Genetic Influences on Dentognathic Morphology in the Jirel population of Nepal

Abstract

Patterns of genetic variation and covariation impact the evolution of the craniofacial complex and contribute to clinically significant malocclusions in modern human populations. Previous quantitative genetic studies have estimated the heritabilities and genetic correlations of skeletal and dental traits in humans and non-human primates, but none have estimated these quantitative genetic parameters across the dentognathic complex. A large and powerful pedigree from the Jirel population of Nepal was leveraged to estimate heritabilities and genetic correlations in 62 maxillary and mandibular arch dimensions, incisor and canine lengths, and post-canine tooth crown areas (N ≥ 739). Quantitative genetic parameter estimation was performed using maximum likelihood-based variance decomposition. Residual heritability estimates were significant for all traits, ranging from 0.269 to 0.898. Genetic correlations were positive for all trait pairs. Principal components analyses of the phenotypic and genetic correlation matrices indicate an overall size effect across all measurements on the first principal component. Additional principal components demonstrate positive relationships between post-canine tooth crown areas and arch lengths and negative relationships between post-canine tooth crown areas and arch widths, and between arch lengths and arch widths. Based on these findings, morphological variation in the human dentognathic complex may be constrained by genetic relationships between dental dimensions and arch lengths, with weaker genetic correlations between these traits and arch widths allowing for variation in arch shape. The patterns identified are expected to have impacted the evolution of the dentognathic complex and its genetic architecture as well as the prevalence of dental crowding in modern human populations.

Introduction

Developmental, functional, and morphological relationships in the human dentognathic complex have been subject to decades of examination (Brown, Abbott, & Burgess, 1983, 1987; Buschang, 2002; Daegling & Hylander, 2000; Dahlberg, 1945; Evans et al., 2016; Gingerich, 1979; Helms & Schneider, 2003; Hylander, 1975, 1978; Knoell, 1977; Lavelle, Flinn, Foster, & Hamilton, 1970; Moss & Simon, 1968; Schroer & Wood, 2015; van Eijden, 2000). There remain, however, significant gaps in knowledge regarding the genetic influences on human dentognathic morphological variation. Functionally, efficient mastication depends upon morphological coordination between the maxillary and mandibular arches and the teeth they support (English et al., 2002; Henrikson et al., 1998; Tate et al., 1994; Toro et al., 2006). Genetic pleiotropy is considered an important contributor to this functional morphological integration (Klingenberg, 2014; Lande & Arnold, 1983). Quantitative genetic methods provide an important bridge between the phenotype and genotype to further the study of dental and craniofacial morphological evolution in humans and non-human primates (Cramon-Taubadel, 2019; Hlusko et al., 2016). In this study, we assess the evolutionary and clinical implications of genetic correlations in the human dentognathic complex via a quantitative genetic framework to tooth and dental arch measurements in the Jirel population of Nepal.

Role of integration in human craniofacial evolution

The human skull is an integrated structure derived from multiple embryological tissue types to serve diverse functions. The skull can be subdivided into theoretically- or empirically-derived developmental, structural or functional components, and close developmental, structural, and genetic relationships among these components can constrain evolutionary change in the skull (e.g., Moss & Young, 1960; Porto et al., 2009).

Genetic, developmental and functional relationships between skeletal and dental components of the masticatory apparatus factor into hypotheses of hominin craniofacial evolution. The modern human dental arcade is morphologically distinct from that of other extant hominoids (Stelzer et al., 2017), and arcade shape varies considerably among fossil hominins (Greenfield, 1992; Johanson & White, 1979; Kimbel & Delezene, 2009; Spoor et al., 2015; Suwa et al., 2009; Ward & Walker, 2001). Humans demonstrate less morphological covariation between the upper and lower jaws than is observed in extant apes (Marroig et al., 2009; Porto et al., 2009; Stelzer et al., 2017). The prevalence of dental crowding in modern human populations has been associated with reduced covariance between arch size and tooth size (Corruccini, 1984; Lieberman et al., 2004), and is often attributed to strong genetic regulation of tooth size and environmental effects on arch and jaw size over the course of development.

Recent studies have made great strides in identifying the genetic underpinnings of dental development and morphogenesis in a variety of animal models (e.g., Albertson & Yelick 2004; Jernvall et al. 1994; Jernvall & Jung 2000; Jernvall & Thesleff 2000; Mahaney et al. 2004; Stock et al. 1996; 1997; Vaahtokari et al. 1996; Weiss et al. 1994; 1998; Zhao et al. 2000). Evidence has indicated that cross-signaling between dental and jaw tissues contributes to the development of the dentognathic complex, and genes including Bmp4, Shh, Msx1, and Fgf8 are involved in both odontogenesis and jaw formation (Cobourne and Sharpe, 2003). Yet evolutionary, developmental, and molecular studies have also demonstrated a degree of independence between tooth and jaw formation (Boughner and Hallgrimsson, 2008). For example, p63 is essential for both dental and upper jaw development but not lower jaw development (Raj and Boughner, 2016; Phen et al., 2018). The co-occurrence of orofacial clefting and tooth agenesis also demonstrates the co-dependence of some aspects of jaw and tooth genetic regulation and development (Phan et al., 2016). Further study of the genetic covariance between dental traits and aspects of jaw morphology in humans and non-human primates is nevertheless needed to understand how change in the genetic covariance structure of the dentognathic complex has impacted its morphological evolution.

