Potential evolutionary trade‐off between feeding and stability in Cambrian cinctan echinoderms

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.

T H E sudden appearance of diverse animal phyla in the fossil record for the first time, a phenomenon known as the Cambrian explosion, is thought to represent one of the most significant events in the evolution of multicellular life. Elucidating the pattern of this fundamental evolutionary radiation has engendered considerable debate among palaeobiologists (e.g. Gould 1989;Conway Morris 1998;Marshall 2006;Erwin et al. 2011;Deline et al. 2018), in part due to the difficulty in interpreting the fossils that characterize this episode. To fully decode the evolutionary and biological significance of a fossil, an extant comparative model is normally required; however, many Cambrian taxa have body plans which are radically different to those of living animals, and hence the choice of interpretive model is problematic (Jenner & Littlewood 2008;Donoghue & Purnell 2009). Echinoderms are a case in point; several extinct Cambrian groups lack pentaradial symmetry and perhaps other synapomorphies of living echinoderms (Smith 2005(Smith , 2008Zamora & Rahman 2014), and these fossil forms are therefore poorly understood.
Cinctans are one such group of aberrant early echinoderms, known exclusively from the Miaolingian Epoch of the Cambrian (c. 509-497 Ma) of Gondwana and Siberia (Smith & Zamora 2009;Zamora et al. 2013a). They are characterized by a flattened, asymmetrical body (theca), a rigid posterior appendage (stele), and an anterolateral mouth with one or an unequal pair of marginal food grooves (Fig. 1). Like all echinoderms, cinctans possess a calcite skeleton with a distinctive microstructure termed stereom, but they lack any trace of radial symmetry, a ubiquitous character of modern echinoderms; it is debated whether this absence is plesiomorphic (e.g. Smith 2005; Zamora & Rahman 2014) or derived (e.g. David et al. 2000). Moreover, it is unclear if they had an ambulacral system homologous to that of extant echinoderms (Parsley 1999;David et al. 2000;Smith 2005;Zamora & Smith 2008). The unusual character combination exhibited by cinctan fossils means they have no extant analogue, and hence many important details of their palaeobiology are controversial or unknown.
To gain a better understanding of cinctan palaeobiology, Rahman et al. (2015a) used computational fluid dynamics (CFD) to investigate the functional performance of the cinctan Protocinctus mansillaensis. CFD is an approach for simulating fluid flows and their interaction with solid surfaces that is widely used in engineering, and which has emerged as a powerful tool in palaeontology (e.g. Rigby & Tabor 2006;Shiino et al. 2009Shiino et al. , 2012Bourke et al. 2014;Rahman et al. 2015a, b;Dynowski et al. 2016;Darroch et al. 2017;Waters et al. 2017;Wroe et al. 2018;Gibson et al. 2019;Gutarra et al. 2019). The method generates quantitative results based on numerical simulations of fluid flows, providing a rigorous framework for testing functional hypotheses in enigmatic fossil taxa without an extant analogue, such as cinctans. Rahman et al. (2015a) carried out CFD simulations of water flow for digital models of P. mansillaensis positioned at different orientations and burial depths in a virtual flume tank. Passive and active feeding scenarios were simulated by varying boundary conditions at the major body openings. The results showed that a position with the mouth facing downstream and the ventral swelling buried produced the least drag and lift, indicating this would have been beneficial for enhancing stability on the seafloor. In this position, flow to the mouth and associated marginal groove was minimal in simulations of passive suspension feeding, demonstrating that such a feeding mode would not have been an effective means of acquiring nutrients. In contrast, the simulations of active suspension feeding showed much stronger flow to the mouth and marginal groove, in agreement with previous interpretations of cinctans as pharyngeal filter feeders (Smith 2005;Zamora & Smith 2008). However, there is substantial morphological variation among cinctans, which exhibit varying degrees of asymmetry and thecal flattening (Smith & Zamora 2009;Zamora et al. 2013b), and therefore P. mansillaensis might not be a suitable model for the function and behaviour of the entire group.
