism and growth, Quart. Rev. Biol. 32 (1957) 217–231.

    Article  Google Scholar 

  3. Borders B.E., Bailey R.L., A compatible system of growth and yield equations for slash pine fitted with restricted three-stage least squares, For. Sci. 32 (1986) 185–201.

    Google Scholar 

  4. Cao Q.V., Prediction of annual diameter growth and survival for individual trees from periodic measurements, For. Sci. 46 (2000) 127–131.

    Google Scholar 

  5. Cao Q.V., Annual tree growth predictions from periodic measurements, Gen. Tech. Rep. SRS-71, U.S. Dep. Agric. For. Serv. Southern Research Station, 2004.

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

    Google Scholar 

  7. Clutter J.L., Compatible growth and yield models for loblolly pine, For. Sci. 9 (1963) 354–371.

    Google Scholar 

  8. DeBell D.S., Harrington C.A., Density and rectangularity of planting influence 20-year growth and development of red alder, Can. J. For. Res. 32 (2002) 1244–1253.

    Article  Google Scholar 

  9. Dent J.B., Blackie M.J., Systems Simulation in Agriculture, Applied Science Publishers Ltd., London 1979, pp. 94–117.

    Google Scholar 

  10. Dippel M., Auswertung eines Nelder-Pflanzenverbandsversuchs mit Kiefer im Forstamt Walsrode Allg. Forst-Jagdztg. 153 (1982) 137–154.

    Google Scholar 

  11. Farmer A.D., Morris D.M., Weaver K.B., Garlick K., Competition effects in juvenile jack pine and aspen as influenced by density and species ratios, J. Appl. Ecol. 25 (1988) 1023–1032.

    Article  Google Scholar 

  12. Freese F., Testing accuracy, For. Sci. 6 (1960) 139–145.

    Google Scholar 

  13. Galiñski W., Witowski J., Zwieniecki M., Non-random height pattern formation in even-aged Scots pine (Pinus sylvestris L.) Nelder plots as affected by spacing and site quality, Forestry 67 (1994) 49–61.

    Article  Google Scholar 

  14. García O., A stochastic differential equation model for height growth of forest stands, Biometrics 39 (1983) 1059–1072.

    Article  Google Scholar 

  15. García O., The state-space approach in growth modelling, Can. J. For. Res. 24 (1994) 1894–1903.

    Article  Google Scholar 

  16. Gompertz B., On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Phil. Trans. Roy. Soc. London 123 (1832) 513–585.

    Google Scholar 

  17. Gram J.P., Om Konstruktion af Normal-Tilvækstoversigter, med særligt Hensyn til Iagttagelserne fra Odsherred, Tidsskrift for Skovbrug 3 (1879) 207–270.

    Google Scholar 

  18. Hann D.W., Hanus M.L., Enhanced diameter-growth-rate equations for undamaged and damaged trees in Southwest Oregon, Research Contribution 39, Forest Research Lab, College of Forestry, Oregon State University, 2002.

  19. Hann D.W., Hanus M.L., Enhanced height-growth-rate equations for undamaged and damaged trees in Southwest Oregon, Research Contribution 41, Forest Research Lab, College of Forestry, Oregon State University, 2002.

  20. Hein S., Dhôte J.-F., Effect of species composition, stand density and site index on the basal area increment of oak trees (Quercus sp.) in mixed stands with beech (Fagus sylvatica L.) in northern France, Ann. For. Sci. 63 (2006) 457–467.

    Article  Google Scholar 

  21. Henriksen H.A., Bryndum H., Bøgeforyngelser i Stagsrode Skov, in: Skovsgaard J.P., Morsing M. (Eds.), Bøgeselvforyngelser i Østjylland, The Research Series No. 13, Danish Forest and Landscape Research Institute, Denmark, 1996, pp. 5–162.

    Google Scholar 

  22. Jakobsen N.K., Natural-geographical regions of Denmark, Geografisk Tidskrift 75 (1976) 1–7.

    Google Scholar 

  23. Johannsen V.K., A growth model for oak in Denmark, Ph.D. thesis, Royal Veterinary and Agricultural University, Copenhagen, Denmark, 1999.

    Google Scholar 

  24. Johannsen V.K., Selection of diameter-height curves for even-aged oak stands in Denmark, Dynamic growth models for Danish forest tree species, Working paper 16, Danish Forest and Landscape Research Institute, 2002.

  25. Kerr G., Effects of spacing on the early growth of planted Fraxinus excelsior L., Can. J. For. Res. 33 (2003) 1196–1207.

    Article  Google Scholar 

  26. Larsen P.H., Johannsen V.K., Skove og Plantager 2000, Statistics Denmark, Centre for Forest, Landscape and Planning, Danish Forest and Nature Agency, Denmark, 2002.

    Google Scholar 

  27. Leary R., Nimerfro K., Brand M.H.G., Burk T., Kolka R., Wolf A., Height growth modelling using second order differential equations and the importance of initial height growth, For. Ecol. Manage. 97 (1997) 165–172.

