Introduction and background

The shape and size of dental arches vary considerably among human populations. Previous studies have described several dental arch shapes, including square, ovoid, and triangular shapes ⁽¹ - being the ovoid shape the most prevalent, accounting for approximately 75% of cases². This pattern has also been observed in the populations that contributed to Chile’s admixed ancestry ^(3-5. Regarding dental arch shapes in European populations, and using preformed templates Ferro et al. ⁽⁵, found a similar distribution (a higher frequency) of ovoid (46.2%) and narrow (43.4%) arches, while the square shape was the least common (10.4%) ⁽⁵. Likewise, Park et al. ⁽⁶⁾ classified arch shapes in young Asian adults, finding that the most common configuration in both the maxilla and mandible was ovoid (52% and 56%, respectively), followed by triangular (28% in both) and square (20% in the maxilla, and 16% in the mandible) ⁽⁶. In a study of Indigenous communities in the Colombian Amazon, Rivera et al. ⁽³ reported a predominance of ovoid arches in both the upper (86%) and lower (75%) arches, with square forms found in 14% and 25% of the cases, respectively, and no triangular arches observed ⁽³.

In comparative studies across ancestral backgrounds, Burris and Harris ⁽⁷ found that African American individuals exhibited more square-shaped maxillary arches, while Euro-descendants showed narrower and more rounded arches ⁽⁷. Similarly, Agurto and Sandoval ⁽⁴, using preformed templates, evaluated the maxillary and mandibular arch shapes of Mapuche and non-Mapuche children in Chile. They found a higher proportion of square arches in the Mapuche group, both in the maxilla and mandible, although the predominant shape in both groups was ovoid ⁽⁴. Only two of the five studies reviewed reported having analyzed the upper jaw using templates-a method that introduces significant subjectivity in shape classification ^{(4, 5)}. Despite the considerable number of studies characterizing dental arch shapes across populations with different ancestries, no study to date has simultaneously compared dental arch morphology in admixed-ancestry populations against their ancestral European and Amerindian groups. From a methodological standpoint, Arai and Will⁸ assessed inter-examiner reliability in the subjective classification of mandibular arch shapes among orthodontic patients into three categories-narrow, ovoid, and square-and found high agreement for extreme shapes (triangular and square), but greater variability for the intermediate (ovoid) shape⁸.

While previous research highlights the relevance of considering ancestry in dental arch shape for the diagnosis and planning of dental and orthodontic treatments, further studies are needed to explore differences in dental arch shape among different populations-particularly of Amerindian, European, and admixed ancestry-in a more objective way. This would help determine if specific differences in dental arch shape exist among these groups, and whether these differences may have clinical implications for the diagnosis and planning of individualized orthodontic treatment.

This study aims to compare the shape and size of dental arches among Amerindian, admixed Chilean, and Euro-descendant populations from both Chile and the United States, in order to understand how ancestral traits are expressed in admixed dental phenotypes, using standard geometric morphometric tools. These techniques allow for a more accurate and comprehensive capture of structural geometry compared to traditional methods based on linear measurements, which only provide information on differences in magnitude or size (i.e., scalar components of morphological variation in a single dimension), or by assigning pre-established shapes to individual cases (i.e., ovoid, square, or triangular templates). Moreover, geometric morphometrics not only enables statistical analysis of shape variation patterns but it also allows for visualizing these changes through the superimposition of Cartesian grids according to the thin-plate spline function. Thus, a recent publication from our laboratory using this approach to study mandibular dental arch variation in the admixed population of the Metropolitan Region of Chile found that the shape of the dental arch is expressed with such continuity that it challenges the assumption of fixed, pre-existing shapes (i.e., "square," "ovoid," or "triangular") ¹¹.

According to our null hypothesis, the shape and/or size of the dental arches in the Chilean admixed population is intermediate between those of the ancestral populations from which it originates.

