3.1 Fossil affinities and preservation
Putative trilobite egg clusters and embryos from the middle Cambrian of the Kaili Formation are described here using different approaches. Morphologically, the outer layers of the fossil spheres are black in color and rich in silicon (Figure 1A, 2H).
By contrast, the inner core of the sphere is filled with high-density minerals (Figs. 1A2, 2C), which indicates that the outer layer and the inner core of the fossil are made up of different materials. The detected quadripartite spheres are reminiscent of blastomeres in an extant embryo (Figs. 1B, 2F). The presence of a sunken portion in the sphere suggests that the shell might have been flexible before fossilization (Fig. 2G).
Inorganic concretions are not rare in sediments. The tomographic image of specimen GRCP 15020 (Fig. 1A2) shows different degrees of compaction of the spheres with some spheres collapsed into amorphous flattened material (Fig. 3J) suggesting that the spheres were elastic; this fact would exclude a priori an abiotic interpretation for these silicon spheres. The observed putative decay stages of the sphere fossils (Figs. 1A2, 3J) also indicate that when the outer layer was broken, the contents were released (Fig. 3) and this layer flattened (Figs. 1A, 2).
Two main variables characterize the morphology of the eggs: the degrees of asymmetry and ellipticity (Stoddard et al., 2017) on the one side and the size range and shape of the egg fossil clusters, with sizes varying in the range of Min diameter = 528 μm and Max diameter = 757 μm (dmean = 612 μm, n = 50) in GRCP 15022 on the other. As some eggs are deformed, we chose to measure the egg with a roundish outline to exclude the impact of deformation. The large quantities of eggs found in the Kaili Biota samples (we collected more than 10,000 within 108 clusters) indicate that the egg-laying animal was potentially a dominant clade in this biota.
In fact, trilobites are highly abundant in the Kaili Biota. We have observed that the early hatching stage of trilobites is normally associated with egg clusters (e.g., GRCP 15022–GRCP 15024). The highly crowded clusters have an obvious shape (Figs. 1C–E), indicative that they are, at least, part of individual egg clutches. Based on our observations is unlikely that external trilobite larvae mixed with the eggs. Some trilobite larvae remained, most probably, at the deposition site (Schwimmer 2019) (Figs. 1E). The trilobite larvae within the egg cluster (Figs. 1C, E) (ca. 0.5 mm) were slightly smaller than the egg (ca. 0.6 mm), which most probably indicates that they had recently hatched. The round-shaped larvae, dark in color (the same color as the egg) (GRCP 15023), are interpreted here as pre-hatching trilobite larva (Figs. 1D, D1). Comparatively, the post-hatched larvae are light in color (Figs. 1C, E). In this context, GRCP 15023 would indicate that a protaspis shield may have formed before hatching.
The number of eggs in each cluster range from approximately 300 in GRCP 15020 to 400 in GRCP 15022. We also found eggs on the substrate sheet with densely packed micro-protrusions (Figs. 2A, B). The eggs and micro-protrusions are made up of similar elements (Figs. 2H, I), the eggs may be associated with the trilobites (Figs. 2A). Additionally, we observed the presence of some cracked eggs that were empty inside (Fig. 2D).
3.2 Taphonomy testing
Most of the extant animal eggs for any single species fall into a narrow range, irrespective of an incredible diversity of shapes present across different animals for any species. However, the spheres’ sizes, within individual clusters, are remarkably varied in some of the fossil specimens analyzed here (e.g., Fig. 3, GRCP 15029). Since it has been observed in some developmentally arrested embryos (e.g. the Xenopus laevis embryos tested here as living surrogates) that soft tissues decay via a process that leads to the liberation of white homogeneous yolky droplets (Figs. 3A–D; see also Raff et al, 2006 for other embryos), we speculated with the possibility that this could happen also in fossilized specimens. In fact, the sizes of our small fossil spheres is similar to the size of the homogeneous droplets observed in decaying X. laevis embryos. Thus, we interpret small fossil spheres (Fig. 3J) as homogenized drops released by the decayed egg masses. Moreover, the amount of well-preserved fossil embryos found in the biota suggest that they became fossilized in a reducing environment that blocked autolysis shortly after death.
3.3 Computational fluid dynamic analysis of the egg and egg cluster models
The behavior of the eggs in their liquid environment was simulated using CFD models. The diameter (L) of the egg model was set at 0.6 mm, which is approximately the same as the average size of the observed fossil spheres. The egg cluster model was based on specimen GRCP 15004 (Fig. 2E). To simulate the current speed at the water-sediment interface in the Kaili Biota (slope face), we used several modern references: 1) the maximum near-bottom water flow speed (< 0.5 m/s) can be inferred for fine-grained sediment environments (Kuijpers et al., 2016); 2) fast near-bottom currents occur over the slope above the level of 0.2 m/s (Csanady et al., 1988).
A 6-mm sublayer was found in the horizontal flow profiles obtained at the water-sediment interface in 200-m deep water on the Oregon continental shelf (Caldwell and Chriss, 1979). In this sublayer, the current speed drops. In the case of the benthic biota of Kaili, which live on the continental shelf (Lan 2018), 0.01, 0.03, 0.05, 0.25, and 0.5 m/s were chosen for our calculations (Figs. 4–6). Re = 2300 is the critical Reynold’s number, which marks the switch from a laminar to a turbulent flow pattern. The calculated Reynolds number (Re = ρUL/µ) (102 –104) of the egg cluster suggests that the cluster experienced a transition from a laminar flow pattern (Re < 2300) (Figs. 5A, 6B) to a turbulent flow pattern (Re > 2300) (Figure 5B, 5C, 6A) when the current speed increased.
The CFD simulations provided some key insights into the behavior of fossilized eggs and egg clusters within fluids. First, the results of the pressure field on the 3D model of the egg cluster showed that the pressure field affecting the eggs within the cluster was nearly isotropic under the lower fluid speed situation (0.05 m/s) (Fig. 4A). As the fluid speed rose (0.25–0.5 m/s), a pressure gradient was established, and thus experienced, from the anterior to posterior part (facing the current) of the egg cluster (Figs. 4B–D).
The 2D egg cluster model showed that the tail vortex of spheres clustered at higher fluid speeds (0.5 m/s) (Figs. 5C, 6A) and was much stronger than that experienced at low fluid speeds (0.03, 0.05 m/s) (Figs. 5B, 6B). The tail vortex disappeared when the fluid speed was reduced to 0.01 m/s (Fig. 5A).
Drag forces depend on the Reynolds number, so when the Re (Re = ρUL/µ) of the egg was < 1, drag force was governed by the surface drag. Conversely, drag force started to be dominated by the pressure drag for eggs at higher Reynolds numbers (Re > 1). Under these conditions, the fluid speed dropped rapidly around the egg cluster (Figs. 4–6), thus generating a smaller drag force load on the central eggs than on the marginal ones.
To understand how drag and lift forces affect single or grouped eggs, we compared forces on one egg (in a cluster or isolated) at different current speeds by using COMSOL 5.4 software. The results indicate that the forces experienced grow much slower for the egg cluster model than for the single egg model (Figs. 7A, 7C) when the current speed increased. The drag coefficient of the single egg model is 0.8–1 times larger than that of each egg in the egg cluster model (Fig. 7B). These different simulations lead us to conclude that, notably, clustered eggs reduce the drag and lift forces experienced by each egg within the current, thus providing a quantitative physical explanation for the clustering of eggs in the trilobites.