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The Allometry of Safety-Factors for Plant Height

Karl J. Niklas
American Journal of Botany
Vol. 81, No. 3 (Mar., 1994), pp. 345-351
Stable URL: http://www.jstor.org/stable/2445462
Page Count: 7
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The Allometry of Safety-Factors for Plant Height
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Abstract

Regression curves for the relation between the critical buckling height Hcrit 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 Hcrit for stems relying principally upon different tissue-types for stiffness. Based on empirically determined H and estimated Hcrit, the safety-factor Hcrit/H (computed on the basis of E/ρ) 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, Hcrit/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 Hcrit 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 Hcrit 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 Hcrit. The upper size-range obtained by the procession of taller plant grades and clades was bounded by the regression curves of Hcrit 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.

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