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Modeling Stand Density Effects on Taper for Jack Pine and Black Spruce Plantations Using Dimensional Analysis

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A taper equation was developed for jack pine and black spruce trees growing at varying density using a dimensional analysis approach. Data used in this study came from stem analysis on 1,135 jack pine (Pinus banksiana Lamb.) and 1,189 black spruce (Picea mariana [Mill.] B.S.P.) trees sampled from 25 even-aged monospecific plantations in the Canadian boreal forest region of Northern Ontario. About half of the trees were randomly selected for model development, with the remainder used for model evaluation. A nonlinear mixed-effects approach was applied in fitting the taper equation. The predictive accuracy of the model was improved by including random-effects parameters for a new tree based on upper stem diameter measurements. Three scenarios of using upper stem diameter measurements to predict random effects were examined for predictive accuracy: one diameter at any height along the bole; two diameters, one each from below and above breast height; and three diameters, one from below and the other two from above breast height. The upper height at which the diameter was measured was limited to 65% of total tree height for practical reasons. For the first scenario, the model calibrated using a diameter measurement from between 34 and 38% of total height provided the best predictions of inside-bark diameters. For the second scenario, the model calibrated using one diameter from near the stump and the other from close to 65% of total height produced the least bias in predicting inside-bark diameters. For the third scenario, the model calibrated using the diameters from near the stump and at approximately 35 and 65% of total height provided the highest prediction accuracy.

Keywords: Picea mariana; Pinus banksiana; calibrated response; fixed response; mixed-effects model; nonlinear regression; stand density; stem profile models; thinning; tree form

Document Type: Research Article

Publication date: June 1, 2009

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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.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
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