Journal Article

Stand variation in <i>Pinus radiata</i> and its relationship with allometric scaling and critical buckling height

Matthew J. Waghorn and Michael S. Watt

in Annals of Botany

Published on behalf of The Annals of Botany Company

Volume 111, issue 4, pages 675-680
Published in print April 2013 | ISSN: 0305-7364
Published online February 2013 | e-ISSN: 1095-8290 | DOI:
Stand variation in Pinus radiata and its relationship with allometric scaling and critical buckling height

Show Summary Details


Background and Aims

Allometric relationships and the determination of critical buckling heights have been examined for Pinus radiata in the past. However, how they relate to more mature Pinus radiata exhibiting a wide range of stem diameters, slenderness and modulus of elasticity (E) at operationally used stand densities is largely unknown. The aim of this study was to examine the relationship between Pinus radiata stand structure variables and allometric scaling and critical buckling height.


Utilizing a Pinus radiata Nelder trial with stand density and genetic breed as variables, critical buckling height was calculated whilst reduced major axis regression was used to determine scaling exponents between critical height (Hcrit), actual height (H), ground line diameter (D), slenderness (S), density-specific stiffness (E/ρ) and modulus of elasticity (E).

Key Results

Critical buckling height was highly responsive to decreasing diameter and increasing slenderness. Safety factors in this study were typically considerably lower than previously reported margins in other species. As density-specific stiffness scaled negatively with diameter, the exponent of 0·55 between critical height and diameter did not meet the assumed value of 0·67 under constant density-specific stiffness. E scaled positively with stem slenderness to the power of 0·78.


The findings suggest that within species density-specific stiffness variation may influence critical height and the scaling exponent between critical height and diameter, which is considered so important in assumptions regarding allometric relationships.

Keywords: Allometric scaling; critical buckling height; Euler buckling; modulus of elasticity; Nelder; Pinus radiata; safety factor; stem slenderness

Journal Article.  4459 words.  Illustrated.

Subjects: Plant Ecology

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