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Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada

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Abstract

Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within- and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance–covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating tree-specific predictions of diameter inside bark, whole tree volume, and sectioned log volume.

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Acknowledgments

This work was supported by Alberta Government and Forest Resource Improvement Association of Alberta (the FRIAA-GYPSY project). Special thanks to ten industry partners led by West Fraser Mills, Weyerhaeuser Canada (Alberta) and Canadian Forest Products, and to Mr Richard Briand, Dr Dick Dempster, and Mr Dave Morgan for project management and coordination. G. Trincado was supported by Instituto de Manejo Forestal at Universidad Austral de Chile for his contribution to this project. Special thanks to the two anonymous reviewers for their constructive comments.

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Authors and Affiliations

  1. Biometrics Unit, Forest Management Branch, Alberta Department of Sustainable Resource Development, 8th Floor, 9920-108 Street, Edmonton, AB, T5K 2M4, Canada

    Yuqing Yang, Shongming Huang & Shawn X. Meng

  2. Instituto de Manejo Forestal, Universidad Austral de Chile, Box 567, Valdivia, Chile

    Guillermo Trincado

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  1. Yuqing Yang
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  2. Shongming Huang
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  3. Guillermo Trincado
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  4. Shawn X. Meng
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Correspondence to Yuqing Yang.

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Communicated by D. Mandallaz.

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Yang, Y., Huang, S., Trincado, G. et al. Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada. Eur J Forest Res 128, 415–429 (2009). https://doi.org/10.1007/s10342-009-0286-2

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  • DOI: https://doi.org/10.1007/s10342-009-0286-2

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