Methods

An analytical, cross-sectional observational study was conducted to compare the shape and size of dental arches among individuals of different ancestries. The Amerindian ancestry group consisted of samples from pre-Columbian populations from the South-Central Andes and Central, Southern, and Far Southern Chile, whose archaeological sites span a time range from 7,500 years ago (Chinchorro culture) to the time of Spanish contact. These materials are housed at the Center for Quantitative Analysis in Dental Anthropology of the Faculty of Dentistry, University of Chile, and are represented by a collection of anatomically standardized photographs of crania , recorded in the field by GM and AD between 2008 and 2014 at the Corporation of Culture and Tourism of Calama (Chile), the R. P. Gustavo Le Paige Museum (Universidad Católica del Norte, Arica, Chile), the National Museum of Natural History (Santiago, Chile), and the Musée de l’Homme (Muséum national d’Histoire naturelle, Paris, France). The admixed sample consisted of photographs of dental models obtained from alginate impressions, from anonymized donations by patients of the Dental Clinic at the Faculty of Dentistry, University of Chile. Finally, the Euro-descendant population was represented by: (i) anatomically standardized photographs of dental models from alginate impressions of patients with one or two German surnames, treated at a private clinic in the east of Santiago city (Lo Barnechea municipality), where, according to data from the Chilegenomic Project, the population has an average European ancestry of 80.3%, compared to 54.1% in the north of Santiago (Independencia municipality), where the University of Chile’s Dental Clinic is located (http://genoma.med.uchile.cl/ancestry); and (ii) standardized photographs of 3D models of white patients from Michigan and Oregon, United States, available from the American Association of Orthodontists Foundation (AAOF) Craniofacial Growth Legacy Collections Project (https://www.aaoflegacycollection.org/aaof_home.html). According to Bryc et al. (2015), Caucasian individuals in the U.S. have an average European ancestry of 98.6%, verified by analysis of autosomal single nucleotide polymorphisms (SNPs) ¹². Inclusion criteria required individuals to have a complete dentition from the upper right to left second molars. The final sample included 53 Amerindian individuals, 118 admixed , and 101 Euro-descendant individuals (see Table 1 for summary; details in Table S1).

Millimeter-scaled photographs were used as material for both the pre-Columbian skulls and the plaster dental models of admixed and Euro-descendant individuals. To record the dental arch shape, a map of 18 homologous landmarks (Table 2, Figure 1) with the tpsDig 2.32 software¹³. In the context of geometric morphometrics, according to Zelditch et al., a landmark is a discrete anatomical point that can be consistently identified in all studied individuals, regardless of ancestry or population group. ¹⁴

The input data for geometric morphometrics consisted of the projection of each landmark onto an xy-plane, resulting in a pair of coordinates per landmark. Each individual was represented by a matrix with 18 rows (one per landmark) and 2 columns (one for the x-axis and one for the y-axis projection). These matrices-or landmark coordinate configurations-were processed and analyzed using the Morpho-J 1.08.01¹⁵⁾ and R Studio¹⁶ softwares, applying standard geometric morphometric tools¹⁴.