Here, we used CFD to simulate fluid flow around three-dimensional digital models of six cinctans that encompassed the group's disparity (Fig. 2). These taxa included weakly to strongly asymmetrical forms, as well as species with and without dorsal protuberances or swellings. In this manner, we were able to analyse stability and feeding across cinctan phylogeny for the first time, shedding new light on the mode of life of this enigmatic extinct group.
Two-dimensional reconstructions of the cinctans in multiple orientations (i.e. dorsal, ventral and frontal) were taken from the published literature (Friedrich 1993;Zamora & Smith 2008;Rahman & Zamora 2009;Zamora et al. 2013b), scaled to life size and used as reference images to guide box modelling (Rahman & Lautenschlager 2017) in Blender v. 2.75 (http://www.blender. org). The accuracy of these reference images was confirmed through first-hand observations of well-preserved fossil specimens, which helped to establish, for example, the height of the theca. A box-modelling approach was preferred over tomographic or surface-based methods because complete, articulated and three-dimensionally preserved fossil specimens are not available for the majority of cinctan taxa. It has been shown that box modelling can be used to create 3-D models that are almost identical to those derived from computed tomography or surface scanning of well-preserved fossil specimens and, moreover, these 3-D models generate very similar results in functional analyses (Rahman & Lautenschlager 2017), justifying our choice of methodology.
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 in STL format and converted into non-uniform rational basis spline (NURBS) surfaces (IGES format) in Geomagic Studio 2012 (http://www.geomagic.com). 3-D models in IGES format are available in Rahman et al. (2020).

Computational fluid dynamics
CFD simulations were carried out in COMSOL Multiphysics v. 5.3 (https://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 (Fig. 3A). This ensured the domain would be sufficiently large to allow the flow to fully develop on all sides of the model (Rahman 2017). Models were positioned with any ventral swellings below the lower boundary of the domain (equivalent to burial within the sediment) and with the mouth facing downstream (180°to the inlet), in agreement with previous studies of cinctan functional morphology (Friedrich 1993;  Jefferies et al. 1996;Parsley 1999;Zamora & Smith 2008;Rahman et al. 2015a). To explore the impact of orientation on our results, we repeated simulations for T. bohemicus with the model orientated at 0°, 45°, 90°and 135°to the inlet.
The physical properties of water (density ¼ 1000 kg/m 3 , dynamic viscosity ¼ 0.001 PaÁs) were assigned to the domain surrounding the cinctan model. A normal inflow velocity inlet (velocity magnitude specified normal to boundary) was defined at the upstream end of the domain and a zero-pressure outlet (tangential stress component set to zero at boundary) 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 (Fig. 3A). 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 boundary layer) ( Fig. 3B, C). The Reynolds-averaged Navier-Stokes equations were solved using the shear-stress transport turbulence model; this uses a combination of the k-ω model in the boundary layer and the k-ϵ model in the freestream to give improved model performance (Menter 2009). A stationary solver was used to compute the steady-state flow patterns.
Ten inlet velocities ranging from 0.05 to 0.50 m/s (Reynolds numbers of 433-8215; width of the model in the flow taken as the characteristic dimension) were simulated for each cinctan model, thereby encompassing the typical range of near-bottom current velocities in modern storm-influenced marine settings (Puig et al. 2001;Valle-Levinson & Matsuno 2003). To evaluate the influence of the mesh on the results, we carried out a sensitivity analysis using different mesh sizes for each model.
The results of CFD simulations were quantified by computing drag forces (by integrating the total stress parallel to the flow direction), and the dimensionless coefficients of drag (C D ) were calculated using the following formula: where F D is the drag force exerted by the fluid (N), ρ is the density of the fluid (kg/m 3 ), U is the characteristic velocity (m/s) and A is the characteristic area (m 2 ). 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. CFD simulation files in MPH format are available in Rahman et al. (2020).

Drag forces and coefficients
In our sensitivity analysis, we compared drag forces for different mesh sizes for each of the six cinctan models (Rahman et al. 2020, table S1). Results were considered mesh independent when the values were generally less than 2% different from those obtained with the next coarsest mesh. Based on these criteria, we selected a mesh for each model (ranging from 388 461 to 940 779 elements in size) that was used in all subsequent analyses.
