Interspecific allometries of critical buckling height and actual plant height

Size‐dependent variations in the critical buckling height Hcrit and actual height H of plants were determined for a total of 111 species with self‐supporting stems ranging in diameter between 0.03 cm ≤ D ≤ 3.0m. For each species, experimentally determined values for the physical properties of stems (Young's elastic modulus and bulk tissue density) were used to compute Hcrit. For small species ( D < 3 cm), empirically determined critical buckling loads were used to compute Hcrit by means of the Elastica equation and the more traditionally employed Greenhill formula; for larger species ( D ≖ 3 cm), Greenhill's formula was used exclusively to estimate Hcrit. Within most of the size‐range examined, the predicted values of Hcrit from the Elastica equation and Greenhill's formula were statistically indistinguishable. Regression analyses showed that the interspecific allometry of Hcrit parallels that of H such that the safety factor against the elastic mechanical failure of stems (i.e., Hcrit/H ) under their own biomass was roughly constant. Since the safety factor against elastic buckling is independent of plant size, a general allometric “rule,” Hcrit/H ≈ 4, appears to govern the evolution of plant size.