    Article  Google Scholar 

  28. Lynch T.B., Moser J.W. Jr., A growth model for mixed species stands, For. Sci. 32 (1986) 697–706.

    Google Scholar 

  29. MacFarlane D.W., Green E.J., Burkhart H.E., Population density influences assessment and application of site index, Can. J. For. Res. 30 (2000) 1472–1475.

    Article  Google Scholar 

  30. MacKinney A.L., Chaiken L.E., Volume, yield, and growth of loblolly pine in the mid-Atlantic coastal region, Tech. Note 33, U.S. Dep. Agric. For. Serv., Appalachian For. Exp. Stn. 1939.

  31. McDill M.E., Amateis R.E., Measuring forest site quality using the parameters of a dimensionally compatible height growth function, For. Sci. 38 (1992) 409–429.

    Google Scholar 

  32. McDill M.E., Amateis R.E., Fitting discrete-time dynamic models having any time interval, For. Sci. 39 (1993) 499–519.

    Google Scholar 

  33. Mitscherlich E.A., Landwirtschaftliche Jahrbücher, 53 (1919) 167–182.

    Google Scholar 

  34. Møller C.M., Boniteringstabeller og Bonitetsvise Tilvækstoversigter for Bøg, Eg og rødgran i Danmark, Dansk Skovforenings Tidsskrift 18 (1933) 537–623.

    Google Scholar 

  35. Møller C.M., Nielsen J., Afprøvning af de Bonitetsvise Tilvækstoversigter af 1933 for Bøg, Eg og Rødgran i Danmark, Dansk Skovbrugs Tidsskrift 38 (1953) 1–167.

    Google Scholar 

  36. Näslund M., Skogsforsöksastaltens gallringsforsök i tallskog, Meddelanden från Statens Skogsforsöksanstalt 29 (1936) 1–169.

    Google Scholar 

  37. Nord-Larsen T., Developing dynamic site index curves for European beech (Fagus sylvatica L.) in Denmark, For. Sci. 52 (2006) 173–181.

    Google Scholar 

  38. Reynolds M.R., Estimating the error in model predictions, For. Sci. 30 (1984) 454–469.

    Google Scholar 

  39. Richards F.J., A flexible growth equation for empirical use, J. Exp. Bot. 10 (1959) 290–300.

    Article  Google Scholar 

  40. Ritchie G.A., Evidence for red: far red signaling and photomorphogenic growth response in Douglas-fir (Pseudotsuga menziesii) seedlings, Tree Physiol. 17 (1997) 161–168.

    PubMed  Google Scholar 

  41. SAS Institute Inc., SAS/ETS© User’s guide, version 6. Cary, N.C., 2nd ed., 1993, 554 p.

  42. Seber G.A.F., Wild C.J., Nonlinear Regression, Wiley series in probability and mathematical statistics, Wiley, New York, 1989.

    Google Scholar 

  43. Skovsgaard J.P., Henriksen H.A., Increasing site productivity during consecutive generations of naturally regenerated and planted beech (Fagus sylvatica L.) in Denmark, in: Spiecker H., Mielikäinen K., Köhl M., Skovsgaard J.P. (Eds.), Growth trends of European forests: Studies from 12 countries, European Forest Institute, Research Report, Vol. 5., Springer-Verlag, Berlin, Heidelberg, 1996, pp. 89–97.

    Google Scholar 

  44. Spiecker H., Mielikäinen K., Köhl M., Skovsgaard J.P. (Ed.), Growth trends of European forests: Studies from 12 countries, European Forest Institute, Research Report, Vol. 5, Springer-Verlag, Berlin, Heidelberg, 1996.

    Google Scholar 

  45. Verhulst P.F., Recherches mathématiques sur la loi d’accroissement de la population, Nouv. mém. Académie Royale des Sciences et Belles-Lettres de Bruxelles, 18 (1845) 1–41.

    Google Scholar 

  46. Verhulst P.F., Deuxième mémoire sur la loi d’accroissement de la population, Mém. Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 20 (1847) 1–32.

    Google Scholar 

  47. Wiedemann E., Die Rotbuche 1931, Mitteilungen der Preußischen Forstlichen Versuchsanstalt, Verlag M.u.H. Schaper, Hannover, Germany 1932.

    Google Scholar 

  48. Zeide B., Analysis of growth equations, For. Sci. 39 (1993) 594–616.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Forest & Landscape, Denmark, Copenhagen University, Hørsholm Kongevej 11, DK-2970, Hørsholm, Denmark

    Thomas Nord-Larsen & Vivian K. Johannsen

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  1. Thomas Nord-Larsen
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  2. Vivian K. Johannsen
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Correspondence to Thomas Nord-Larsen.

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Nord-Larsen, T., Johannsen, V.K. A state-space approach to stand growth modelling of European beech. Ann. For. Sci. 64, 365–374 (2007). https://0-doi-org.brum.beds.ac.uk/10.1051/forest:2007013

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Annals of Forest Science

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