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

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 of tissues) is presented based on a survey of 22 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, end-loaded 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 of petiole indicated that EI ≈ k Lp and EI ≈ k Lp for Type I and II petioles, respectively, where k and k 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).

Fossil leaf economics quantified: calibration, Eocene case study, and implications

“…Previous work in two species has shown that petiole cross-sectional area correlates with supported mass and area within species (Niklas 1991a; Yamada et al 1999). Additionally, several studies have examined relationships among petiole biomechanical properties within and across species (Niklas 1991a(Niklas ,b, 1994(Niklas , 1999. Our study is the first to our knowledge to demonstrate general scaling between petiole and lamina dimensions across diverse species, and to develop from these interrelationships a prediction of M^.…”

“…However, previous experiments that mimicked the fossilization process indicated little to no change in the two-dimensional shape of leaf blades and at most a 10% inflation in the width of xylem-rich tissues, such as petioles, that are buried in fine-grained sediment (Wal-ton 1936;Niklas 1978;Rex and Chaloner 1983;Rex 1986) such as the two fossil locahties studied here (MacGinitie 1969;Wolfe and Wehr 1987); a 10% inflation of PW would lead to a 7.6% overestimation of M^.…”

“…Because complete petioles with bases are only rarely preserved, our protocol allows measurement of a greater number of fossils than these alternatives. It is possible that a combination of petiole width and depth correlates more strongly with IsA/^ than does PW alone, but original petiole depth is rarely preserved in compressed fossils (Niklas 1978;Rex 1986). …”

“…For example, although petiole length has important biomechanical properties (Niklas 1994), it is much less frequently available from fossils, because of incompleteness, than petiole width. We report results (Fig.…”

“…We report results (Fig. 2) important in the mechanical support of the leaf (Salisbury 1913;Niklas 1994;see "Model Fitting and Justification"). We apply our method to 187 fossil leaves from two Eocene fossil floras (Republic, Washington, Klondike Mountain Formation; and Bonanza, Utah, Green River Formation) (Figs.…”