Evolutionary quantitative genetics of the primate dentognathic complex

Quantitative genetics enables the decomposition of phenotypic variance and covariance into its genetically- and environmentally-derived components. One central parameter of quantitative genetics is the heritability (h²) of a trait, which is proportional to the generational response to selection in a population (Lush, 1937). Previous quantitative genetic analyses of craniofacial and dental morphology in humans and non-human primates demonstrate moderate to high heritability estimates in dental and skeletal features, with population- and species-level variation in the degree of genetic integration and modularity (baboons: Hlusko, Do, & Mahaney, 2007; Hlusko, Lease, & Mahaney, 2006; Hlusko, Sage, & Mahaney, 2011; Hlusko, Suwa, Kono, & Mahaney, 2004; Hlusko, Weiss, & Mahaney, 2002; Hlusko & Mahaney, 2003, 2009; Joganic et al., 2018, 2012; Koh et al., 2010; Sherwood et al., 2008; Sherwood & McNulty, 2011; humans: Alvesalo & Tigerstedt, 1974; Hughes et al., 2014; Paul et al., 2020; Šešelj et al., 2015; Sherwood et al., 2008; Stojanowski et al., 2018, 2019; Švalkauskien & Šalomskien, 2015; Townsend et al., 2009; macaques: Cheverud & Buikstra, 1981; Hardin, 2019a, 2020; Joganic et al., 2012; tamarins: Cheverud, 1996; Hardin, 2019b).

The multivariate extension of the breeder’s equation (Lush, 1937) states that traits influenced by the same genes through pleiotropy or linked through epistasis may respond indirectly to selection pressures on traits with which they are genetically correlated (Lande, 1979; Lande & Arnold, 1983). These genetic correlations contribute to genetic and phenotypic modularity in suites of traits. Most of the studies above have utilized the concept of variational modularity, which defines a module as a suite of traits that are internally closely integrated and weakly integrated with other external traits (Wagner & Altenberg, 1996). High degrees of modularity, with greater independence among suites of traits, are theorized to reduce evolutionary constraint and thereby increase evolvability (Klingenberg, 2014; Wagner & Altenberg, 1996; Wagner, Pavlicev, & Cheverud, 2007).

Genetic modularity by tooth type in mice and baboons, for example, is thought to represent an ancestral state that reduced constraint on the evolution of the heterodont mammalian dentition (Hlusko et al., 2011). A similar genetic correlation structure has also been observed in rhesus macaques (Hardin, 2020), yet stronger genetic correlations between tooth types have been observed in some primate populations, including humans (Stojanowski et al., 2017) and brown-mantled tamarins (Hardin, 2019b). These findings demonstrate variation in the genetic modularity of the dentition across primate species with distinct evolutionary histories, including expansion of the canine-premolar honing complex in baboons and macaques, re-organization of the craniofacial complex in hominins, and body size reduction in callitrichines.

Quantitative genetic studies of the human face and dentition

Previous quantitative genetic studies of human facial traits have included soft tissue and skeletal features, traditional cephalometrics and landmark-based methods, and a variety of methodological designs and analyses including twin studies, genome wide association studies (GWAS), quantitative trait loci (QTL) mapping, and pedigree-based estimation of parameters (e.g., Alvesalo & Tigerstedt, 1974; Baydaş, Erdem, Yavuz, & Ceylan, 2007; Brito et al., 2011; Carels et al., 2001; Claes & Shriver, 2016; Cole et al., 2016, 2017; Crouch et al., 2018; Martínez-Abadías et al., 2009; Šešelj et al., 2015; Sherwood et al., 2008, 2011; Weinberg, Parsons, Marazita, & Maher, 2013). These studies have found moderate to high heritability estimates throughout the face, with several studies finding especially high heritability estimates in the orbital and nasal regions relative to other facial regions (Carson, 2006; Cole et al., 2017; Kim et al., 2013; Martínez-Abadías et al., 2009; Tsagkrasoulis et al., 2017). Studies of human dental dimensions also indicate high heritability estimates across tooth types (Dempsey & Townsend, 2001; Hughes et al., 2014; Paul et al., 2020; Stojanowski et al., 2017; Townsend et al., 2009). A smaller set of studies have estimated genetic correlations between human craniofacial traits, finding positive genetic correlations in some regions of the skull (Martínez-Abadías et al., 2009; Sherwood et al., 2008) and, in one study, negative correlations between horizontal and vertical measurements (Cole et al., 2017).

