title: Changes in the factor of safety within the superstructure of a dicot tree.
abstract: The objective of this study was to determine whether the factor of safety for mechanical stability varied among stems differing in size and age within the superstructure of a large dicot tree. Two factors of safety were selected for study: the quotient of the critical buckling height and the actual length of stems, Hcrit/L, and the quotient of the modulus of rupture (the force per unit area required to break a stem) and the working stress (the force per unit area resulting from the biomass measured distal to a stem), M(R)/σ(w). These two dimensionless safety factors were determined for a total of 420 shoot segments comprising much of the aboveground biomass of a Robinia pseudoacacia (Fabaceae) tree measuring 18.7 m in height and 1347 kg in mass, and 0.46 m in diameter (40 yr old) at 1.2 m from the ground.An S-shaped trend was observed when each of the two factors of safety was plotted as a function of stem age. Each factor decreased from a local maximum for the most distal (peripheral) stems in the canopy to a local minimum value for stems ∼10 yr old; each factor increased again to another local maximum for stems 11-18 yr old, and then decreased steadily toward the base of the trunk. This trend was the result of the allometric relationships among stem diameter, length, biomass, and material properties (stiffness and strength) with respect to stem age. Although they were disproportionately more slender than their older counterparts, peripheral stems were sufficiently stiff and strong to sustain the stresses resulting from their weight and that of foliage without deflecting under these loads, yet they were sufficiently flexible to easily bend and thereby presumably provide a mechanism to reduce the drag forces acting on the entire tree. In contrast, the internally imposed mechanical forces acting on progressively older stems increased at a greater rate than the observed rate of increase in stem stiffness, strength, or diameter. The probability of mechanical failure, which must be considered from a demographic perspective (i.e., an age-dependent phenomenon), thus increased from older branches to the base of the trunk. Reports of similar allometric trends based on interspecific comparisons among diverse dicot species comply with the allometry observed for the R. pseudoacacia tree and suggest that the S-shaped trend for the factor of safety holds for stems differing in age drawn from individual trees and for the trunks of conspecifics differing in age drawn from a dense population.