*2.2. Case Studies*

We applied and tested *show.asymmetry* on different case studies. First, we applied the function to a collection of sexed modern human crania. We compared levels of asymmetry in two different groups, male (N = 10) and female (N = 10), to observe if asymmetry patterns differ among sexes. We also computed a PCA on the asymmetric component as described in Section 2.1.

The second case study pertains to two fossil *Homo* skulls we studied to look at the patterns of taphonomic distortion. The two specimens refer to *Homo heidelbergensis* from Petralona and the *Homo neanderthalensis* from Saccopastore 1. The Neanderthal specimen shows extensive asymmetry in the parietotemporal region next to the slight clockwise rotation of the facial complex with respect to the neurocranium [29] (Figure 1).

**Figure 1.** Fossil specimens for *show.asymmetry* case studies. (**a**) Petralona, (**b**) Saccopastore 1, and (**c**) Steinheim skulls.

Petralona represents a well-preserved *Homo heidelbergensis* skull discovered by Malkotsis and colleagues in 1959 in a cave site near the Petralona village (Thessaloniki, Greece). The cranium lacks the right zygomatic arch. The mastoid processes are broken. The upper portion of the sphenoid bone is missing. A wide opening intervenes in between the cranial and nasal cavities and the maxillary sinuses [37]. As highlighted by Rightmire [38], there are slight deformations of the vault. Although the frontal bone is undeformed, the right parietal bulges more than its left counterpart, and the right temporal squama is displaced laterally. The palate is rotated about the sagittal plane of the braincase, indicating some twisting of the facial skeleton towards its right side.

Saccopastore 1 was discovered in 1929 in the aggradational succession of the Aniene River Valley (Rome, Italy). The cranium is almost complete, although it lacks both zygomatic arches and the left orbital region is damaged. Some additional and severe damages were due to its accidental discovery in a gravel pit during construction works. The most extensive damage occurred to the browridge region, which is missing. The neurocranium also presents two pick stroke marks. For the application of *show.asymmetry*, the two holes were closed digitally, while the browridge could not be restored.

The last case study regards the application of *show.asymmetry* to evaluate the effect of retrodeformation on asymmetry. To avoid biases due to the inclusion of deformed specimens in morphometric analysis, or misinterpretation of morphological traits, paleontologists have applied the so-called retodeformation protocol to artificially restore symmetry in digital models [23,26,29,39]. This symmetrization procedure is powerful and effective, ye<sup>t</sup> it cannot discriminate between taphonomic distortion and natural asymmetry. We decided to test *show.asymmetry* on a highly deformed specimen before and after the retrodeformation procedure to see if the retrodeformed specimen shows a lower than expected level of asymmetry (as judged by comparison to living *Homo sapiens* specimens) and whether *show.asymmetry* captures this essential feature of the retrodeformation process. We used the Steinheim skull case-study presented in [40] (this volume). Steinheim cranium was found in 1933 in a gravel pit 70 km north of Steinheim an der Murr (Baden-Württemberg, Germany) and, despite a longstanding debate, is commonly attributed to *Homo heidelbergensis*, or otherwise linked to the Neanderthal lineage [41,42].
