**1. Introduction**

The study of fossil specimens has been revolutionised by the foundation of modern morphometrics [1]. Symmetry is one prominent feature of biological objects, and possibly the one affected the most by taphonomic processes [2–5]. However, symmetry also offers the possibility to restore the original shapes of fossil remains that are found broken or incomplete [6,7]. This is key to the interpretation of these specimens, since taphonomic alteration affecting diagnostic features may lead to incorrect taxonomic attributions and dubious phylogenetic reconstructions [7–9]. Digital methods for the reconstruction and restoration of broken fossil remains are nowadays available thanks to an ensemble of techniques that commonly fall under the heading of 'virtual anthropology' [10–12]. Specimens can be handled in a safe, virtual environment [7] and undergo restoration protocols that can include the realignment of dislocated fragments [13–16] or the digital removal of the plaster from traditional reconstructions [8,17] without the risk of damaging the original material. These protocols can be associated with symmetrisation, which helps to

**Citation:** Buzi, C.; Profico, A.; Di Vincenzo, F.; Harvati, K.; Melchionna, M.; Raia, P.; Manzi, G. Retrodeformation of the Steinheim Cranium: Insights into the Evolution of Neanderthals. *Symmetry* **2021**, *13*, 1611. https:// doi.org/10.3390/sym13091611

Academic Editor: Chiarella Sforza

Received: 27 July 2021 Accepted: 20 August 2021 Published: 2 September 2021

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recreate missing portions or 'undo' the effects of plastic deformation. In the former case, symmetrisation 'fills the gaps' (i.e., missing portions) in one half of the fossil by mirroring the preserved counterparts [7,18–22]. In the latter case, referred to as retrodeformation, the plastic distortion of the original shape is corrected by relying on biological symmetry, as calculated by the acquisition of bilateral landmarks, curves, or patches of semilandmarks [4,7,8,23–28]. Mardia and colleagues [3] defined two types of bilateral symmetry: one referring to structures present as two separate copies on both sides of the specimen as mirror images (matching symmetry), the other defined (in three-dimensional objects) by the midsagittal plane passing through the specimen and thus determining an internal left–right symmetry (object symmetry) [2,3]. One key difference between matching and object symmetry is that genuine asymmetry is ignored by the former, but still apparent under the latter. In the case of the vertebrate skull, which provides an example of object symmetry [3], this implies that retrodeformation preserves genuine asymmetry, whereas mirroring does not. Moreover, mirroring can generate artefacts, or a biased morphology, if the only preserved portion is itself distorted [7]. On the other hand, the application of retrodeformation can be affected by the state of preservation of the object [4].

A perfect example of the combination of missing parts and plastic deformation affecting a single specimen is given by the cranium from Steinheim (hereafter, Steinheim), which is the holotype of the abandoned species *Homo steinheimensis* (Berckhemer, 1936) [29]. This human fossil was found in July 1933 in a gravel pit 70 km north of the town of Steinheim an der Murr, Baden-Württemberg, Germany [30,31] (Figure 1). It was recovered from Pleistocene fluvial deposits along the Murr river, which were well known at the time of the discovery for having yielded well-preserved fossils of Pleistocene mammals [30,32]. Since the discovery came from a well-studied area, the fossil received proper geological contextualisation. It was therefore possible to estimate the specimen's age based on the biochronological dating of the faunal assemblage, roughly corresponding to OIS 9 (i.e., 300–320 ka to 250 ka) [30,32–35].

**Figure 1.** The cranium from Steinheim: (**a**) the cranium (left side) at the moment of recovery (from [30]); (**b**) a digital rendering of the cranium (front side).

The complex pattern of deformation that affected Steinheim, as well as its incomplete status and the presence of extensive incrustations, made it difficult to discern whether its peculiar morphology represents the original shape of the individual, or it is the product of taphonomic deformation [36,37]. This uncertainty contributed to a longstanding debate concerning the Steinheim phylogenetic position [36,38–40]. The cranium is characterised by a peculiar mixture of archaic and derived traits, which originated different proposals about its position within or close to the Neanderthal lineage—as representing a 'pre-Neanderthal stage' along the so-called process of accretion—or even as a specimen somehow related to the origin of *Homo sapiens* [41–45]. However, not only most of the left side of the facial skeleton in Steinheim is missing, but also the cranium presents a peculiar plastic deformation, further complicating the recognition of its features. For example, the highly diagnostic infraorbital plate and orbitomaxillary region are preserved only on the left side. This part of Steinheim's face shows an angled transverse profile, which was interpreted in the past as 'anticipating' the modern human morphology to some degree [30,43], but has been conversely interpreted as the result of the retention of archaic facial morphology, also observed in some Western European earlier taxa (i.e., *Homo antecessor*) [46–48]. The relatively low and long neurocranium of Steinheim, possessing a rather vertical occipital plane, also shows a slightly angled coronal profile, or a 'roofed' appearance [36], with the maximum cranial width occurring in the lower portion [35].