Quantitative genetic studies including both dental and skeletal measurements from a human population are rare; previous examples used phenotypic data collected from lateral cephalographs to estimate heritability but not genetic correlations (Carels et al., 2001; Johannsdottir et al., 2005), although dental variables included in these studies measured the orientations and positions of teeth relative to cephalometric planes rather than the size of the tooth crown. The combined quantitative genetic analyses of dental and arch measurements presented here allows us to assess genetic correlations between functionally related, yet developmentally distinct components of the human dentognathic complex.

The Jiri Dental Study

Here, we present the results of quantitative genetic analyses of maxillary and mandibular arch and tooth dimensions from the Jirel population of eastern Nepal. Previous quantitative genetic studies have contributed greatly to the study of genetic patterning in the mammalian dentition, yet none have examined genetic correlations between craniofacial and dental traits. This is due, in part, to significant barriers to effective quantitative genetic evaluation of dentognathic trait covariation, namely the requirement of complex pedigrees associated with large phenotypic datasets. The Jirel pedigree, established through the Jiri Helminth Project (Williams-Blangero & Blangero, 1989, 1990; Williams-Blangero et al., 1998), is one of the most powerful documented human pedigrees currently available for study. The Jiri Dental Study was established to leverage the resources from previous studies of the Jirel population and extend the research into dental and skeletal health.

We used the Jirel pedigree data and measurements collected through the Jiri Dental Study to estimate the heritabilities of and genetic correlations between dimensions of the dentition and dental arch. We predicted that 1) dental measurements would be highly heritable and closely genetically correlated across tooth types; 2) heritabilities would be greater in dental measurements than in arch measurements; and 3) genetic correlations would be stronger within dental or arch measurements than between dental and arch measurements.

Materials and Methods

Study population

Members of the Jirel ethnic group, a Tibeto-Burman language speaking group, live in the Jiri region of the Dolakha district (Blangero, 1987). Long-term study of the Jirel population began in 1985 and has produced a powerful extended pedigree containing over 62,000 pairwise relationships that are informative for quantitative genetic analysis (Williams-Blangero & Blangero, 2006). The Jirel population is especially well-suited to quantitative genetic study because a large proportion of the population can be found in the restricted geographic area of the Jiri region (Williams-Blangero et al., 2002). The use of extended, multiple household pedigrees allows for discrimination between genetic and shared environmental effects and thereby produces less biased estimates of heritability and genetic correlation than those produced by other pedigree structures. Pairwise biological relationships present in the sample are provided (Table 1).

Table 1.

Major pairwise relationships among members of the Jirel pedigree.

Parent-offspring	2,388
Siblings	1,997
Grandparent-grandchild	1,114
Avuncular	3,426
Half-siblings	248
Double 1st cousins	52
Third degree	8,317
Fourth degree	11,071
Fifth degree	14,443
Sixth degree	10,172
Seventh degree	7,032
Eight degree	1,733
Ninth degree	193
Total	62,186

Dental impressions were collected from 994 individuals (420 males, 574 females) of the Jirel population through the Jiri Dental Study, established in 2009. Individuals ranged from 18 to 76 years of age, with a mean age of 37.3 years of age. Individuals included in the study had no history of orthodontic or dental treatment excluding dental extractions. Following dental examination and cleaning performed by a local dentist, dental impressions were collected using vinylpolysiloxane impression materials (VP Mix Putty and VP Mix HP, Henry Schein, Melville NY). Dental impressions were transported to the United States and casts were made using Epo-tek 301 epoxy (Epoxy Technology) tinted with brown pigment. All protocols and procedures were approved by the Wright State University Institutional Review Board and the Nepal Health Research Council, Kathmandu, Nepal.

Measurements

High-resolution images of each dental cast were collected using a Canon EOS 20-D (Canon USA, Lake Success, NY) digital camera equipped with a 50 mm macro lens. To maximize contrast, dental casts were placed in shallow trays of blue sand to a depth at which tooth crowns, but not gums, were visible. Images of dental casts were imported to the semi-automated Dental Cast Analysis Program (DCAP) implemented in Matlab (Mathworks v.2011b) (Thomas, 2011). Within DCAP, landmarks were manually placed at the mesial-, distal-, buccal-, and lingual-most points of each tooth crown. Based on these landmarks, 34 curvilinear and linear measures of arch length, depth, and width and 12 mesio-distal incisor and canine lengths were automatically collected by DCAP (Table 2, Figure 1). The boundaries of each tooth were automatically detected using the watershed function in MATLAB and the surface area of each premolar and molar crown, excluding third molars, was measured as the projected area in pixels within the automatically-detected boundaries of the tooth crown, resulting in 16 crown area measurements (Table 2). Automatically collected measurements were checked and manually adjusted as needed. Crown areas were collected from worn teeth, but not from those with broken enamel. Teeth with wear that could potentially impact the reliability of measurement were excluded from data collection. Analyses were performed on measurements from 935 of the original 994 individuals without incidence of microdontia, supernumerary teeth, or other dental anomalies.

