DOI: 10.5061/dryad.12jm63xth
title: Potential evolutionary trade-off between feeding and stability in Cambrian cinctan echinoderms

description: 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.
description: 3-D digital models of the cinctans <i>Graciacystis
 ambigua</i>, <i>Gyrocystis testudiformis</i>,
 <i>Lignanicystis barriosensis</i>, <i>Protocinctus
 mansillaensis</i>, <i>Trochocystites bohemicus</i> and
 <i>Undatacinctus quadricornuta</i> 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.