Flexural Stiffness Allometries of Angiosperm and Fern Petioles and Rachises: Evidence for Biomechanical Convergence

Abstract

Abstract.-Evidence for convergence in biomechanical and anatomical features of leaves (elastic modulus E, second moment of area I, taper of petioles, the longitudinal distribution of petiolar and laminar weight, and volumes oftissues) is presented based on a survey of22 species (distributed among dicots, monocots, and ferns). In general, regardless of taxonomic affinity, petioles were found to be mechanically constructed in one of two ways: Type I petioles-as cantilevered, endloaded beams with relatively uniform flexural stiffness (EI) (simple and palmate leaves); and Type II petioles-as tapered cantilevered beams whose static loadings (biomass) and EI increase basipetally (pinnate leaves). In general, collenchyma and sclerenchyma were found to be peripherally located in transections through Type I and II petioles, respectively. Statistical analyses within each species and among species with either type ofpetiole indicated that EI "" k,Lp2.98 and EI "" k 2Lp2.0S for Type I and II petioles, respectively, where k, and k 2 are dimensional constants and Lp is petiolar length. The data are interpreted to indicate that Type I and II petioles mechanically operate to deal with static loadings in two distinct ways, such that Type II petioles function in an analogous manner to branches supporting separate leaves (leaflets). The convergence in mechanical "designs" among taxonomically distinct lineages (angiosperms and ferns) is interpreted as evidence for selection on mechanical attributes of load supporting structures (petioles).

Petiole mechanics, leaf inclination, morphology, and investment in support in relation to light availability in the canopy of Liriodendron tulipifera

“…Thus, changes in the thickness of foliage elements with irradiance were the primary determinants of modifications in EI. Ample evidence from previous studies demonstrates that petiole flexural stiffness scales positively with lamina load and petiole length, but also that both E and I may depend on foliage size (Niklas 1991b(Niklas , 1992a(Niklas , 1992b(Niklas , 1996.…”

“…Given that the largest portion of the effective second moment of area of the lamina may be attributable to major veins, our approach to determine I L may have led to an overestimation of effective E L . Nevertheless, previous investigations have demonstrated that the flexural stiffness of the major veins separated from the rest of the lamina is considerably lower than that of the petioles of similar shape and size (Niklas 1991b), indicating that embedding of veins in the lamina matrix significantly increases the composite leaf elastic modulus.…”

“…7 has also been used to estimate the petiolar deflection if the lamina is attached (e.g. Niklas 1991bNiklas , 1992b, leaf lamina cannot be approximated as a point load affixed at the tip of the petiole, because the weight of lamina is distributed over a long distance away from the axis of rotation, and the effective bending moments are larger than those for a point load applied at the junction between the petiole and lamina. Simulations demonstrate that the shape of load distribution along the lamina may significantly alter the maximal bending moment at the petiole attachment to the leaf lamina, and thereby modify the deflection curve for the entire leaf (Appendix I).…”

Sclerenchyma

“…Sclerenchyma is best defined by its mechanical function, but providing hardness is only one of its possible mechanical roles, demonstrated, for example, in the tips of thorns. More widely important is the provision of rigidity and both tensile and shear strength in plant stems (Niklas, 1991). See also: Plant Biomechanics…”

“…In sclerenchyma an equally important function of lignification is to attach the cells to one another and so stabilise the mechanical architecture of the plant. For example the sclerenchymatous ring in cereal straw (Travis et al, 1996) and other plant stems (Niklas, 1991) is well adapted for stiffness under the bending stress of wind, while in vines a central location for the sclerenchma combines strength in tension with flexibility in bending. Parallel isolated strands of sclerenchyma in grass leaves combine some flexibility with shear strength, influencing grazing by herbivores (Vincent, 1991).…”