BIOMECHANICS OF PSILOTUM NUDUM AND SOME EARLY PALEOZOIC VASCULAR SPOROPHYTES

Abstract

The elastic modulus E, flexural rigidity EI, static loading P, and volume fractions V of tissues of the aerial portions of Psilotum nudum are examined in terms of two Voigt models: 1) total elastic modulus ET of a branch element is considered the additive property of the elastic modulus of tissues times their respective volume fraction, i.e., ET = (EV), + (EV)2 + … (EV)n, and 2) ET is considered the product of the elastic modulus of cell walls and the apoplastic volume fraction, i.e., ET = EcwVa. The parameters EI and P, together with the length (l) of each branch element are combined into a dimensionless ratio, Pl2/EI (the load parameter L), to describe the relationship between static loading (Pl2) and the ability to sustain loading (EI). The load parameter of branch elements was found to decrease as the level of branching within aerial portions of this race of Psilotum was ascended. The magnitude of P also decreased acropetally. However, the decrease in L is primarily due to a disproportionate decrease in EI. The load parameter of the basalmost branch of aerial portions is smaller for larger aerial portions of this race of P. nudum. Thus, larger specimens are subtended by more rigid branch elements than smaller aerial portions. The Voigt models provide satisfactory approximations of the data from this race Psilotum and indicate that the principal load supporting tissues are the cortical sclerenchyma and other lignified tissues in older (lower branch elements). The mechanics of the three dimensional branching of P. nudum is extended to consider the aerial portions of some early Paleozoic vascular sporophytes (Algaophyton, Rhynia). Analyses indicate that biomechanical speculation about these fossils is potentially flawed by the ambiguity of anatomical data.