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Improving Taper Equations of Loblolly Pine with Crown Dimensions in a Mixed-Effects Modeling Framework

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A mixed-effects modeling framework was applied to Max and Burkhart's (1976) (MB) taper equation for loblolly pine (Pinus taeda L.). The advantages of such a strategy over ordinary least squares were: (1) more accurate specification of the correlation structure of the data and (2) the ability to assess the potentially explainable variation at the tree level. Significant relationships were established between tree-level crown dimensions and parameter estimates. The study data comprised 197 plantation-grown loblolly pine trees of 10 different ages in Uruguay. Four versions of MB were evaluated: (1) the original equation, (2) the original equation fitted with mixed effects, and two adapted versions: (3) the first included crown variables and fixed effects, (4) the second included crown variables and mixed effects. The crown variables were tree-level crown length and crown length ratio. The best of the four competing equations included both of the crown variables as well as tree-level random effects, suggesting that some linear tree-level variability may yet be explained by variables not considered in this study. Testing on an independent validation data set did not show over-fitting problems. For prediction purposes, the equations with added crown variables were more precise but not less biased. FOR. SCI. 50(2):204–212.

Keywords: Max and Burkhart taper equation; Pinus taeda; crown variables; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; natural resource management; natural resources; sources of variation

Document Type: Regular Article

Affiliations: 1: Department of Forest Resources, College of Natural Resources University of Idaho Moscow ID 83843 Phone: (208) 885-5165;, Fax: (208) 885-6226, Email: lleites@uidaho.edu 2: Department of Forest Resources, College of Natural Resources University of Idaho Moscow ID 83843 Phone: (208) 885-7115;, Fax: (208) 885-6226, Email: andrewr@uidaho.edu

Publication date: April 1, 2004

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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