Irish and Kenyhercz 2013.5 38 Over 20 years ago, Edward Harris proposed an approach to compare mesiodistal (MD) and bucco- lingual (BL) crown diameters that employed prin- cipal components analysis (PCA) (Harris, 1997; Harris and Bailit, 1988; Harris and Rathbun, 1991). One major goal, like that of other workers (e.g., Penrose, 1954), was to remove overall “size” -- which is ineffective for biological affinity estimates and phylogenetic analyses. However, relative size is important, i.e., how it is apportioned among crowns along the tooth rows. To get at such data, Harris used three size predictors in multiple linear regression to calculate PC 1 residuals; these and the other uncorrected components were then used in analysis. This approach is called tooth size ap- portionment (TSA) analysis. It was used by several other researchers (e.g., Hemphill, 1991; Hemphill et al., 1992; Irish and Hemphill, 2001, 2004) to quantify sample differences ranging from global to local in scale -- before its appeal diminished. Like clothing, analytical methods go in and out of style. When “sexy” approaches involving lasers, aDNA, and stable isotopes emerge, the “old ways” are often forgotten. The purpose here is to show that “old” is not the same as “out-dated;” through TSA, useful results can be achieved with easy-to- obtain odontometric data – all without destructive sampling and at a fraction of the cost. MATERIALS Up to 32 MD and BL measurements in the left maxillary and mandibular dentitions of 12 (n=712 inds) sub-Saharan and 18 (n=1251) North African samples for the present study were recorded. Non- metric findings in these same samples support a known biocultural dichotomy between popula- tions living north and south of the Sahara (Irish, 1997, 1998a,b, 2005, 2006). The names (incl. abbre- viations in Figs. 3 and 6), composition, and origins of these 30 samples are presented in the aforemen- tioned publications. Their approximate geographic locations are plotted in Figure 1. METHODS Following Harris’ [and Hemphill’s (1991)] ap- proach, sexes-pooled mean measurements were obtained for each sample (sex dimorphism relates to crown size not shape). Ordinarily, either these data or their z-scores would be submitted to PCA to obtain a rotated (Harris) or unrotated Size does matter: Variation in tooth size apportionment among major regional North and sub-Saharan African populations Joel D. Irish 1 and Michael W. Kenyhercz 2 1Research Centre in Evolutionary Anthropology and Palaeoecology, Liverpool John Moores University 2Department of Anthropology, University of Alaska, Fairbanks, AK 99775-7720 Keywords: Odontometrics, Prinicipal Components Analysis, Dental Anthropology, Africa, Biological Affinity ABSTRACT In the 1980s Edward Harris pro- posed an approach using principal components analysis to compare mesiodistal and buccolingual crown diameters in humans. A major goal was to remove overall “size” from the measurements – which is ineffective for biological affinity. Relative size, however, is important, i.e., to assess how it is apportioned along the tooth rows. To get at such data, Harris utilized three size predictors in multi- ple linear regression to calculate PC 1 residuals, which were then used with other uncorrected components in analysis. Here we demonstrate that it is still an effective method, by comparing 32 MD and BL measure- ments in 12 (n=712) and 18 (n=1251) samples from sub-Saharan and North Africa. Plotting of the first three components (50% of variance) shows clear separation between regions. North Africans are characterized by: 1) small LI1s, and BL dimensions of the UM1, LI2, and LM1, and 2) large MD diame- ters of the UM2 and LM1, and BL diameters of the LM2 and LM3. Comparisons of North Africans only show the ability to distinguish among sam- ples from the Maghreb, Egypt, and Nubia. In other words, basic crown diameters can be successfully used for affinity estimation, if relative size, a.k.a., “shape” is accounted for. Correspondence to: Joel D. Irish, Research Centre in Evolutionary Anthropology and Palaeoecology, School of Natural Sciences and Psychology, Liverpool John Moores University, Byrom Street, Liverpool L3 3AF, United Kingdom. j.d.irish@ljmu.ac.uk 39 (Hemphill) solution. The PC1 size factor would be addressed through use of residuals as noted above. However, this approach was questioned by Jungers et al. (1995), among others, who prefer size correction via Darroch and Mosimann’s (1985) geometric mean (GM). Following their lead, the product of all 32 measurements in this study by sample was calculated, the 32nd root obtained, and the resulting GM used as divisor of each measurement to effect correction. These DM val- ues were then submitted to PCA, to yield unrotat- ed PC loadings and factor scores. RESULTS AND DISCUSSION To illustrate the effectiveness of DM size correc- tion, the eight sexes-pooled mean MD maxillary measurements for combined samples of North