A re-evaluation of Reineke's rule and stand density index

The self-thinning rule established by Reineke in 1933, N ∝ 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.