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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

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