Table 2.

Full descriptions, abbreviations, and shorthand descriptions of all measurements.

Description	Abbreviation	Shorthand
Full Arch Widths
Distance from lingual margin of left P3 to lingual margin of right P3	lrup3w	Palate width at P3
Distance from lingual margin of left P4 to lingual margin of right P4	lrup4w	Palate width at P4
Distance from lingual margin of left M1 to lingual margin of right M1	lrum1w	Palate width at M1
Distance from lingual margin of left M2 to lingual margin of right M2	lrum2w	Palate width at M2
Distance from lingual margin of left P3 to lingual margin of right P3	lrlp3w	Palate width at P3
Distance from lingual margin of left P4 to lingual margin of right P4	lrlp4w	Palate width at P4
Distance from lingual margin of left M1 to lingual margin of right M1	lrlm1w	Palate width at M1
Distance from lingual margin of left M2 to lingual margin of right M2	lrlm2w	Palate width at M2
Full Arch Lengths
Arch length from distal left M2 to distal right M2	ulfa	Full-arch length at M2
Arch length from distal left M2 to midline	ullha	Half-arch length at left M2
Arch length from distal right M2 to midline	ulrha	Half-arch length at right M2
Arch length from distal left C1 to distal right C1	utcal	Full-arch length at C1
Arch length from distal left P4 to distal right P4	utmal	Full-arch length at P4
Arch length from distal left M2 to distal right M2	llfa	Full-arch length at M2
Arch length from distal left M2 to midline	lllha	Half-arch length at left M2
Arch length from distal right M2 to midline	llrha	Half-arch length at right M2
Arch length from distal left C1 to distal right C1	ltcal	Full-arch length at C1
Arch length from distal left P4 to distal right P4	ltmal	Full-arch length at P4
Half Arch Widths and Depths
Distance from distal margin of right C1 to midline perpendicular to midline	urcw	Palate half-width at right C1
Distance from distal margin of left C1 to midline perpendicular to midline	ulcw	Palate half-width at left C1
Distance from mesial-most point to distal margin of right C1 on midline	urch	Palate depth at right C1
Distance from mesial-most point to distal margin of left C1 on midline	ulch	Palate depth at left C1
Distance from distal margin of right C1 to midline perpendicular to midline	lrcw	Palate half-width at right C1
Distance from distal margin of left C1 to midline perpendicular to midline	llcw	Palate half-width at left C1
Distance from mesial-most point to distal margin of right C1 on midline	lrch	Palate depth at right C1
Distance from mesial-most point to distal margin of left C1 on midline	llch	Palate depth at left C1
Distance from distal margin of right M1 to midline perpendicular to midline	urmw	Palate half-width at right M1
Distance from distal margin of left M1 to midline perpendicular to midline	ulmw	Palate half-width at left M1
Distance from mesial-most point to distal margin of right M1 on midline	urmh	Palate depth at right M1
Distance from mesial-most point to distal margin of left M1 on midline	ulmh	Palate depth at left M1
Distance from distal margin of right M1 to midline perpendicular to midline	lrmw	Palate half-width at right M1
Distance from distal margin of left M1 to midline perpendicular to midline	llmw	Palate half-width at left M1
Distance from mesial-most point to distal margin of right M1 on midline	lrmh	Palate depth at right M1
Distance from mesial-most point to distal margin of left M1 on midline	llmh	Palate depth at left M1
Dental Measurements
Right I1 mesiodistal length	rui1md	Right I1 length
Right I2 mesiodistal length	rui2md	Right I2 length
Right C1 mesiodistal length	rucmd	Right C1 length
Right P3 crown area	rup3ca	Right P3 area
Right P4 crown area	rup4ca	Right P4 area
Right M1 crown area	rum1ca	Right M1 area
Right M2 crown area	rum2ca	Right M2 area
Left I1 mesiodistal length	lui1md	Left I1 length
Left I2 mesiodistal length	lui2md	Left I2 length
Left C1 mesiodistal length	lucmd	Left C1 length
Left P3 crown area	lup3ca	Left P3 area
Left P4 crown area	lup4ca	Left P4 area
Left M1 crown area	lum1ca	Left M1 area
Left M2 crown area	lum2ca	Left M2 area
Right I1 mesiodistal length	rli1md	Right I1 length
Right I2 mesiodistal length	rli2md	Right I2 length
Right C1 mesiodistal length	rlcmd	Right C1 length
Right P3 crown area	rlp3ca	Right P3 area
Right P4 crown area	rlp4ca	Right P4 area
Right M1 crown area	rlm1ca	Right M1 area
Right M2 crown area	rlm2ca	Right M2 area
Left I1 mesiodistal length	lli1md	Left I1 length
Left I2 mesiodistal length	lli2md	Left I2 length
Left C1 mesiodistal length	llcmd	Left C1 length
Left P3 crown area	llp3ca	Left P3 area
Left P4 crown area	llp4ca	Left P4 area
Left M1 crown area	llm1ca	Left M1 area
Left M2 crown area	llm2ca	Left M2 area

