Linking stand-level self-thinning allometry to the tree-level leaf biomass allometry

Long-term experimental plots of Norway spruce and European beech are investigated for a link between stand-level self-thinning and tree-level leaf biomass allometry. Self-thinning refers to the finding of Reineke (1933), who postulated for unthinned forest stands that $$ N = bd_q^\beta , $$ with β = -1.605; i.e. an increase of mean (quadratic) diameter d _q by 1% results in a decrease of tree number N by 1.605%. On the individual tree level, leaf biomass (w _L) can be related allometrically to the tree diameter d: w _L = ad ^α. If we assume that (a) the stands have reached the ceiling leaf area, (b) the specific leaf area (leaf area/leaf weight) is constant, and (c) differences resulting from the use of mean quadratic diameter or individual tree diameter are negligible, then the decrease in the stands' leaf biomass due to the trees lost in self-thinning must be compensated by an equivalent increase in the remaining trees' leaf biomass. This means, the absolute slope of the individual trees' leaf biomass allometry α and the self-thinning allometry β would be equal and just have the opposite sign: α = -β. The analysis of the two long-term plots reveals that α is stronger than β, both for spruce (β = -1.744, α = 1.840) and especially for beech (β = -1.791, α = 2.181). The cause is traced back to a changing average specific leaf area during stand development [assumption (b) is wrong]. The results do not only bridge a gap between tree and stand allometry, but also emphasize an important effect for the understanding and modelling of the resource allocations in trees and forests.