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A Maximum Size-Density Relationship between Lorey's Mean Height and Trees per Hectare

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A linear relationship between the logarithm of Lorey's mean height and the logarithm of number of trees per hectare at maximum density can be derived from well known maximum size-density relationships associated with Reineke's stand density index and the power self-thinning principle. This leads to a system of three mathematically interrelated maximum size-density equations relating the three classically most important measures of tree size to density at its maximum. Given any two of these three equations, the third can be derived. Data obtained from unthinned control plots in a shortleaf pine (Pinus echinata Mill.) thinning study from Oklahoma are used to demonstrate these relationships. Slope estimates for the Reineke and Lorey maximum size-density lines are fitted simultaneously using three-stage least-squares with parameter constraints. First-difference models were used in the estimation procedure to reduce autocorrelation among remeasured plot data.

Keywords: density management diagram; density-dependent mortality; self-thinning; stand density index; tree mortality

Document Type: Research Article

Publication date: August 1, 2007

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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
    Other SAF Publications
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