Allometric theory and the mechanical stability of large trees: Proof and conjecture

Recent allometric theory has postulated that standing leaf mass will scale as the 3/4 power of stem mass and as the 3/4 power of root mass such that stem mass scales isometrically with respect to root mass across very large vascular plant species with self-supporting stems. We show that the isometric scaling of stem mass with respect to root mass (i.e., M-S proportional to M-R) can be derived directly from mechanical theory, specifically from the requirement that wind-induced bending moments acting at the base of stems must be balanced by a counter-resisting moment provided by the root system to prevent uprooting. This derivation provides indirect verification of the allometric theory. It also draws attention to the fact that leaf, stem, and root biomass partitioning patterns must accommodate the simultaneous performance of manifold functional obligations.