Skulls and transvariation.

The reconstruction of the history of human populations is made possible by the application of different approaches. In Physical Anthropology, the analysis of metric characters of the skull is fundamental and regularly applied to determine the biological relationships between populations alongside archaeological, genetic, and linguistic information. The purpose of this study is to propose a new index (DA) to evaluate the distance between pairs of skull populations based on a multivariate set of craniometric variables. The new measure reflects the concept of transvariation area developed by the Italian statistician Corrado Gini in 1916. As an illustrative example, an application to a practical case will be presented. Specifically, an expert anthropologist is asked to identify 3 craniometric variables and to assign the respective weights in terms of importance to evaluate the distance between pairs of 9 groups of skulls with different geographical origin and ethnic affiliation. The results indicate that DA is an efficient measure to evaluate and summarize the distance between groups. Moreover, due to its immediate geometric interpretation, it can easily be interpreted graphically. The usefulness of this new measure in Physical Anthropology, its natural extension to other scientific domains, and other potential applications are discussed.