The allometry of safety-factors for plant height

Regression curves for the relation between the critical buckling height H_crit, and the diameter D of columnar support members composed exclusively of different tissues were established based on Greenhill's formula and previously reported mean values for the density-specific stiffness and density-specific strength of parenchyma, primary xylem, sclerenchyma, and wood. These regression curves were used to determine the extent to which the actual heights H of 249 plant species approach or transgress the H_crit for stems relying principally upon different tissue-types for stiffness. Based on empirically determined H and estimated H_crit, the safety-factor H_crit/H (computed on the basis of E/p) against elastic instability resulting from self-loading imposed on stems was determined for dicot and gymnosperm tree species (N = 56), mosses (N = 40), pteridophytes (N = 16), dicot herbs (N = 120), and palms (N = 17). With the exception of tree species, H_crit/H was size-dependent, decreasing with increasing D. This was a consequence of the scaling exponents (i.e., the slopes of the regression curves) for tree H_crit, vs. D and H vs. D which were nearly identical, whereas the scaling exponents for H vs. D for “nonwoody” species were in excess of those for H_crit^, vs. D. With the exception of a few very tall specimens of palm species, however, the majority of nonwoody and woody species did not exceed their estimated H_crit. The upper size-range obtained by the procession of taller plant grades and clades was bounded by the regression curves of H_crit, vs. D established for progressively stiffer plant tissues: parenchyma Å primary xylem Å sclerenchyma Å wood. This appears to be a consequence of the incorporation of progressively stiffer tissues within the stems of taller nonwoody species and the adjustment in the girth of stems, which developmentally occurs for trees.