In the simulations with T. bohemicus at different orientations, the drag forces and coefficients were lowest with the model orientated at 180°to the inlet; the drag coefficients were 6-39% higher at the other modelled orientations (Rahman et al. 2020, table S2). The drag forces were highest when the model was orientated at 45°to the inlet, whereas the drag coefficients were highest with the model orientated at 0°, 45°or 135°to the inlet (depending on the inlet velocity).
Comparing results for all six cinctan models orientated with the mouth facing downstream, the drag forces were highest for U. quadricornuta, followed by T. bohemicus and Gy. testudiformis, with P. mansillaensis, L. barriosensis and Gr. ambigua producing the lowest drag forces ( Fig. 4; Rahman et al. 2020, table S3). The drag force increased as the inlet velocity increased, but the drag coefficient varied less consistently with velocity, increasing as the inlet velocity increased in U. quadricornuta, but decreasing as velocity increased in Gr. ambigua, P. mansillaensis and T. bohemicus. Moreover, in Gy. testudiformis, the drag coefficient increased with velocity up to 0.15 m/s, before decreasing steadily as the velocity increased up to 0.50 m/ s, whereas in L. barriosensis the drag coefficient decreased as velocity increased up to 0.20 m/s, then increased with velocity up to 0.50 m/s. Similar to the drag forces, the drag coefficients were highest for U. quadricornuta, followed by Gy. testudiformis, with P. mansillaensis, Gr. ambigua, T. bohemicus and L. barriosensis producing the lowest drag coefficients for all simulated inlet velocities (Fig. 4;Rahman et al. 2020, table S3).

Flow patterns
In all cases, the velocity of the flow decreased as it approached the cinctan model and the lower boundary of the domain, with a steep velocity gradient developed close to the fluid-solid interface (the boundary layer). In addition, there was a region of low-velocity recirculating flow (the wake) immediately downstream of the model (Figs 5, 6; Rahman et al. 2020, figs S1-S13). Both the thickness of the boundary layer and the size of the wake decreased as the inlet velocity increased.
Flow patterns were substantially different depending on the orientation of T. bohemicus to the inlet. With the model orientated at 0°or 45°to the inlet, flow velocity around the mouth and adjacent food grooves was relatively high, governed by ambient flow rates (Rahman et al. 2020, fig. S1A, B). In contrast, when the model was orientated at 135°or 180°to the inlet, only low-velocity flow from within the wake was directed towards the mouth and food grooves (Rahman et al. 2020, fig. S1D, E). With the model orientated at 90°to the inlet, flow velocity around the mouth and food grooves was low and there was no recirculation to these parts of the model (Rahman et al. 2020, fig. S1C).
For the simulations with cinctan models orientated at 180°to the inlet, the extent to which flow within the wake was redirected to the mouth and food groove(s) varied between models. There was very little flow to these parts of the model in Gr. ambigua (Figs 5A, 6A; Rahman , figs S10, S11) and U. quadricornuta (Figs 5F, 6F; Rahman et al. 2020, figs S12, S13).
The shape of the wake ranged from approximately bilaterally symmetrical in Gr. ambigua and P. mansillaensis to more asymmetrical in Gy. testudiformis, L. barriosensis, T. bohemicus and U. quadricornuta (Fig. 5). In L. barriosensis, there was considerable flow underneath the model, through the two passageways in the ventral surface ( Fig. 5C; Rahman et al. 2020, fig. S6).   fig. S1D, E) would be expected to have improved particle retention efficiency (Shimeta & Jumars 1991). Taken together, our results indicate that an orientation with the mouth facing downstream was optimal for both stability (through drag reduction) and feeding (through enhanced particle capture). To maintain this favourable position, cinctans would have needed to adjust their orientation as the current direction varied, perhaps by using small movements of the stele to re-orientate themselves, or by allowing themselves to be passively reorientated by ambient currents, similar to some extant bryozoans, cnidarians and urochordates (Koehl 1976;Warner 1977;Young & Braithwaite 1980). The drag forces and drag coefficients computed from the CFD simulations were also greatly influenced by the morphology of the modelled cinctans ( Fig. 4; Rahman et al. 2020, table S3). Undatacinctus quadricornuta, which possessed well-developed projections on the dorsal surface, consistently produced the most drag of all the models included in the analysis. Gyrocystis testudiformis, which had a swollen dorsal integument, also generated substantial drag. In contrast, Gr. ambigua, L. barriosensis and P. mansillaensis, which were characterized by low relief, strongly flattened body shapes, produced the least drag. Trochocystites bohemicus produced the second highest drag forces, but among the lowest drag coefficients; this was a product of its considerably larger projected frontal area (up to more than double that of the other cinctans), which was taken as the reference area when calculating the drag coefficients. Consequently, we infer that the cinctans with flattened body shapes that minimized the drag coefficients (i.e. Gr. ambigua, L. barriosensis, P. mansillaensis and T. bohemicus) were less susceptible to dislodgement than high-relief forms like Gy. testudiformis and U. quadricornuta.
