Theoretical approach to the functional optimisation of spiriferide brachiopod shell: Optimum morphology of sulcus

Evidence suggests that biological forms that provide physiological and autecological functions have evolved to adapt to environmental conditions and to optimise requisite morpho-functions. We examined whether shell morphology is functionally optimised to generate passive feeding flow in the Devonian spiriferide brachiopod Paraspirifer bownockeri. This study was based on quantitative results from a computational fluid dynamics simulation and the Lagrangian multiplier method. We estimated the optimum development of the ventral median shell depression, which is called the sulcus, by minimising the pressure difference along the gape. This estimation was made under the constraint that the number of spiral flow rotations must be greater than one, which is effective for spiriferide feeding because of its alignment with the spiral lophophore. During mathematical optimisation, the equation resulted in a suitable flow velocity of approximately 0.1 m/s. At this velocity, the pressure difference was minimised, regardless of sulcus development. The constraint equation showed that the number of spiral flow rotations increased with sulcus development. The optimal solution was similar to the original sulcus form of Paraspirifer under an ambient flow of approximately 0.1 m/s. This result suggests that the variation of shell outline in spiriferids could provide a variety of preferential conditions for ambient flow and that the flow intensity could be adjusted by sulcus development to generate a robust passive feeding flow along the spiral feeding organs.