Modeling size-density trajectories for even-aged beech (Fagus silvatica L.) stands in France

Published Date

September 2016, Volume 73, Issue 3, pp 765-776

First online: 29 June 2016

Title 

Modeling size-density trajectories for even-aged beech (Fagus silvatica L.) stands in France

• Author 

• François Ningre 
• , Jean-Marc Ottorini
• , Noël Le Goff

Abstract

Key message

We studied the size-density trajectories of pure even-aged unthinned beech stands in the ranges of 625–40,000 trees per hectare initial densities and of 12–33 years of age. A new piecewise polynomial function family was fitted to the trajectories, giving way to various applications. Initial number of stems per hectare (N 0) and mean girth at breast height at the onset of mortality (Cg 0) were parameters of the trajectory model, in addition to the parameters of the maximum size-density line. The two former parameters were tied by a linear relationship, which allowed the prediction of trajectories not considered in this study. Furthermore, the generic trajectory equation fitted the trajectories of thinned stands not used in the estimation of the parameters.

Context

This paper models the size-density trajectories of pure even-aged beech stands, including the early development stage, which is not as well documented as are the later stages.

Aims

The work reported in this paper concerns the development of a novel approach to size-density trajectories, considered as a mortality model to provide references to managers of beech forests.

Material and methods

A 33-year-old beech spacing trial beginning at 12 years of age provided the opportunity to study the size-density trajectories of unthinned stands of this species. The beech data helped us to develop a new piecewise function to model these trajectories. The model we chose was a polynomial segment smoothly joining two linear functions.

Results

The fits of this model allowed us to estimate the parameters of the size-density trajectories of all stands, which were the quadratic mean girths at mortality onset and at maximum density. A linear relationship between these characteristics allowed us to reduce the number of parameters needed to fit the trajectories and made it possible to predict a stand trajectory from any initial density not observed in the experimental stands.

Conclusion

A single-parameter function family could be used to fit the size-density trajectories of beech stands. The predicted trajectories have various applications in beech silviculture and growth simulators.

