Advertisement

European Journal of Forest Research

, Volume 126, Issue 2, pp 253–262 | Cite as

Regional mixed-effects height–diameter models for loblolly pine (Pinus taeda L.) plantations

  • Guillermo TrincadoEmail author
  • Curtis L. VanderSchaaf
  • Harold E. Burkhart
Original Paper

Abstract

A height–diameter mixed-effects model was developed for loblolly pine (Pinus taeda L.) plantations in the southeastern US. Data were obtained from a region-wide thinning study established by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. The height–diameter model was based on an allometric function, which was linearized to include both fixed- and random-effects parameters. A test of regional-specific fixed-effects parameters indicated that separate equations were needed to estimate total tree heights in the Piedmont and Coastal Plain physiographic regions. The effect of sample size on the ability to estimate random-effects parameters in a new plot was analyzed. For both regions, an increase in the number of sample trees decreased the bias when the equation was applied to independent data. This investigation showed that the use of a calibrated response using one sample tree per plot makes the inclusion of additional predictor variables (e.g., stand density) unnecessary. A numerical example demonstrates the methodology used to predict random effects parameters, and thus, to estimate plot specific height–diameter relationships.

Keywords

Height–diameter relationship Forest inventory Linear mixed-effects model Pinus taeda 

Notes

Acknowledgments

Data for this study and financial support were provided through the Loblolly Pine Growth and Yield Research Cooperative, Department of Forestry, Virginia Polytechnic Institute and State University.

