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A Re-Evaluation of Reineke's Rule and Stand Density Index

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The self-thinning rule established by Reineke in 1933, N α d −1.605 (N, d = number of stems and quadratic mean diameter, respectively) assumes the same allometric relationship between size and density for a wide spectrum of species under self-thinning conditions. We re-evaluate this rule based on 28 fully stocked pure stands of common beech (Fagus sylvatica L.), Norway spruce (Picea abies [L.] Karst.), Scots pine (Pinus sylvestris L.), and common oak (Quercus petraea [Mattuschka] Liebl.) in Germany that date back to the year 1870. OLS regression of the model ln(N) = a + b · ln(d) results in b values of −1.789 for common beech, −1.664 for Norway spruce, −1.593 for Scots pine, and −1.424 for common oak. The allometric coefficient for common beech differs significantly from the other species. There is also a significant difference between the b values of Norway spruce and common oak. Except for Scots pine, the above allometric coefficients deviate significantly (common beech) and close-to-significantly (Norway spruce, common oak) from the coefficient −1.605 postulated by Reineke in 1933. To cover the species–specific oscillation of mortality rates, we additionally calculate the self-thinning coefficient for each survey period. Ecological implications of the species-specific scaling exponents are stressed and consequences regarding tools for regulating stand density are discussed. FOR. SCI. 51(4):304–320.

Keywords: Allometry; Fagus sylvatica L; Picea abies (L.) Karst; Pinus sylvestris L; Quercus petraea (Mattuschka) Liebl; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; natural resource management; natural resources; self-thinning; self-tolerance; space sequestration

Document Type: Regular Article

Affiliations: 1: Prof Dr and Chair of Forest Yield Science Technische Universität München Am Hochanger 13 D-85354 Freising Germany Phone: 0049-8161-714710;, Fax: 0049-8161-714721, Email: 2: Technische Universität München Am Hochanger 13 D-85354 Freising Germany Phone: 0049-8161-714708, Email:

Publication date: August 1, 2005

More about this publication?
  • 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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