Reconstructing the function and behaviour of extinct groups of echinoderms is problematic because there are no modern analogues for their aberrant body plans. Cinctans, an enigmatic group of Cambrian echinoderms, exemplify this problem: their asymmetrical body plan differentiates them from all living species. Here, we used computational fluid dynamics to analyse the functional performance of cinctans without assuming an extant comparative model. Three-dimensional models of six species from across cinctan phylogeny were used in computer simulations of water flow. The results demonstrate that cinctans with strongly flattened bodies produced much less drag than species characterized by dorsal protuberances or swellings, suggesting the former were more stable on the seafloor. However, unlike the flattened forms, cinctans with high-relief bodies were able to passively direct flow towards the mouth and associated food grooves, indicating that they were capable of more efficient feeding on particles suspended in the water. This study provides evidence of a previously unknown evolutionary trade-off between feeding and stability in Cambrian cinctan echinoderms.

3-D digital models of the cinctans Graciacystis ambigua, Gyrocystis testudiformis, Lignanicystis barriosensis, Protocinctus mansillaensis, Trochocystites bohemicus and Undatacinctus quadricornuta were constructed. Two-dimensional reconstructions of the cinctans in multiple orientations were taken from the published literature, scaled to life size and used as reference images to guide box modelling in Blender v. 2.75 (http://www.blender.org). For each model, a primitive cube was used as a base object. First, the cube was subdivided to increase the number of elements. The vertices and edges of this object were then translated, rotated and scaled to fit the outline of the reference images in dorsal, ventral and frontal views. Additional elements were added in different orientations by extruding existing elements, thereby modelling other parts of the fossil. Finally, files were exported from Blender and converted into non-uniform rational basis spline surfaces in Geomagic Studio 2012 (http://www.geomagic.com).

CFD simulations were carried out in COMSOL Multiphysics v. 5.3 (www.uk.comsol.com). The computational domain consisted of a 3-D half cylinder measuring 360 mm in length and 176 mm in diameter. Cinctan models were centrally fixed to the flat lower boundary of the half cylinder such that the domain extended at least three times the length of the fossil upstream, ten times the length of the fossil downstream and five times the size of the fossil in all other directions. Models were positioned with any ventral swellings below the lower boundary of the domain and with the mouth facing downstream. The physical properties of water were assigned to the domain surrounding the cinctan model. A normal inflow velocity inlet was defined at the upstream end of the domain and a zero-pressure outlet was defined at the downstream end. Slip boundary conditions were assigned to the top and sides of the domain, allowing the fluid to pass along the walls without friction, and a no-slip boundary condition was assigned to the lower surface of the domain and the surfaces of the model, fixing the fluid velocity at zero. The domain was meshed using free tetrahedral elements, with thin layers of prismatic elements inserted along the interface between the fluid and solid surfaces to better capture the flow in this region. The Reynolds-averaged Navier–Stokes equations were solved using the shear-stress transport turbulence model. A stationary solver was used to compute the steady-state flow patterns. Ten inlet velocities ranging from 0.05 to 0.50 m/s were simulated for each cinctan model. The results of CFD simulations were quantified by computing drag forces, and the dimensionless coefficients of drag were calculated. The projected frontal area was taken as the characteristic area. Additionally, CFD results were visualized as two-dimensional cross-sections of flow velocity magnitude with flow vectors.