Figure 1.

Examples of measurements collected from dental casts of the maxilla (A) and mandible (B). LL: left lower; RL: right lower; LU: left upper; RU: right upper; I: incisor; C: canine; P: premolar; M: molar; urcw:palate half-width at right C1; ulch: palate depth at right C1; urmh: palate depth at right M1; ulmw: palate half-width at left M1; lrmw: palate half-width at right M1; llmh: palate depth at left M1; lrch: palate depth at right C1; llcw: palate half-width at left C1.

To assess intraobserver error, measurements were collected from 50 dental casts twice by the same analyst from 50 dental casts, with the second round of data collection occurring approximately 1 month after the first. The percentage error from these repeated measurements ranged from 0.6% to 5.3% for arch measurements, and from 0.0 to 4.7% for dental measurements (see Thomas, 2011 for trait-by-trait error estimates). Interobserver error was also assessed through repeated measurement of eight dental casts by two analysts. The percentage error from these repeated measurements ranged from 0.0% to 8.7% for arch measurements and 0.0% to 5.4% for dental measurements (Thomas, 2011). Interobserver measurement error was greater for molar breadths and lengths than for molar crown areas, due in part to the impact of tooth rotation, so crown areas were used in subsequent analyses.

Phenotypic analyses

Phenotypic correlations accounting for the effects of age, sex, age² (age-squared), and their interactions (sex by age, sex by age²) and kinship were estimated in the open-source software package SOLAR (Almasy & Blangero, 1998). Principal components analyses of the full phenotypic correlation matrix (x = 62), the dental phenotypic correlation matrix (x = 28) and the arch phenotypic correlation matrix (x = 34) were performed using the eigen function in R Version 3.6.1. Eigenvalues and loadings for principal components accounting for at least 5% of the total variance were examined and compared to those from the principal components of the genetic correlation matrices. This 5% cutoff was chosen a priori to ensure that only those principal components with the greatest explanatory power were interpreted.

Quantitative genetic analyses

Quantitative genetic analyses were performed to estimate the narrow-sense heritability (h²) for each trait and the genetic correlation (ρ_G) for each pair of traits. For all 62 measurements, h² was estimated using a maximum likelihood-based variance decomposition approach in SOLAR (Almasy & Blangero, 1998). Prior to analyses, an inverse Gaussian transformation was applied to each measurement to correct for deviations from multivariate normality. Environmental contributions to ${\sigma }_P^2$ associated with age, sex, age², and their interactions (sex by age, sex by age²) were removed, resulting in the residual phenotypic variance (${\sigma }_{Pr}^2$). Residual h² ($h_r^2$) values were estimated for trait x as:

$$h_{xr}^2={\sigma }_{Ax}^2/{\sigma }_{Pxr}^2$$

The total phenotypic variance (${\sigma }_{Pt}^2$), including the effects of age and sex covariates and their interactions, was used to estimate the total h² ($h_t^2$) for trait x as:

$$h_{xt}^2={\sigma }_{Ax}^2/{\sigma }_{Px}^2$$

Bivariate analyses were performed in SOLAR to estimate ρ_G for every pair of traits, providing a measure of the degree to which genetic contributions to the two traits are shared through pleiotropy and, to a lesser degree, epistasis. During estimation of ρ_G, environmental and genetic contributions to phenotypic correlations (ρ_P) between traits x and y were modeled such that:

$${\rho }_P={\rho }_G\left(\sqrt{h_{xr}^2}\sqrt{h_{yr}^2}\right)+{\rho }_E\left(\sqrt{1-h_{xr}^2}\sqrt{1-h_{yr}^2}\right)$$

where ρ_E is the environmental correlation. Bivariate analyses produced ρ_G estimates for 1,891 pairs of traits.