References

  1. Arabatzis AA, Burkhart HE (1992) An evaluation of sampling methods and model forms for estimating height–diameter relationships in loblolly pine plantations. For Sci 38:192–198Google Scholar
  2. Avery TE, Burkhart HE (2002) Forest measurements. 5th edn. McGraw-Hill, New YorkGoogle Scholar
  3. Assman E (1970) The principles of forest yield studies. Pergamon, OxfordGoogle Scholar
  4. Baskerville GL (1972) Use of logarithmic regression in the estimation of plant biomass. Can J For Res 2:49–53CrossRefGoogle Scholar
  5. Burkhart HE, Parker RC, Strub MR, Oderwald RG (1972) Yield of old-field loblolly pine plantations. School of Forestry and Wildlife Resources, Va Polytech Institute and State University Publication FWS, pp 3–72Google Scholar
  6. Burkhart HE, Cloren DC, Amateis RL (1985) Yield relationships in unthinned loblolly pine plantations on cutover, site-prepared lands. South J Appl For 9:84–91Google Scholar
  7. Calama R, Montero G (2004) Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain. Can J For Res 34:150–163CrossRefGoogle Scholar
  8. Castedo Dorado F, Barrio Anta M, Parresol BR, Álvarez González JG (2005) Stochastic height–diameter model for maritime pine ecoregions in Galicia (northwestern Spain). Ann For Sci 62:455–465CrossRefGoogle Scholar
  9. Eerikäinen K (2001) Stem volume models with random coefficients for Pinus kesiya in Tanzania, Zambia, and Zimbabwe. Can J For Res 31:879–888CrossRefGoogle Scholar
  10. Eerikäinen K (2003) Predicting the height–diameter pattern of planted Pinus kesiya stands in Zambia and Zimbabwe. For Ecol Manage 175:355–366CrossRefGoogle Scholar
  11. Epstein R, Nieto E, Weintraub A, Chevalier P, Gabarró J (1999) A system for the design of short term harvesting strategy. Eur J Oper Res 119:427–439CrossRefGoogle Scholar
  12. Fang Z, Bailey RL (2001) Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. For Sci 47:287–300Google Scholar
  13. Gregoire TG, Schabenberger O (1996a) Non-linear mixed effects modeling of cumulative bole volume with spatially correlated within-tree data. J Agri Biol Environ Stat 1:107–109CrossRefGoogle Scholar
  14. Gregoire TG, Schabenberger O (1996b) A non-linear mixed-effects model to predict cumulative bole volume of standing trees. J Appl Stat 23:257–271CrossRefGoogle Scholar
  15. Hall DB, Clutter M (2004) Multivariate multilevel nonlinear mixed effects models for timber yield predictions. Biometrics 60:16–24CrossRefPubMedGoogle Scholar
  16. Huang S, Titus SJ, Wiens DD (1992) Comparison of nonlinear height–diameter functions for major Alberta tree species. Can J For Res 22:1.297–1.304CrossRefGoogle Scholar
  17. Hui G, Gadow Kv (1993) Zur Entwicklung von Einheitshöhenkurven am Beispiel der Baumart Cunninghamia lanceolata. Allg Forst Jagdztg 164:218–220Google Scholar
  18. Jayaraman K, Zakrzewski WT (2001) Practical approaches to calibrating height–diameter relationships for natural maple stand in Ontario. For Ecol Manage 148:169–177CrossRefGoogle Scholar
  19. Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974CrossRefPubMedGoogle Scholar
  20. Lappi J (1986) Mixed linear models for analyzing and predicting stem form variation of Scots pine. Commun Inst For Fenn 134:1–69Google Scholar
  21. Lappi J (1991) Calibration of height and volume equations with random parameters. For Sci 37:781–801Google Scholar
  22. Lappi J, Bailey RL (1988) A height prediction model with random stand and tree parameters: an alternative to traditional site index methods. For Sci 34:907–927Google Scholar
  23. Littell RC, Milliken GA, Stroup WW, Wolfinger RD (1996) SAS® System for mixed models. SAS Institute Inc., CaryGoogle Scholar
  24. López Sánchez CA, Gorgoso Varela J, Castedo Dorado F, Rojo Alboreceda R, Rodriguez Soalleiro R, Alvarez Gonzalez JG, Sanchez Rodriguez F (2003) A height–diameter model for Pinus radiata D, Don in Galicia (Northwest Spain). Ann For Sci 60:237–345CrossRefGoogle Scholar
  25. Lynch T, Murphy P (1995) A compatible height prediction and projection system for individual trees in natural, even-aged shortleaf pine stands. For Sci 41:194–209Google Scholar
  26. Lynch TB, Holley AG, Stevenson DJ (2005) A random-parameter height-dbh model for cherrybark oak. South J Appl For 29:22–26Google Scholar
  27. Martin F, Flewelling J (1998) Evaluation of tree height prediction models for stand inventory. West J Appl For 13:109–119Google Scholar
  28. Mehtätalo L (2004) A longitudinal height–diameter model for Norway spruce in Finland. Can J For Res 34:131–140CrossRefGoogle Scholar
  29. Rencher AC (2000) Linear models in statistics. John Wiley, New YorkGoogle Scholar
  30. Schabenberger O, Pierce FJ (2002) Contemporary statistical models for the plant and soil sciences. CRC, Boca RatonGoogle Scholar
  31. Schöeder J, Álvarez González JG (2001) Comparing the performance of generalized diameter–height equations for maritime pine in Northwestern Spain. Forstw Cbl 120:18–23CrossRefGoogle Scholar
  32. Sharma M, Zhang SY (2004) Height–diameter models using stand characteristics for Pinus banksiana and Pinus mariana. Scand J For Res 19:442–451CrossRefGoogle Scholar
  33. Soares P, Tomé M (2002) Height–diameter equation for first rotation eucalypt plantations in Portugal. For Ecol Manage 166:99–109CrossRefGoogle Scholar
  34. Tasissa G G, Burkhart HE (1998) An application of mixed effects analysis to modeling thinning effects on stem profile of loblolly pine. For Ecol Manage 103:87–101CrossRefGoogle Scholar
  35. Tasissa G, Burkhart HE, Amateis RL (1997) Volume and taper equations for thinned and unthinned loblolly pine trees in cutover, site-prepared plantations. South J Appl For 21:146–152Google Scholar
  36. Temesgen H, Gadow Kv (2004) Generalized height–diameter models: an application for major tree species in complex stands of interior British Columbia. Eur J For Res 123:45–51CrossRefGoogle Scholar
  37. Verbeke G, Molenberghs G (1997) Linear mixed models in practice: a SAS-oriented approach. Springer, Berlin Heidelberg New YorkCrossRefGoogle Scholar
  38. Zeide B, VanderSchaaf C (2002) The effect of density on the height–diameter relationship. In: Proceedings of the 11th biennial southern silvicultural research conference. Outcalt Kenneth W (ed) Gen Tech Rep SRS-48 Asheville, NC: Department of Agriculture, Forest Service, Southern Research Station, pp 463–466Google Scholar
  39. Zhang S, Burkhart HE, Amateis RL (1997) The influence of thinning on tree height and diameter relationships in loblolly pine plantations. South J Appl For 21:199–205Google Scholar
  40. Zhang L, Peng C, Huang S, Zhou X (2002) Development and evaluation of ecoregion-based jack pine height–diameter models for Ontario. For Chron 78:530–538CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Guillermo Trincado
    • 1
    Email author
  • Curtis L. VanderSchaaf
    • 1
  • Harold E. Burkhart
    • 1
  1. 1.Department of ForestryVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations