Size does matter : Variation in tooth size apportionment among major regional North and sub-Saharan African populations

In the 1980s Edward Harris proposed 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 multiple 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 measurements 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 diameters of the UM2 and LM1, and BL diameters of the LM2 and LM3. Comparisons of North Africans only show the ability to distinguish among samples 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


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.Nonmetric findings in these same samples support a known biocultural dichotomy between populations living north and south of the Sahara (Irish, 1997(Irish, , 1998a(Irish, ,b, 2005(Irish, , 2006)).The names (incl.abbreviations in Figs. 3 and 6), composition, and origins of these 30 samples are presented in the aforementioned publications.Their approximate geographic locations are plotted in Figure 1.

METHODS
Following Harris' [and Hemphill's (1991)] approach, 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.

ABSTRACT
In the 1980s Edward Harris proposed 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 measurementswhich 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 multiple 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 diameters of the UM2 and LM1, and BL diameters of the LM2 and LM3.Comparisons of North Africans only show the ability to distinguish among samples 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 (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 values were then submitted to PCA, to yield unrotated PC loadings and factor scores.

RESULTS AND DISCUSSION
To illustrate the effectiveness of DM size correction, 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    obvious separation, as previously as identified by dental nonmetric (Irish, 1997(Irish, , 1998a(Irish, ,b, 2005(Irish, , 2006) ) and other biocultural findings.The PC loadings in the table provide specifics on TSA.High magnitude 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 samples (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    in the proximity of "northern" peoples (e.g., Somalia) --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 estimation, if overall size is accounted for and "shape" is considered.Thus, (relative) size does matter.

Fig. 4 .
Fig. 4. Ward's cluster analysis of all five factor scores (showing three main clusters as identified in the text).

Fig. 5 .
Fig. 5. Average MD and BL DM-values in upper and lower jaws.

Fig. 6 .
Fig. 6.Samples plot of first three factor scores for North Africans only.
Irish 1 and Michael W. Kenyhercz 2 1 Research Centre in Evolutionary Anthropology and Palaeoecology, Liverpool John Moores University 2 Department of Anthropology, University of Alaska, Fairbanks, AK 99775-7720