References

1. Bédéneau M, Sindou C, Ruchaud F, Bailly A, Crémière L (2001) Un partenariat scientifique original: la Coopérative de Données Sur la Croissance des Arbres et des Peuplements forestiers. Rev For Fr LIII – 2:171–178
2. Cao QV, Dean TJ (2008) Using a segmented regression to model the size-density relationship in direct-seeded slash pine stands. For Ecol Manag 255:948–952CrossRef
3. Colin F, Ningre F, Fortin M, Huet S (2012) Quantification of Quercus petraea Liebl. forking based on a 23-year-long longitudinal survey. For Ecol Manag 282:133–141
4. Curtis RO (1970) Stand density measures: an interpretation. For Sci 16:403–414
5. Curtis RO (1982) A simple index of stand density for Douglas-fir. For Sci 28:92–94
6. Dhôte J-F, Hatsch E, Rittié D (2000) Forme de la tige, tarifs de cubage et ventilation de la production en volume chez le Chêne sessile. Ann For Sci 57:121–142
7. Drew TJ, Flewelling JW (1979) Stand density management: an alternative approach and its application to Douglas-fir plantations. For Sci 25:518–532
8. Fisher RA (1934) Statistical methods for research workers. Oliver & Boyd, Edinburgh
9. Fridman J, Ståhl G (2001) A three-step approach for modelling tree mortality in Swedish forests. Scand J For Res 16:455–466CrossRef
10. Hibbs DE, Carlton GD (1989) A comparison of diameter- and volume-based stocking guides for red alder. West J Appl For 4:113–115
11. Hibbs, DE, DeBell, DS (1994) Management of young red alder. In: “The Biology and Management of Red Alder”, Oregon State University Press, Corvallis, Oregon, USA.
12. Lee Y (1971) Predicting mortality for even-aged stands of lodgepole pine. For Chron 47:29–32CrossRef
13. Le Goff N, Ottorini J-M, Ningre F (2011) Evaluation and comparison of size-density relationships for pure even-aged stands of ash (Fraxinus excelsior L.), beech (Fagus silvatica L.), oak (Quercus petraea Liebl.), and sycamore maple (Acer pseudoplatanus L.) Ann. For Sci 68:461–475
14. Le Moguedec G, Dhôte J-F (2012) Fagacées: a tree-centered growth and yield model for sessile oak (Quercus petraea L.) and common beech (Fagus sylvatica L.). Ann For Sci 69:257–269CrossRef
15. Monserud RA, Lederman T, Sterba H (2005) Are self-thinning constraints needed in a tree-specific mortality model? For Sci 50:848–858
16. Newton PF, Weetman GF (1994) Stand density management diagrams for managed black spruce stands. For Chron 70:65–74CrossRef
17. Ningre F, Colin F (2007) Frost damage on the terminal shoot as a risk factor of fork incidence on common beech (Fagus sylvatica L.). Ann For Sci 64:79–86
18. Oliver, CD, Larson, BC (1996) Forest stand dynamics. Wiley, New York.
19. Penner M, Swift DE, Gagnon R, Brissette J (2006) A stand density management diagram for balsam fir in New Brunswick. For Chron 82:700–711CrossRef
20. Pienaar LV, Turnbull KJ (1973) The Chapman-Richards generalization of von Bertalanffy’s growth model for basal area growth and yield in even-aged stands. For Sci 19:2–22
21. Pilard-Landeau, B, Simon, E (2008) Guide des sylvicultures – La hêtraie Nord Atlantique. ONF, Direction Territoriale Ile de France Nord-Ouest, Direction Forêt, 154 pp.
22. Pinheiro JC, Bates DM (2000) Mixed-effects models in S and S-PLUS. Springer, New York, 528 pp
23. Pretzsch H (2009) Forest dynamics, growth and yield: from measurement to model. Springer, Science & Business MediaCrossRef
24. Puettmann KJ, Hann DW, Hibbs DE (1993) Evaluation of the size-density relationships for pure red alder and Douglas-fir stands. For Sci 39:7–27
25. R Development Core Team, Foundation for Statistical Computing (Vienna, Austria). (2012) A Language and Environment for Statistical Computing. ISBN 3–900051–07-0. url=http://​www.​R-project.​org/
26. Reineke LH (1933) Perfecting a stand-density index for even-aged forests. J Agric Res 46:627–638
27. Sales Luis JF, Fonseca TF (2004) The allometric model in the stand density management of Pinus pinaster Ait. in Portugal. Ann For Sci 61:807–814
28. Smith NJ, Hann DW (1984) A new analytical model based on the 3/2 power rule of self-thinning. Can J For Res 14:605–609CrossRef
29. Smith NJ, Hann DW (1986) A growth model based on the self-thinning rule. Can J For Res 16:330–334CrossRef
30. Tang S, Meng CH, Meng FR, Wang YE (1994) A growth and self thinning model for pure even-aged stands: theory and applications. For Ecol Manag 70:67–73CrossRef
31. Turnblom EC, Burk TE (2000) Modeling self-thinning of unthinned Lake states red pine stands using nonlinear simultaneous differential equations. Can J For Res 30:1410–1418CrossRef
32. VanderSchaaf CL (2010) Estimating individual stand-density trajectories and a maximum size-density relationship species boundary line slope. For Sci 56:327–335
33. VanderSchaaf CL, Burkhart HE (2008) Using segmented regression to estimate stages and phases of stand development. For Sci 54:7–27
34. VanderSchaaf CL, Burkhart HE (2012) Development of planting density-specific management diagrams for loblolly pine. South J Appl For 36:126–129CrossRef
35. Yoda K, Kira KT, Ogawa H, Hozumi H (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions. J Biol Osaka City Univ, Ser D 14:107–129

For further details log on website :
http://link.springer.com/article/10.1007/s13595-016-0567-0