Where’s the Variation? Variance Components in Tooth Sizes of the Permanent Dentition

Abstract

Studies have shown that there are only a few canonical axes of tooth size variation in the permanent dentition. Despite the numerous measurements that might be taken (e.g., crown length and breadth of 32 teeth = 64 variables), most of the canonical structure is explained by 3 or 4 overarching axes of variation. This study used maximum likelihood components of variance analysis to determine where the major sources of statistical variation are among the crown dimensions in the permanent dentition. Mesiodistal and buccolingual crown dimensions were measured on all permanent teeth (excluding M3s and averaging sides) in 100 American whites and 100 American blacks, evenly divided by sex. The SAS program varcomp estimated the sources of variation across 7 aspects of the dentition, namely race, sex, arcade, tooth (incisor, canine, premolar, molar), position (mesial, distal), dimension (MD, BL), and a residual term. Most variation is shared; residual variance was just 21.8% of the total. Considering the six components of shared variance, the greatest (82.8%) was due to tooth type (I, C, P, M). In contrast, only 4.9% was attributable to the black-white race difference, which confirms results of other biological data that the preponderance of variation is within groups, not among them. More striking is the lack of variation between males and females (1.2%)—confirming the insensitivity of tooth crown dimensions for forensic purposes. Very little shared variance (0.6%) was due to tooth position, indicating that the mesial “pole” tooth that is metrically and morphologically more stable does not possess much more informational content statistically. Whether the tooth was maxillary or mandibular accounted for 6.9%. In a practical sense, the large variance due to tooth type implies that dental anthropologists commonly will want to include variables from all tooth types (I, C, P, M) rather than multiple measurements within a tooth type, since tooth type is the canonical axis of variation.