Species-specific allometric scaling under self-thinning: evidence from long-term plots in forest stands

Experimental plots covering a 120 years' observation period in unthinned, even-aged pure stands of common beech (Fagus sylvatica), Norway spruce (Picea abies), Scots pine (Pinus sylvestris), and common oak (Quercus Petraea) are used to scrutinize Reineke's (1933) empirically derived stand density rule ( $$N \propto \bar d^{-1.605} $$, N = tree number per unit area, $$\bar{d}$$ = mean stem diameter), Yoda's (1963) self-thinning law based on Euclidian geometry ($$\bar w \propto N^{- 3/2}, $$$$\bar w$$ = mean biomass per tree), and basic assumptions of West, Brown and Enquist's (1997, 1999) fractal scaling rules ($$w \propto d^{8/3}, $$$$\bar w \propto N^{-4/3}, $$w = biomass per tree, d = stem diameter). RMA and OLS regression provides observed allometric exponents, which are tested against the exponents, expected by the considered rules. Hope for a consistent scaling law fades away, as observed exponents significantly correspond with the considered rules only in a minority of cases: (1) exponent r of $$N \propto \bar d^r $$ varies around Reineke's constant -1.605, but is significantly different from r=-2, supposed by Euclidian or fractal scaling, (2) Exponent c of the self-thinning line $$\bar w \propto N^c $$ roams roughly about the Euclidian scaling constant -3/2, (3) Exponent a of $$w \propto d^a $$ tends to follow fractal scaling 8/3. The unique dataset's evaluation displays that (4) scaling exponents and their oscillation are species-specific, (5) Euclidian scaling of one relation and fractal scaling of another are coupled, depending on species. Ecological implications of the results in respect to self-tolerance (common oak > Norway spruce > Scots pine > common beech) and efficiency of space occupation (common beech > Scots pine > Norway spruce > common oak) are stressed and severe consequences for assessing, regulating and scheduling stand density are discussed.