The genetic correlation matrix was decomposed to reduce those 1,891 ρ_G estimates to principal components from which patterns could be more easily identified. Principal components analyses of the full genetic correlation matrix (x = 62), as well as matrices comprising only correlations between dental traits (x = 28) and only correlations between arch measures (x = 34), were performed using the eigen function in R Version 3.6.1. The first principal component or dominant eigenvector of the genetic variance-covariance matrix (G matrix) theoretically represents the genetic line of least resistance to evolutionary change (Schluter, 1996), also described as the direction of maximal response to selection (Adams, 2011; Klingenberg, Debat, & Roff, 2010; Klingenberg & Leamy, 2001). The first principal component of the genetic correlation matrix does not necessarily carry the same theoretical meaning as the first principal component of the G matrix, and, in this study, principal components analyses serve primarily to improve the interpretability of the findings. Eigenvalues and loadings for principal components accounting for at least 5% of the total variance were examined for each of the three genetic correlation matrices.

Results

Phenotypic analyses

Phenotypic distributions of age and the 62 measurements collected from 935 individuals are illustrated by sex (Figure 2). Male and female distributions tend to overlap, yet mean female trait values are smaller on average than mean male trait values for all measurements.

Figure 2.

Density plots for all measurements and age by sex

Phenotypic correlations across all traits are positive, and principal components of the full phenotypic correlation matrix demonstrate distinct relationships between arch depths, tooth size, and arch widths. The first principal component of the full phenotypic correlation matrix accounts for 47.5% of the total variance. Loadings on PC1 are similar across all measurements, ranging from −0.066 to −0.152 (Supplementary Table 1). Individuals with larger arch measurements and larger teeth would occupy one end of this axis and individuals with smaller arch measurements and smaller teeth would occupy the other end. The second principal component accounts for 9.7% of the total variance. This axis represents variation in arch dimensions and post-canine tooth crown areas, with arch widths loading most positively and arch lengths and post-canine crown areas loading most negatively on PC2. Deep yet narrow arches and large post-canine tooth crown areas would occupy one end of the axis and individuals with short, wide arches and small post-canine tooth crown areas would occupy the other end. The third principal component accounts for 5.5% of the total variance. Anterior arch depths load most positively and post-canine tooth crown areas load most negatively on PC3. This component would place short anterior arches with large post-canine tooth crown areas on the negative end of the axis and deep anterior arches with small post-canine tooth crown areas on the positive end.

Decomposition of the phenotypic correlation matrix for the 28 dental measurements emphasizes relationships between tooth types and regions. The first principal component of the dental phenotypic correlation matrix accounts for 60.7% of the total variance. All measurements load similarly on PC1 (Supplementary Table 1), ranging from −0.152 to −0.210. Individuals with large teeth would occupy one end of this axis and individuals with small teeth would occupy the other end. The second principal component accounts for 8.5% of the total variance. Incisor and canine mesio-distal lengths load most negatively and premolar and molar crown areas load most positively on PC2. Individuals with mesio-distally shorter anterior teeth and larger post-canine teeth would occupy one end of this axis and individuals with mesio-distally longer anterior teeth and smaller post-canine teeth would occupy the other end. The third principal component accounts for 6.5% of the variance. Mandibular tooth dimensions load negatively or near zero, and maxillary tooth dimensions load most positively on PC3. Individuals with large maxillary teeth relative to mandibular tooth size would occupy one end of this axis and those with small maxillary teeth relative to mandibular tooth size would occupy the other end.

Principal components analysis for the 34 arch measurements is consistent with those of the full phenotypic dataset. The first principal component of the arch phenotypic correlation matrix accounts for 47.1% of the total variance, and all measurements load similarly on PC1, ranging from −0.091 to −0.207. Individuals with larger arch measurements would occupy one end of this axis and individuals with smaller arch measurements would occupy the other end. The second principal component accounts for 14.1% of the total variance. This component largely describes arch shape, with arch widths loading most negatively and arch depths loading most postively on PC2. Individuals with short, wide arches would occupy one end of this axis and individuals with deep, narrow arches would occupy the other end. The third principal component accounts for 5.1% of the variance. Anterior arch depths load most positively and post-canine arch lengths load most negatively on PC3. Individuals with anteriorly deep arches and short post-canine arch lengths would occupy one end of the axis and individuals with anteriorly short arches and long post-canine arch lengths would occupy the other end.

Heritability estimates

The covariates age, age², sex, and their interactions account for up to 15.1% of the phenotypic variance and were included in $h_r^2$ estimation for all measurements. Estimates of $h_r^2$ (Figure 3, Table 3) range from 0.27 to 0.90, and all estimates of $h_r^2$ are significantly different from zero (p<0.05). Among dental measurements, the range in $h_r^2$ estimates is 0.31 to 0.90. Residual heritabilities for post-canine crown areas (range: 0.64 to 0.90) are greater than those for incisor and canine mesiodistal lengths (range: 0.31 to 0.53). The range in $h_r^2$ estimates among arch measurements is 0.27 to 0.86. The median $h_r^2$ is 0.67 among dental measurements, 0.57 among maxillary arch measurements, and 0.51 among mandibular arch measurements.