The recovered patterns of fluid flow were consistent with some existing interpretations of cinctan functional morphology (Friedrich 1993;Parsley 1999;Zamora & Smith 2008). For example, Zamora & Smith (2008) hypothesized that the ventral passageways in L. barriosensis would have allowed water flow under the theca, as observed in our results ( Fig. 5C; Rahman et al. 2020, fig.  S6). However, the CFD simulations also revealed flow patterns that had not been proposed previously, most strikingly the finding that there was considerable variation in the strength of recirculation downstream of the cinctan model depending on the height of the theca (Figs 5, 6; Rahman et al. 2020, figs S2-S13). Flow towards the mouth and food grooves was strongest when the thecal height was greater than 5 mm (i.e. Gy. testudiformis and U. quadricornuta) but minimal in the models that measured less than about 3 mm in height (i.e. Gr. ambigua, L. barriosensis and P. mansillaensis). In T. bohemicus, which was intermediate in height between these two sets of cinctans, flow to the mouth and food grooves was comparable in strength to that in Gy. testudiformis and U. quadricornuta when the inlet velocity was greater than 0.30 m/s, but more similar to Gr. ambigua, L. barriosensis and P. mansillaensis at lower velocities. This strongly suggests that high-relief forms would have had access to a greater supply of nutrients than low-relief ones.
It is debated whether cinctans were passive suspension feeders with a system of tentacles (Parsley 1999;David et al. 2000)  under a passive feeding scenario. Based on this, they inferred that P. mansillaensis and all other cinctans were most likely to have been active suspension feeders, with an inhalant current generated by pharyngeal gill slits (as previously proposed; e.g. Smith 2005; Zamora & Smith 2008). Our results for Gr. ambigua, L. barriosensis, P. mansillaensis and T. bohemicus at inlet velocities less than 0.30 m/s agree with this, with the very limited flow to the mouth and food grooves pointing towards active suspension feeding as the most plausible feeding mode. However, the strong recirculation of fluid flow to the mouth and food grooves in Gy. testudiformis, U. quadricornuta and T. bohemicus at inlet velocities greater than 0.30 m/s is more consistent with passive suspension feeding on particles transported by ambient currents, which would have been advantageous due to the energetic costs of active pumping (LaBarbera 1984;Vogel 1994). This indicates that cinctans were adapted for different modes of suspension feeding, distributed across phylogeny (Fig.  2). Moreover, the variability in flow patterns observed for T. bohemicus (Figs 5E, 6E; Rahman et al. 2020, figs S10, S11) suggests that it might have been a facultatively active suspension feeder, switching between passive and active feeding depending on the current velocity, similar to some modern barnacles (Crisp & Southward 1961;Trager et al. 1990).
Two potentially important aspects not incorporated into our CFD simulations due to limitations in computing power are the surface roughness of the seafloor and the presence of neighbouring organisms. High surface roughness creates turbulence within the boundary layer, enhancing mixing of nutrients and thereby increasing the availability of food for both passive and active suspension feeders (Denny 1988). However, cinctans lived on soft substrates (Lefebvre & Fatka 2003; Zamora &Álvaro 2010), which would have been characterized by relatively low surface roughness and limited mixing in the boundary layer. The presence of dense communities of epibenthic organisms would also have enhanced turbulence (Denny 1988), but there are no fossil accumulations representing life assemblages of cinctans, and so it is unknown whether individuals lived in close proximity to each other or not.
