The interspecific size-density relationship among crowded plant stands and its implications for the -3/2 power rule of self-thinning

I present a geometric model that explains the interspecific size-density relationship among crowded plant stands in terms of two descriptors of the volume occupied by an average individual in each stand: the density of biomass per unit of occupied volume and the ratio of height to base width. The model predicts that stand measurements form a linear band when the logarithm of aboveground stand biomass is plotted against the logarithm of plant density. The band appears narrow because biomass per unit of volume and the ratio of height to width are biologically constrained and vary much less than stand biomass or density. In the absence of systematic trends in either parameter, simple geometry would fix the slope of the band at -1/2. Thus, the extent of deviation from -1/2 is of primary biological interest, since that deviation reflects biological trends in plant shape or packing density across the plant kingdom. Aboveground biomass, density, and height data from 370 plant stands revealed systematic trends in both parameters across the plant kingdom. Small plants growing at high densities tend to be relatively more slender and to pack more biomass per unit of volume than do larger plants in less dense stands. These trends relate to differences among plant groups. Herbaceous monocots are more slender and pack more biomass per unit of volume than herbaceous dicots, which are in turn higher in both measures than trees. As predicted by the model, such trends yield an interspecific relationship with a slope shallower than the ideal -1/2 value. The interspecific band encloses dynamic self-thinning lines that differ widely in slope; therefore, the static and dynamic relationships can be considered independently and are not simply facets of a single thinning "law." Many proposed interpretations of the constant in the dynamic self-thinning equation can be more clearly applied to a new constant calculated for single stands from the product of biomass per unit of volume and the ratio of height to width.