Shape deformation during fossilization can prevent accurate reconstruction of an organism's form during life, hampering areas of paleontology ranging from functional morphology to systematics. Retrodeformation attempts to restore the original shape of deformed fossil specimens and requires an adequate knowledge of the deformation process. Although tectonic processes and retrodeformation are relatively well understood, research on quantifying the effect of compressive deformation on fossil morphology is scant. Here we investigate the factors that can cause changes in the shape of fossil specimens during compressive deformation. Three-dimensional (3D) models of trilobite cranidia/cephala are subjected to simulated deposition and compaction using rigid body simulation and scaling features of the open-source 3D software Blender. The variation in pitch and roll angle is lowest on flat surfaces, intermediate on tilted surfaces, and highest on irregular surfaces. These trends are reflected in the morphological differences captured by principal component scores in geometric morphometric analyses using landmarks. In addition, the different shapes of trilobite cranidia/cephala according to their systematic affinity influence the degree of angular variation, which in turn affects their posture—normal or inverted. Inverted cranidia/cephala show greater morphological variability than those with normal postures.

Harpetid and trinucleid trilobites share a similar and unusual morphology, the most striking feature of which is a wide, flattened cephalic brim with many pits or holes. This similarity was once interpreted as a sign that these two groups of trilobites were closely related, but in recent years it has instead been assumed that the ‘harpiform’ brim arose in both groups independently. However, relatedness and similarity can be difficult to disentangle in fossil taxa without close living relatives, and this assumption about the harpiform brim has never been explicitly tested. Our study re-evaluates the relationship between Harpetida and Trinucleioidea in order to test a longstanding assumption about trilobite relationships and as a case study in evaluating different kinds of morphological similarity in extinct groups. We inferred a new phylogenetic tree using parsimony methods and discrete morphological character data from a broad sampling of harpetids, trinucleids, and their relatives. Despite their gross morphological similarities, we found that harpetids and trinucleids were readily distinguished in our analyses, a result consistent with a hypothesis of multiple origins for the harpiform brim. By mapping brim-related characters across our new phylogeny, we identified a sequence of morphological innovations that arose in parallel in both groups and led ultimately in each case to the evolution of the harpiform brim. These results indicate that harpiform brims are a prime example of parallel evolution—the similar development of a morphological trait in distantly related taxa that nevertheless share a similar original morphology. In addition, our phylogeny supports the idea that trinucleids are specialized, harpiform asaphids, rather than an independent order of trilobites. We also provide new information on the relationships of the putative ‘basal-most’ members of Trinucleioidea, the Liostracinidae, and confirm recent assessments that this family is more distantly related to trinucleids.