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The Allometry of Saguaro Height

Karl J. Niklas and Stephen L. Buchman
American Journal of Botany
Vol. 81, No. 9 (Sep., 1994), pp. 1161-1168
Stable URL: http://www.jstor.org/stable/2445478
Page Count: 8
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The Allometry of Saguaro Height
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Abstract

The allometry of plant height H with respect to mean stem diameter D was determined based on 118 saguaro plants. The slope obtained for the reduced major axis regression analysis of the data was 2.36 ± 0.085, indicating that taller plants are disproportionately more slender than their shorter, presumably younger counterparts. The consequences of this positive, extremely anisometric relation on the elastic stability of stems were estimated by computing the critical bucking height Hcrit for each of the 118 stems on the basis of the mean density-specific stiffness (i.e., the quotient of Young's elastic modulus E and bulk tissue density ρ) determined for a single section from a mature saguaro stem. E/ρ was nearly equivalent to that of tissue samples of sclerenchyma isolated from other plant species. Since the slope of Hcrit vs. D equals 2/3 ≈ 0.67 when E/ρ ≈ a constant, the safety-factor for saguaro stems (i.e., Hcrit/H) appeared to be size-dependent such that it decreased with increasing plant height (i.e., Hcrit/H $\propto$ D-1.69). However, the mean safety-factor computed for the 118 saguaro specimens was 9.64, indicating that, on the average, plant height was well below Hcrit. Additionally, circumstantial evidence suggests that saguaro stems become more stiff as they increase in size (and age) and that the rate of stem growth decelerates over time. The former would obtain a near size-independent safety-factor against elastic buckling while the latter protracts the time required to reach the critical buckling height. Comparisons among the allometries of H and Hcrit for saguaro, other cacti, nonwoody, and highly branched tree species indicated that saguaro size overlaps with the lower size-range of the largest known dicot and gymnosperm tree specimens likely as a consequence of the high E/ρ of mature saguaro stems.

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