A specific name was initially proposed for this specimen (*Homo steinheimensis* Bereckhemer, 1936) [29], but it is currently considered invalid [40,49], despite that this name has been resurrected at the taxonomic rank of subspecies [50,51]. Steinheim is now generally considered as belonging to the Neanderthal lineage [45,52–54] and possibly related to other Middle Pleistocene populations (e.g., Atapuerca Sima de los Huesos, SH), with which it shares several derived traits in addition to its the geographical and chronological attributions [45,53,54].

## **2. Materials and Methods**

The description of Steinheim's morphology is influenced by the extensive deformation of the skull [32,37]. A representation of the major directions of the deformation has been obtained by observations on the CT scan of the fossil and a review of literature [32,37,55] and is shown in Figure 2.

**Figure 2.** A simplified representation of the deformation of Steinheim. The blue lines resume the extent and area of influence of the deformation; the red arrows resume the directions of the morphological modification, associated with the areas in which the effects are visible. The solid lines point to the more evident effects of the deformation; the dashed lines represent additional possible effects. (**a**): anterior view; (**b**): right-lateral view; (**c**): inferior view; (**d**): superior view.

Prossinger and colleagues [37] performed the first digital segmentation of the cranium, resulting in a model cleared from the encrustations but still heavily affected by taphonomic distortions. Such distortions are observed in the internal structure of the cranium, including a shift to the right of the midsagittal plane of the splanchnocranium, an inward 'inflation' of the left orbital roof, and a rightward rotation of the axis of the *crista galli* in the anterior endocranial surface [37]. Since the left portion of the face is missing, it is difficult to assess how much of this morphology is determined by the deformation [37]. The right orbit is characterized by an angled shape with a sloped inferior margin. The preserved infraorbital plate shows an angled transverse profile with a point of bending roughly corresponding to the infraorbital foramen [33]. Curiously, this is associated with a moderate inflation of the anterior portion of the infraorbital plate, whereas the lateralmost portion appears flattened [35]. Through investigations conducted via CT scan and digital imaging, it was possible to assess the relative size of the frontal sinuses inside the well-developed supraorbital torus [36] and to diagnose a possible meningioma located in the upper part of the neurocranium [56].

To obtain a reconstruction consistent with object symmetry (sensu Mardia and colleagues [3]), we started by applying retrodeformation [4]. The choice of landmarks (Figure 3) was thus constrained by a criterion of symmetry: each landmark chosen on the left side must have a counterpart on the right side [4]. The incomplete state of Steinheim narrowed the choice of possible homologous landmarks and the choice of bilateral curves and surfaces for the definition of semilandmarks (Figure 3).

**Figure 3.** The configurations used: the bilateral landmarks (dark red); the bilateral curves, right (light blue) and left (dark blue); the patches of surface semilandmarks sampled on the left side (yellow) and their projection on the right side (orange).

It was possible to define only a few landmarks on the small preserved portion of the left side of the face, comprising the nasomaxillary region (Figure 3). In defining surface semilandmarks, we excluded the preserved portion of the temporal squama because it is affected by local breakage and subsequent reconstruction (see Figure 1) [36–38]. Similarly, in defining the patches of semilandmarks, the upper part of the left parietal was excluded, as this portion of the neurocranium is more affected by breakage and surface damage (Figure 3). The basioccipital is also damaged, cracked, and partly shifted inside the neurocranium itself, and therefore, no landmarks were placed on this region.

The high-resolution CT scan of Steinheim was kindly provided by Prof. Dr. Christoph P.E. Zollikofer (Department of Anthropology, University of Zurich). The CT data, obtained in the form of a DICOM stack, were processed in Amira [57] to obtain a 3D mesh, subsequently converted into the .ply format. We defined 52 bilateral landmarks on the skull and 8 curves. The curves were later processed in R by the function *equidistantCurve* (*Morpho* R package) [58] to sample evenly spaced semilandmarks along each curve. The coordinates of 500 semilandmarks were obtained by applying a *k*-means clustering algorithm to the vertex coordinates from a portion of the mesh corresponding to the left part of the cranium, from which we excluded the temporal squama and the damaged area of the coronal suture (Figure 3). The set of surface semilandmarks built this way was rotated and projected on the right side. In sum, we defined 8 curves (120 points), 52 bilateral landmarks, and 1000 surface semilandmarks for a total of 1172 paired coordinates (Figure 3). After the retrodeformation, applied according to the protocol in Schlager and colleagues [4], we calculated and visualized the local displacement between the starting and retrodeformed meshes using the function *localmeshdiff* (*Arothron* R package) [59]. The retrodeformed model of Steinheim was eventually subjected to a principal component analysis (PCA) in the shape space, together with the original model and a comparison sample including modern humans (N = 17), Neanderthals (N = 5), and Middle Pleistocene humans (N = 3). The comparison sample for the PCA is reported in Supplementary Table S1. The cranial landmark configuration used for the analysis was built upon the preserved portions of Steinheim and is figured in Supplementary Figure S1.
