Trajectory smoothness – an important criterion in ichnotaxonomy and its implications for identifying tracemakers

Trace fossils are vital for studying organism–environment interactions in deep time. However, due to uncertainties of the tracemakers, ichnotaxonomy remains independent of biological affinity and relies instead on ichnotaxobases – diagnostic features that inform on construction and function. Previous analyses of the trajectories of trails have emphasized various morphological traits, such as straight or looping paths, meanders, branches or self-overcrossing. Here we introduce a new criterion for classifying trace fossils: trajectory smoothness. Defined mathematically, smoothness measures the continuity of a curve’s derivative and reflects the fluency of movement. Smooth traces suggest intentionality and directionality, commonly linked with slender-bodied tracemakers, whereas unsmooth traces with abrupt turns suggest short or round-bodied producers. Applying ε–δ definitions and spectral analyses, we identify smooth trajectories in the ichnotaxa Cochlichnus anguineus, C. luguanensis, Gordia marina, G. nodosa, Helminthopsis abeli, H. granulata, H. tenuis, Parapsammichnites pretzeliformis, Psammichnites gigas and Spirodesmos archimedeus. In contrast, Helminthopsis hieroglyphica, Psammichnites plummeri and P. implexus exhibit unsmooth trajectories. Helminthoidichnites is reviewed, and the type ichnospecies H. tenuis Fitch, Citation1850 is distinguished from H. irregularis isp. nov., as the former exhibits a smooth trajectory whereas the latter does not. Similarly, specimens of Gordia displaying unsmooth trajectories are relocated within G. angularis isp. nov. The concept of trajectory smoothness in ichnology allows us to unravel significant encrypted biological and evolutionary information about the producers (e.g. locomotory mode, body profile) and enhances the importance of robust ichnotaxonomic practices in untangling animal behaviour evolution in deep time.