Figure 3.

Residual heritability (h2r) estimates in the mandible and maxilla (pink and green circles) for anterior and post-canine dental and arch measurements

Table 3.

Sample sizes (N) and residual (h²_r) and total (h²_t) heritability estimates from tooth and dental arch measurements, with standard error of h²_r (SE), p-values (p), proportion of phenotypic variance removed through covariates age, age², sex, and their interactions (Vcov/Vphen), and the environmental variance as a proportion of the total phenotypic variance (e²_t).

Trait	N	h 2 r	SE	p*	Vcov/Vphen	h 2 t	e2t
lrup3w	678	0.78	0.085	7.95E-16	0.077	0.716	0.207
lrup4w	698	0.86	0.074	1.14E-21	0.066	0.802	0.133
lrum1w	748	0.77	0.072	1.47E-21	0.105	0.691	0.204
lrum2w	756	0.73	0.075	2.52E-20	0.083	0.665	0.252
lrlp3w	674	0.71	0.076	1.12E-16	0.043	0.678	0.279
lrlp4w	687	0.73	0.084	1.69E-16	0.050	0.698	0.252
lrlm1w	779	0.71	0.078	1.13E-19	0.062	0.665	0.273
lrlm2w	796	0.64	0.077	2.77E-17	0.055	0.605	0.340
ulfa	796	0.56	0.085	7.24E-12	0.151	0.472	0.377
ullha	796	0.52	0.087	4.08E-10	0.111	0.459	0.430
ulrha	796	0.27	0.084	1.94E-04	0.116	0.237	0.646
utcal	795	0.68	0.074	2.52E-19	0.026	0.665	0.308
utmal	796	0.63	0.078	3.65E-17	0.108	0.561	0.332
llfa	822	0.44	0.083	7.71E-09	0.103	0.397	0.500
lllha	822	0.36	0.086	1.10E-06	0.090	0.323	0.587
llrha	822	0.34	0.086	6.80E-06	0.076	0.318	0.606
ltcal	822	0.60	0.076	3.50E-17	0.010	0.596	0.394
ltmal	822	0.47	0.081	4.16E-10	0.095	0.424	0.481
urcw	767	0.56	0.089	8.56E-12	0.020	0.545	0.436
ulcw	766	0.57	0.085	1.00E-12	0.016	0.558	0.427
urch	767	0.42	0.086	1.00E-07	0.003	0.414	0.584
ulch	766	0.45	0.087	1.00E-07	0.004	0.435	0.560
lrcw	805	0.45	0.080	1.96E-10	0.019	0.443	0.538
llcw	806	0.51	0.076	1.27E-13	0.028	0.500	0.473
lrch	805	0.36	0.084	1.10E-06	0.000	0.360	0.640
llch	806	0.39	0.081	1.00E-07	0.001	0.386	0.613
urmw	739	0.50	0.091	7.01E-09	0.058	0.466	0.476
ulmw	745	0.55	0.089	5.78E-10	0.055	0.520	0.425
urmh	739	0.61	0.082	7.30E-14	0.032	0.592	0.376
ulmh	745	0.66	0.086	2.97E-14	0.053	0.626	0.322
lrmw	773	0.58	0.081	2.35E-14	0.049	0.555	0.395
llmw	776	0.42	0.085	2.52E-08	0.042	0.405	0.553
lrmh	773	0.66	0.083	3.34E-15	0.020	0.650	0.330
llmh	776	0.64	0.076	1.26E-16	0.034	0.619	0.347
rui1md	935	0.43	0.076	9.98E-10	0.045	0.412	0.543
rui2md	935	0.31	0.076	1.70E-06	0.047	0.298	0.655
rucmd	935	0.45	0.078	8.77E-11	0.047	0.433	0.520
rup3ca	819	0.70	0.072	1.04E-21	0.020	0.690	0.290
rup4ca	819	0.70	0.074	1.14E-19	0.014	0.687	0.299
rum1ca	778	0.82	0.071	1.06E-24	0.054	0.778	0.167
rum2ca	756	0.64	0.091	1.28E-13	0.087	0.584	0.329
lui1md	935	0.53	0.076	8.26E-13	0.045	0.501	0.454
lui2md	935	0.31	0.077	5.00E-06	0.035	0.296	0.669
lucmd	935	0.33	0.074	2.00E-07	0.050	0.315	0.635
lup3ca	826	0.79	0.063	7.55E-28	0.017	0.778	0.205
lup4ca	813	0.66	0.075	5.29E-18	0.015	0.647	0.338
lum1ca	772	0.86	0.065	1.31E-26	0.060	0.813	0.128
lum2ca	754	0.72	0.082	2.93E-19	0.064	0.669	0.267
rli1md	935	0.44	0.071	1.30E-11	0.053	0.420	0.528
rli2md	935	0.48	0.071	7.33E-14	0.020	0.475	0.505
rlcmd	935	0.45	0.071	1.82E-12	0.074	0.416	0.510
rlp3ca	881	0.83	0.059	5.36E-33	0.032	0.805	0.163
rlp4ca	851	0.81	0.064	2.96E-27	0.008	0.800	0.193
rlm1ca	760	0.90	0.062	3.45E-29	0.057	0.846	0.096
rlm2ca	769	0.80	0.073	1.96E-22	0.062	0.754	0.184
lli1md	935	0.43	0.076	9.98E-10	0.045	0.412	0.543
lli2md	935	0.31	0.076	1.70E-06	0.047	0.298	0.655
llcmd	935	0.45	0.078	8.77E-11	0.047	0.433	0.520
llp3ca	875	0.68	0.071	4.05E-21	0.023	0.665	0.312
llp4ca	851	0.72	0.071	4.26E-22	0.002	0.715	0.284
llm1ca	776	0.87	0.058	3.71E-30	0.048	0.827	0.125
llm2ca	763	0.70	0.069	4.04E-19	0.085	0.640	0.275

