Detecting Human Population Diversity within an Archaeological Context: A Comparison of Finite Mixture Analysis and Discriminant Function Analysis

Quantifying levels of variation to differentiate between human groups is problematic in prehistoric contexts due to the lack of clearly defined populations among humans. Group differences are typically assessed by comparing cranial morphology or body shape through some variant of discriminant function analysis (DFA), which relies on a priori assumptions of group membership. Alternate methods, such as finite mixture analysis (FMA), take a model‐free approach and use internal characteristics of the sample to identify population substructure and estimate probabilities of group membership. Differences between these methodologies are explored using 3D coordinate data of Arikara crania from Larson (39WW2) and Sully (39SL4); Larson is temporally constrained and historically documented as reflecting a single population, whereas Sully has been shown to represent a single population, despite the evidence that multiple cultures were present at the site. It was anticipated that DFA and FMA demonstrate similar results in differentiating between the number of human groups present in archaeological samples. The coordinate data are translated, rotated, and scaled using a Procrustes superimposition and the fitted coordinates are subjected to a principal component analysis. The resulting principal components were used as variables in the DFA and FMA to assess variation in shape differences within the samples. Results show that an unconstrained approach, such as FMA, is preferential as an exploratory analytical approach to differentiate between human groups. The ability of these analyses to detect groups within a context wherein population substructure is not known is discussed, as well as the implications for the manner in which human variation is quantified.