and sub-Saharan Africans are plotted in Figure 2. North Africans exhibit smaller dimensions in all cases. Compare this line graph to that at the top of Figure 5 after size correction. It can be seen that relative between-sample size (a.k.a. shape) varies; that is, it is apportioned differentially along the tooth row: in this example, North Africans have relatively larger UI1, UP4, UM1, and UM3 MD dimensions. Five components with eigenvalues of >2.0 were retained (see Table 1); they account for >63% of the total variance. Plotting of first three factor scores (<50% of variance) yielded the distribution in Fig- ure 3. The North and sub-Saharan samples show Fig.1. Origins of the 30 North (red dots) and sub- Saharan (blue) samples. Fig. 2. MD maxillary measurements in pooled North and sub-Saharan samples. 40 Measure PC1 PC2 PC3 PC4 PC5 DM_MUI1 -.098 -.246 .123 .596 .356 DM_MUI2 .546 .466 -.026 -.082 .401 DM_MUC .151 -.575 .234 -.224 .209 DM_MUP3 .429 .343 -.083 .111 .527 DM_MUP4 -.294 .138 -.130 .219 .242 DM_MUM1 -.419 .252 .028 -.238 .175 DM_MUM2 .099 .543 .467 -.113 -.317 DM_MUM3 -.377 .371 .246 .393 -.407 DM_BUI1 .085 -.698 .057 .053 .110 DM_BUI2 .400 -.310 .196 -.512 .471 DM_BUC .429 -.654 .115 -.175 .035 DM_BUP3 .777 .121 .158 .319 .117 DM_BUP4 .456 -.179 .344 .437 -.073 DM_BUM1 -.588 -.170 .501 .095 .262 DM_BUM2 .287 -.153 .784 -.099 -.328 DM_BUM3 .600 .067 .255 .243 -.080 DM_MLI1 -.512 -.234 -.023 .635 .064 DM_MLI2 -.342 -.265 -.329 .539 -.220 DM_MLC .498 -.078 -.225 -.329 -.511 DM_MLP3 .653 .323 -.352 .144 -.138 DM_MLP4 -.044 .366 -.649 .022 .053 DM_MLM1 -.079 .523 -.329 -.013 .346 DM_MLM2 -.479 .432 .079 -.368 .333 DM_MLM3 -.379 .382 .092 -.162 .319 DM_BLI1 -.684 -.489 -.162 -.025 -.212 DM_BLI2 -.645 -.499 -.257 -.179 -.219 DM_BLC -.030 -.659 -.222 -.603 .025 DM_BLP3 .674 .068 -.170 -.003 -.292 DM_BLP4 .299 .132 -.644 -.081 -.353 DM_BLM1 -.705 .402 .088 -.150 -.125 DM_BLM2 -.279 .517 .388 -.282 -.521 DM_BLM3 -.094 .628 .203 -.145 -.019 TABLE 1. PCA loadings (high-magnitude values in boldface) obvious separation, as previously as identified by dental nonmetric (Irish, 1997, 1998a,b, 2005, 2006) and other biocultural findings. The PC loadings in the table provide specifics on TSA. High magni- tude negative PC1 loadings characterize North Africans on the right of the x-axis in Figure 3, i.e., relatively large LI1, and BL-only values for UM1, LI2, and LM1. High positive PC1 loadings for the sub-Saharan samples show a relatively large LP3, MD-only for UI2, and BL-only for UP3 and UM3. The TSA differences on PC2 and PC3 similarly account for sample locations on the y- and z-axes (Figure 3). To utilize information in all five PCs, Ward’s cluster analysis was used to classify sam- ples (Figure 4) based on the factor scores derived from DM_values (Figure 5). Three main clusters are evident in Figure 4: (1) sub-Saharan only, (2) North African only, and (3) North African with four sub-Saharan samples. Interestingly, the latter samples are from regions 41 Fig. 3. Samples plot of first three factor scores. Fig. 4. Ward’s cluster analysis of all five factor scores (showing three main clus- ters as identified in the text). 42 Fig. 5. Average MD and BL DM-values in upper and lower jaws. 43 Fig. 6. Samples plot of first three factor scores for North Africans only. in the proximity of “northern” peoples (e.g., Soma- lia) -- which may reflect evidence of admixture. Finally, to demonstrate that TSA analysis can be applied on a regional scale as well, just the 18 North African samples were compared. Figure 6 illustrates that, even at this finer-grained level of study, some differentiation among the Nubian, Egyptian, and Maghreb samples is possible. In other words, the results presented here indicate that an “old” method and basic crown diameter data can be successfully used for affinity estima- tion, if overall size is accounted for and “shape” is considered. Thus, (relative) size does matter. ACKNOWLEDGMENTS We thank Heather Edgar, Helen Liversidge, and Loren Lease for the invitation to the AAPA sym- posium in honor of Edward Harris. Thanks also go to everybody at the institutions from which JDI collected the data. Funding was provided to JDI by the National Science Foundation (BNS- 0104731), Wenner-Gren Foundation (#7557), Na- tional Geographic Society (#8116-06), Institute for Bioarchaeology, ASU Research Development Pro- gram, Hierakonpolis Expedition, and American Museum of Natural History. LITERATURE CITED Darroch JN, Mosimann JE. 1985. Canonical and principal components of shape. Biometrika 72:241-252. Harris EF. 1997. A strategy for compareing odon tometrics among groups. Dent Anthropol 12:1- 6. Harris EF, Bailit HL. 1988. A principal components analysis of human odontometrics. Am J Phys Anthropol. 75:87-99. Harris EF, Rathbun TA. 1991. Ethnic differences in the apportionment of tooth sizes. In: Kelley MA, 44 Larsen CS, editors. 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