^*h₀: h²_r = 0

Genetic correlation estimates

All estimates of ρ_G from the Jirel population are positive, ranging from 0.13 to 1.0 (Figure 4, Supplementary Table 2). Estimates of ρ_G for left-right antimeres are very close or equal to 1.0 (Table 4). Homologous pairs of maxillary and mandibular teeth (e.g., right P³ and right P₃) are also closely genetically correlated (Table 5). Of the 1,891 ρ_G estimates, 1,874 estimates are significantly different from zero (p<0.05) and 1,681 estimates are significantly different from one (p<0.05). Most ρ_G estimates that are not significantly different from zero are between arch depth and width measurements. Estimates of ρ_G are especially high between post-canine tooth crown areas (range: 0.72 to 1.00), full arch widths (range: 0.71 to 1.00), full arch lengths (range: 0.66 to 1.00), and between anterior tooth lengths (range: 0.64 to 1.00). Estimates of ρ_G are lower between dental dimensions and full arch widths (range: 0.15 to 0.77), and between post-canine tooth crown areas and mandibular arch depth at the canines (range: 0.27 to 0.55).

Figure 4.

Heatmap of genetic correlation estimates from dental, maxillary and mandibular measures. Values are highlighted in blue (low) to white (high)

Table 4.

Genetic correlations between dimensions of left-right antimeres.

Measurement	ρG
I1 length	1.00
I2 length	1.00
C1 length	1.00
P3 area	1.00
P4 area	1.00
M1 area	1.00
M2 area	1.00
I1 length	1.00
I2 length	1.00
C1 length	1.00
P3 area	0.99
P4 area	0.99
M1 area	0.98
M2 area	1.00

Table 5.

Genetic correlations between crown areas of maxillary-mandibular homologues.

	Measurement	ρG
Right	I1-I1 length	0.96
	I2-I2 length	0.91
	C1-C1 length	0.96
	P3-P3 crown area	0.92
	P4-P4 crown area	0.91
	M1-M1 crown area	0.97
	M2-M2 crown area	0.86
Left	I1-I1 length	0.94
	I2-I2 length	0.78
	C1-C1 length	0.90
	P3-P3 crown area	0.93
	P4-P4 crown area	0.95
	M1-M1 crown area	0.96
	M2-M2 crown area	0.92

Principal components analysis of the genetic correlation matrices (Supplementary Table 3) demonstrates similar patterns to the principal components of the phenotypic correlation matrices. The first principal component of the full genetic correlation matrix accounts for 70.3% of the total variance, with all variables loading similarly on PC1, with loadings ranging from −0.086 to −0.155. The second principal component accounts for 11.2% of the total variance. Arch widths load most negatively and post-canine tooth crown areas load most positively on PC2. The third principal component accounts for 6.0% of the total variance. Post-canine arch widths and post-canine tooth crown areas load most negatively on PC3 and arch depths and anterior tooth lengths load most positively on PC3.

As was the case with the dental phenotypic correlation matrix, the principal components of the dental genetic correlation matrix indicate slightly stronger genetic correlations within anterior tooth lengths or post-canine crown areas than between anterior and post-canine tooth measurements (Supplementary Table 3). The first principal component of the dental measurement genetic correlation matrix accounts for 78.8% of the total variance and all dental measurements load similarly on PC1, ranging from −0.205 to −0.172. The second principal component accounts for 9.9% of the total variance. