Skip to main content
Log in

Models of the longitudinal distribution of ring area as a function of tree and stand attributes for four major Canadian conifers

  • Original Paper
  • Published:
Annals of Forest Science Aims and scope Submit manuscript

Abstract

Context

It is widely accepted that ring area increment generally increases from the tree apex to the crown base and is more-or-less constant below the crown base (Pressler’s law), but few quantitative models of this distribution have been developed.

Aims

The aim of this study was to develop a model of ring area increment using easily obtained crown features and other tree or stand characteristics in order to further the understanding and prediction of tree growth, form, and wood quality.

Methods

The models were fit to stem analysis observations from white spruce, black spruce, balsam fir, and lodgepole pine.

Results

In the final model, which includes tree crown and stand variables, ring area increment within the crown region was slightly curvilinear, the slope of ring area increment below the crown was non-zero, and the effect of butt swell was appreciable up-to a relative height of 0.10.

Conclusions

The high accuracy of the mixed effects model suggests that the three-component model form is appropriate for describing ring area profiles, whereas some tree-to-tree variation remains unexplained. The tree and stand variables used in these models can be easily measured in the field or obtained from remote sensing techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig 3
Fig. 4

Similar content being viewed by others

References

  • Barczi J-F, Rey H, Caraglio Y, De Reffye P, Barthélémy D, Dong QX, Fourcaud T (2008) AmapSim: a structural whole-plant simulator based on botanical knowledge and designed to host external functional models. Ann Bot 101:1125–1138

    Article  PubMed  Google Scholar 

  • Bevilacqua E, Puttock D, Blake TJ, Burgess D (2005) Long-term differential stem growth responses in mature eastern white pine following release from competition. Can J For Res 35:511–520

    Article  Google Scholar 

  • Burnham KP, Anderson DR (1998) Model selection and inference: a practical information-theoretic approach. Springer, New York, 353 pp

    Book  Google Scholar 

  • Courbet F (1999) A three-segmented model for the vertical distribution of annual ring area. Application to Cedrus atlantica Manetti. For Ecol Manage 119:177–194

    Article  Google Scholar 

  • Cruickshank M (2002) Accuracy and precision of measuring cross-sectional area in stem disks of Douglas-fir infected by Armillaria root disease. Can J For Res 32:1542–1547

    Article  Google Scholar 

  • Deleuze C, Houllier F (1995) Prediction of stem profile of Picea abies using a process-based tree growth model. Tree Phys 15:113–120

    Article  Google Scholar 

  • Deleuze C, Houllier F (2002) A flexible radial increment taper equation derived from a process-based carbon partitioning model. Ann For Sci 59:141–154

    Article  Google Scholar 

  • Fang Z, Bailey RL (2001) Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. For Sci 47:287–300

    Google Scholar 

  • Farrar JL (1961) Longitudinal variation in the thickness of the annual ring. For Chron 37:323–330, 349

    Google Scholar 

  • Fonweban J, Gardiner B, Macdonald E, Auty D (2011) Taper functions for Scots pine (Pinus sylvestris L.) and Sitka spruce (Picea sitchensis (Bong.) Carr.) in Northern Britain. Forestry 84:49–60

    Article  Google Scholar 

  • Gaffrey D, Sloboda B (2001) Three mechanics, hydraulics and needle-mass distribution as a possible basis for explaining the dynamics of stem morphology. J For Sci 47:241–254

    Google Scholar 

  • Gilmore DW, Seymour RS (1997) Crown architecture of Abies balsamea from four canopy positions. Tree Phys 17:71–980

    Article  Google Scholar 

  • Groom JD, Hann DW, Temesgen H (2012) Evaluation of mixed-effects models for predicting Douglas-fir mortality. For Ecol Manage 276:139–145

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Groot A, Saucier J-P (2008) Volume increment efficiency of Picea mariana in northern Ontario, Canada. For Ecol Manage 255:1647–1653

    Article  Google Scholar 

  • Houllier F, Leban J-M, Colin F (1995) Linking growth modelling to timber quality assessment for Norway spruce. For Ecol Manage 74:91–102

    Article  Google Scholar 

  • Huang S, Wiens DP, Yang Y, Meng SX, Vanderschaaf CL (2009) Assessing the impacts of species composition, top height and density on individual tree height prediction of quaking aspen in boreal mixedwoods. For Ecol Manage 258:1235–1247

    Article  Google Scholar 

  • Hyink DM, Zedaker SM (1987) Stand dynamics and the evaluation of forest decline. Tree Phys 3:17–26

    Article  Google Scholar 

  • Ikonen VP, Kellomäki P, Väisänen H, Peltola H (2006) Modelling the distribution of diameter growth along the stem in Scots pine. Trees 20:391–402

    Article  Google Scholar 

  • Jozsa LA, Middleton GR (1994) A discussion of wood quality attributes and their practical implications. Special Publication No. SP-34, Forintek Canada Corp., Vancouver. 51 p

  • Kershaw JA Jr, Maguire DA (2000) Influence of vertical foliage structure on the distribution of stem cross-sectional area increment in western hemlock and balsam fir. For Sci 46:86–94