A generalized least squares analysis, or Procrustes analysis, was performed using the Morpho-J⁽ program¹⁵⁾. This consists of removing differences in rotation, translation, and scale from each matrix, yielding two components of morphometric variation: i) centroid size, calculated as the square root of the sum of distances from each landmark to the centroid of the configuration (a size variation estimator), and ii) shape space or Kendall space, consisting of the coordinate configurations of each individual’s dental arch, separated by an angular distance measured in radians, known as Procrustes distance. These configurations were then projected as points onto a plane tangent to shape space, defined by the first two principal components (PCs) resulting from a Principal Component Analysis (PCA). This analysis belongs to the family of multivariate factorial statistics, which reduce the original variables (in this case, the landmark configurations) into new variables or components that represent the total variance in hierarchical, decreasing percentage form (%PC1 > %PC2 > … %PCn) (see Fig. 2 in the Results section). In geometric morphometrics, the variables used to test the hypotheses regarding shape variation are the coordinates obtained by projecting each point in the PCA space onto its respective axis or PC scores. The exploratory PCA analysis is complemented by a Discriminant Function Analysis (DFA), which uses the PC scores from the previously performed PCA as input data, allowing us to know the percentage of original observations (individuals) that are assigned to the centroids of their respective groups (i.e. correctly classified) after performing a cross-validation test with a significant number of resamples with 1 replacement at a time (leave-one-out cross-validation or jackknife) (9,999 resamples in our case). This resampling method does not require assumptions of multivariate normality or homogeneity of variance-covariance matrices, as described by Manly (2006)¹⁷, since it relies on randomization and empirical distributions derived directly from the observed data ¹⁷. When classification accuracy exceeds 80% (correct assignments), individuals are considered to belong effectively to the groups to which they were assigned a priori. Otherwise (with values below 80% of correctly classified cases), individuals originally assigned to different groups are considered, in practice, to constitute a single group. The input data for performing the DFA with cross-validation were the PC scores obtained in Morpho-J, while the DFA itself was performed in the PAST program¹⁸. In turn, the data that reveal the pattern of size variation are the respective centroid sizes of each individual. As these are scalar values, a one-way ANOVA was applied or, when appropriate, its non-parametric equivalent, the Kruskal-Wallis test. In both cases, to determine the relative contribution of each group of observations to the final result, a Dunn post-hoc test was carried out, providing Bonferroni-corrected p-values for each pairwise comparison. This final set of analyses was conducted in the integrated R Studio environment¹⁶, using the “car”¹⁹⁾ package for hypothesis testing, “ggplot2”²⁰ for data visualization, and “dunn.test”²¹ for the Dunn test.

Results

Analysis of the shape components: The analysis of the shape components or principal components (PCA) showed a high degree of overlap between Euro-descendant individuals and those belonging to Chile's admixed population, but not for Amerindian individuals, who were substantially separated from the rest with respect to the second shape component (PC2) (Figure 2). The first two shape components explained 66.2% of the total variance.

In this morphometric space, Amerindian individuals presented arch shapes ranging from ovoid to square, while Euro-descendant individuals tended to exhibit more triangular shapes. The admixed population, in turn, displayed intermediate shapes between ovoid and triangular (Figure 3).

On the other hand, discriminant function analyses with replacement resampling revealed high accuracy in distinguishing Amerindian individuals from both Euro-descendant and admixed individuals (Table 3).

The percentages of individuals from the known groups (listed in the first column) assigned to each group (listed in the first row) are shown. For correct interpretation, this table should be read by rows.

The same cross-validation technique was applied to determine the position of the Euro-descendants from the private clinic in Santiago within the morphometric space occupied by Euro-descendants from the United States. In this case, classification accuracy was very low, confirming that the three samples of Euro-descendants do not exhibit substantial differences in dental arch shape and therefore constitute a single group (Table 4).

Centroid size analysis: Individuals of Amerindian ancestry exhibited the largest mean centroid size (126.50 ± 18.36 mm), followed by those of admixed ancestry (117.32 ± 8.58 mm) and European ancestry (108.03 ± 7.10 mm). The Kruskal-Wallis test (H = 80.28, p = 3.694e-18) and Dunn's post-hoc test with Bonferroni correction revealed statistically significant differences between Amerindian and Euro-descendant individuals (p = 5.704e-15), and between admixed and Euro-descendant individuals (p = 2.488e-12), but not between admixed and Amerindian individuals (p = 0.067) (Figure 4).

Finally, the analysis of the effect of allometry (i.e., the effect of centroid size on the shape component with the highest variance, PC1) yielded non-significant Pearson correlation coefficients for both Amerindian (r = 0.059, p = 0.671) and admixed individuals (r = -0.139, p = 0.135). The absence of an allometric effect indicates that variation in size is not influencing the pattern of variation in the dental arch shape component in these populations. In the case of the Euro-descendant sample, although an allometric effect was observed, it was expressed with low intensity (r = -0.197, p = 0.048).

Discussion

The main finding of our study is that the dental arch shape of individuals from Chile’s admixed population does not differ significantly from that of Euro-descendant individuals, whereas the dental arch shape of individuals of Amerindian ancestry differs significantly from both the admixed and the Euro-descendant populations, being more square than in the latter two groups. This result is consistent with previous reports in the literature, as observed in populations of Amazonian Indigenous ancestry ⁽³, and with the higher proportion of square arches found in the Mapuche population compared to the non-Mapuche population in Chile ⁴. Finally, in Euro-descendant individuals, the predominant similarity to triangular shapes aligns with what has been observed in previous studies conducted in both the United States and Italy ^{(5, 7)}.

