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Allometric theory and the mechanical stability of large trees: proof and conjecture
Author(s) -
Niklas Karl J.,
Spatz HannsChristof
Publication year - 2006
Publication title -
american journal of botany
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.218
H-Index - 151
eISSN - 1537-2197
pISSN - 0002-9122
DOI - 10.3732/ajb.93.6.824
Subject(s) - allometry , root (linguistics) , biology , biomass (ecology) , bending moment , scaling , botany , mathematics , ecology , physics , geometry , thermodynamics , philosophy , linguistics
Recent allometric theory has postulated that standing leaf mass will scale as the 3/4 power of stem mass and as the 3/4 power of root mass such that stem mass scales isometrically with respect to root mass across very large vascular plant species with self‐supporting stems. We show that the isometric scaling of stem mass with respect to root mass (i.e., M S ∝ M R ) can be derived directly from mechanical theory, specifically from the requirement that wind‐induced bending moments acting at the base of stems must be balanced by a counter‐resisting moment provided by the root system to prevent uprooting. This derivation provides indirect verification of the allometric theory. It also draws attention to the fact that leaf, stem, and root biomass partitioning patterns must accommodate the simultaneous performance of manifold functional obligations.