Fenestrate graptolite theoretical morphology: Geometric constraints on lophophore shape and arrangement in extinct hemichordates

A geometric analysis of lophophore shape and arrangement in the fenestrate dendroid graptolite genus Dictyonema reveals that the shape of the zooid domain in the majority of Dictyonema species colonies is highly elliptical, with the long axis of the ellipse perpendicular to the proximodistal axis of the stipe. A complex lophophore, bilaterally symmetrical and consisting of two tentaculated arms that are laterally directed and perpendicular to the stipe axis, provides the best geometric solution to completely filling the elliptical zooid domain seen in the majority of Dictyonema species. Working under the assumption that fenestrate graptolites, like fenestrate bryozoans, needed to form a continuous filtering surface with contact between adjacent lophophores, two optimum close-parking models exist for lophophores with elliptical zooid domains: either a proximodistal-row arrangement or a lateral-row arrangement of the lophophores. Of the two possible geometries, the most probable close-packing arrangement of hypothetical biplumed lophophores within the fenestrate graptolite meshwork is in proximodistal rows.