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.