Additionally, our study confirms the results recently reported by Vidaurre et al. (2024), which demonstrate the existence of a continuous spectrum of arch shapes, with clear areas of overlap between them ¹¹. This result, along with ours, has important clinical implications, as it suggests that commercially available preformed arches do not reflect the observed variability and therefore do not conform to the dimensions and shapes of dental arches that naturally occur across different populations-especially when ancestry is taken into account. Several studies illustrate this issue. For example, Oda et al. ⁽²², in their analysis of the mandibular arch in a Japanese population, found that preformed arches were significantly narrower than natural dental arches. Similarly, Ahmed et al. ⁽²³, also focusing on the mandibular arch, reported in a sample from Pakistan that no commercial arch fully matched the natural arch dimensions of individuals. Lombardo et al. ²⁴, analyzing both the maxillary and mandibular arches, reached similar conclusions in a study of a population in Italy, while Mughal et al. ⁽²⁵, who evaluated both arches, warned against the use of overly wide arches in Pakistani patients due to the risk of post-treatment instability. These findings reinforce the notion that prefabricated commercial arches do not represent the true anatomical variability of this structure.

As for the dental arch size, in the admixed population it does not differ significantly from the size observed in Amerindian individuals, with both being larger than that of Euro-descendant individuals. This finding is consistent with previous studies documenting that populations from the Americas (Amerindian and admixed) and the Arctic (Aleuts and Eskimos) tend to have larger teeth than European populations ⁽²⁶. The absence of statistically significant differences in centroid size between Amerindians and the admixed population in our sample is consistent with the larger tooth size reported in the Americas, while the smaller centroid size in the dental arches of Eurodescendant individuals aligns with the smaller tooth size documented in European populations ²⁶.

Finally, although the potential forensic application of differences in dental arch shape in relation to population ancestry is not the focus of this research, it is a topic of justified interest given the need for highly effective, specific, and reproducible markers for use in forensic identification across a variety of contexts-from determining the vitality of wounds on a corpse (i.e., whether they were inflicted during life or post-mortem) ²⁷, to predicting a person’s visible external characteristics, particularly the face, through DNA phenotyping ⁽²⁸. In this context, and despite the substantial advances in forensic techniques in recent decades ²⁹, the challenge of identifying intermediate phenotypic traits-those found in most populations-remains. Taking this background into account, and given the continuous nature of the pattern of variation in dental arch shape (this study), it is clearly not advisable to use this phenotype for forensic identification purposes, at least in Chile’s admixed population and, by extension, in other Latin American populations.

Although comparisons among studies may be limited due to methodological differences, our work contributes to characterizing the shape and size of dental arches in an admixed sample (i.e., composed of two or more ancestries) and comparing them with populations of other ancestries-an aspect rarely addressed in the literature, with the exception of Agurto and Sandoval ⁽⁴. Furthermore, we applied geometric morphometrics, a technique that is more accurate and efficient than traditional methods for capturing biological complexity ^{(9, 10)}. Its use in the analysis of dental arch shape variation by ancestry, thus it represents a novel and promising approach.

One limitation of this study is the lack of age information available for the pre-Columbian individuals. This is relevant because dental arch shape can still change after the eruption of the second permanent upper molar at around age 12 ⁽³⁰. However, given that such shape variation does not occur beyond age 15, and considering that over 90% of the individuals in our sample are older adults, this factor does not affect the results obtained.

We hope this study contributes to a better understanding of human morphological diversity and encourages new interdisciplinary approaches to the study of admixing in Chile, taking into account the potential impact of ancestry on orthodontic treatment outcomes.

Conclusions

The Chilean admixed population exhibits a dental arch shape that does not differ significantly from that of Euro-descendant individuals, and a size similar to that of Amerindian individuals.