Our results are suggestive of a trade-off between feeding and stability in cinctans. Taxa with flattened body shapes, such as Gr. ambigua, L. barriosensis and P. mansillaensis, minimized drag and thus enhanced their stability on the seafloor; however, there was almost no flow to the mouth and food grooves, and so they had to expend energy to actively pump water for feeding. In contrast, high-relief forms such as Gy. testudiformis and U. quadricornuta were much less stable due to the large amounts of drag generated, but they were able to passively direct fluid flow to the mouth and food grooves, thereby feeding more efficiently by relying on ambient water currents. Cinctan phylogeny (Fig. 2) places Gy. testudiformis and U. quadricornuta in distinct clades, and they independently evolved different strategies for increasing relief to aid passive suspension feeding (a swollen dorsal integument and dorsal projections on marginal plates, respectively). Trochocystites bohemicus, which is close to the base of the cinctan tree (Fig. 2), had the best of both worlds; it was characterized by a large but relatively flattened body that reduced the drag coefficient (enhancing stability) and increased flow to the mouth and food grooves (enhancing passive feeding), but only at higher current velocities. However, the apparent advantages provided by the morphology of T. bohemicus might have been partly offset by its higher energetic demands; metabolic cost scales as a higher power of mass than energy intake in modern suspension feeders (Sebens 1979(Sebens , 1982Sebens et al. 2017).
Evolutionary trade-offs, where beneficial changes in a trait are associated with detrimental changes in the same or a different trait, are thought to be pervasive across the tree of life (Agrawal et al. 2010). However, demonstrating their existence in fossil taxa has proved challenging, in part due to the difficulties in evaluating functional performance in extinct organisms in a rigorous and quantitative manner. Our results suggest there was an evolutionary trade-off between feeding and stability in Cambrian cinctan echinoderms, with morphological changes that increased the height of the animal inferred to have improved feeding efficiency but reduced stability on the seafloor. Thus, this trade-off points to the creation of multiple locally optimal morphologies in the fitness landscape of cinctans, contributing to the roughness of the landscape (Marshall 2006(Marshall , 2014. One of the studied species, T. bohemicus, deviated from this pattern, indicating that while the trade-off might have been generally true for cinctans, it was not a universal pattern.

CONCLUSION
Our analysis of Cambrian cinctan echinoderms demonstrates that morphology greatly influenced functional performance.
Flattened forms (i.e. Gr. ambigua, L. barriosensis and P. mansillaensis) produced lower drag and were more stable on the seafloor, whereas high-relief forms (i.e. Gy. testudiformis and U. quadricornuta) generated stronger recirculation to the mouth and food grooves, aiding passive suspension feeding. Thus, cinctan functional morphology was partly a trade-off between feeding and stability. This study provides further evidence of the great potential of computational fluid dynamics for elucidating the function and evolution of ancient organisms (Rahman 2017).
Acknowledgements. This study relied on the work of James O'Shea, who very sadly died in January 2018. James was an outstanding student with enormous potential. He is deeply missed by all who knew him. We thank Andrew Smith for the invitation to submit this article. We are grateful to Brad Deline, Bertrand Lefebvre, Sally Thomas and an anonymous reviewer for their comments on earlier versions of this manuscript. IAR was funded by the Oxford University Museum of Natural History. JO'S was funded by a Palaeontological Association Undergraduate Research Bursary (PA-UB201507). SZ was funded by the Spanish Ministry of Science, Innovation and Universities (CGL2017-87631), co-financed by the European Regional Development Fund and the project 'Aragosaurus: Recursos Geológicos y Paleoambientales' (E18_17R) funded by the Government of Aragon.
Author contributions. IAR and SZ conceived the study. J'OS and SL created 3-D models. IAR carried out CFD simulations. IAR wrote the manuscript with scientific and editorial input from SL and SZ.