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On Relative Maxima of Diameter Growth, Basal Area Growth, Volume Growth, and Mean Annual Increment for Individual Trees

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A mathematical demonstration for the fact that maximum individual tree diameter growth occurs at an earlier age than maximum individual tree basal area growth is reviewed. This demonstration assumes that the growth functions are continuous, are twice differentiable with respect to age, and increase monotonically to one maximum, thereafter to decline monotonically. The relationship of the age of maximum individual tree volume growth to the age of basal area growth is also discussed. Mathematical demonstrations are given for the fact that the culmination of mean annual increment occurs earlier for diameter than for basal area, and results on age of maximum growth and mean annual increment are also given for arbitrary power functions in diameter.

Keywords: differential; growth rate

Document Type: Research Article

Publication date: August 1, 2011

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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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