    Google Scholar 

  • Kershaw JA Jr, Benjamin JG, Weiskittel AR (2009) Approaches for modeling vertical distribution of maximum knot size in black spruce: a comparison of fixed- and mixed-effects nonlinear models. For Sci 55:230–237

    Google Scholar 

  • Labyak LF, Schumacher FX (1954) The contribution of its branches to the main-stem growth of Loblolly pine. J For 52:333–337

    Google Scholar 

  • Larson PR (1963) Stem form development of forest trees. For Sci Monogr 5

  • Lavigne MB (1991) Effects of thinning on allocation of growth and respiration in young stands of balsam fir. Can J For Res 11:459–464

    Google Scholar 

  • Leckie D, Gougeon F, Hill D, Quinn R, Armstrong L, Shreenan R (2003) Combined high-density Lidar and multispectral imagery for individual tree crown analysis. Can J Remote Sens 29:633–649

    Article  Google Scholar 

  • Li C (2009) Toward full, multiple, and optimal wood fibre utilization: a modeling perspective. For Chron 85:377–381

    Google Scholar 

  • Maguire DA, Bennett WS (1996) Patterns in vertical foliage distribution of foliage in young coastal Douglas-fir. Can J For Res 26:1991–2005

    Article  Google Scholar 

  • Mansfield SD, Parish R, Goudie JW, Kang K-Y (2007) The effects of crown ratio on the transition from juvenile to mature wood production in lodgepole pine in western Canada. Can J For Res 37:1450–1459

    Article  Google Scholar 

  • Max TA, Burkhart HE (1976) Segmented polynomial regression applied to taper equations. For Sci 22:283–289

    Google Scholar 

  • Mitchell KJ (1975) Dynamics and simulated yield of Douglas-fir. For Sci Monogr 17

  • Newberry JD (1991) A note on Carmean’s estimate of height from stem analysis data. For Sci 37:368–369

    Google Scholar 

  • Osawa A, Ishizuka M, Kanazawa Y (1991) A profile theory of tree growth. For Ecol Manage 41:33–63

    Article  Google Scholar 

  • Ottorini J-M, Le Goff N, Cluzeau C (1996) Relationships between crown dimensions and stem development in Fraxinus excelsior. Can J For Res 26:394–401

    Article  Google Scholar 

  • Panshin AJ, de Zeuw C (1970) Textbook of wood technology. McGraw-Hill, New York, 705 p

    Google Scholar 

  • Pitt D, Lanteigne L (2008) Long-term outcome of precommercial thinning in northwestern New Brunswick: growth and yield of balsam fir and red spruce. Can J For Res 38:592–610

    Article  Google Scholar 

  • Pinheiro JC, Bates DM, DebRoy S, Sarkar D, and the R Core team (2009) NLME: Linear and Nonlinear Mixed Effects Models. R package version 3.1-96

  • Pinherio JC, Bates DM (2000) Mixed-Effects Models in S and S-Plus. Springer-Verlag, New York

    Book  Google Scholar 

  • Pressler MR (1864) Das Gesetz der Stammbildung. Arnoldische Buchhandlung, Leipzig, 153 p

    Google Scholar 

  • Saranpää P (2003) Wood density and growth. In: Barnett, J.R. and Jeronimidis, G (eds) Wood quality and its biological basis. CRC Press, Boca Raton, pp. 87–117

  • Sprugel DG, Hinckley TM, Schaap W (1991) The theory and practice of branch autonomy. Annu Rev Ecol Syst 22: 309–334

    Google Scholar 

  • Watt MS, Zoric B, Kimberley MO, Harrington J (2011) Influence of stocking on radial and longitudinal variation in modulus of elasticity, microfibril angle, and density in a 24-year-old Pinus radiate thinning trial. Can J For Res 41:1422–1431

    Article  Google Scholar 

  • Weiner J (1984) Neighbourhood interference amongst Pinus rigida individuals. J Ecol 72:183–195

    Article  Google Scholar 

  • Xu P, Walker JCF (2004) Stiffness gradients in radiata pine trees. Wood Sci Technol 38:1–9

    Article  Google Scholar 

Download references

Acknowledgments

Special thanks go to: Mr. Jim Goudie of the BC Ministry of Forests, Lands, and Natural Resource Operations for providing the lodgepole pine data; Dr. Doug Pitt of the Canadian Forest Service for supplying the balsam fir data, Mr. Andrew Innerd for sharing white spruce samples; Mr. Ian Cameron of Azura Formetrics for assistance with the statistical analysis; and Mr. Gurp Thandi of the Canadian Forest Service for creating the map presented in this manuscript. The authors would also like to thank the two anonymous reviewers for providing constructive comments and suggestions.

Funding

Funding of this research was provided by the Canadian Wood Fibre Centre (Canadian Forest Service).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Francesco Cortini.

Additional information

Handling Editor: Jean-Michel Leban

Contributions of the co-authors

Francesco Cortini: data analysis, modeling, and writing

Arthur Groot: experimental design, modeling, and writing

Cosmin N. Filipescu: modeling and writing

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cortini, F., Groot, A. & Filipescu, C.N. Models of the longitudinal distribution of ring area as a function of tree and stand attributes for four major Canadian conifers. Annals of Forest Science 70, 637–648 (2013). https://doi.org/10.1007/s13595-013-0305-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13595-013-0305-9

Keywords

Navigation