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/rho) 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 --> primary xylem --> sclerenchyma --> 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.