Smoothness analyses of trace fossils: expanding quantitative toolkits to unravel bilaterian movement ecology during the Ediacaran–Cambrian transition

Trace fossils provide unique insights into early animal evolution during the Ediacaran-Cambrian transition. Throughout this critical interval, the smoothness (continuity of derivatives) of combined locomotory and feeding trace fossils (i.e. grazing) significantly increased, potentially indicating diverse evolutionary innovations. We propose several quantitative metrics, including smoothness criteria, minimum normalized radius of curvature and power spectral density, to explore these trace fossils, benchmarked by diverse modern analogues. We classify the trace fossils into unsmooth, regional-smooth and smooth trajectories. A noticeable appearance of regional-smooth and smooth trace fossils among different localities took place around the terminal Ediacaran (since ~545 Ma). Through comparison with extant animals, this period is consistent with the rise to dominance of slender mobile bilaterian eumetazoans with a hydrostatic body, coordinated musculature and long-range sensation to maintain course. The increase of body-length-to-width ratio, and locomotory and navigational capacities of the trace-makers are also quantitatively assessed during metazoan evolutionary radiation. Our results pinpoint the time window for the emergence of ecologically dominant benthic mobile bilaterians in an exponential fashion. We also expand quantitative ichnology, offering new criteria to explore palaeobiological and evolutionary implications of animal-sediment interactions at macroevolutionary scale.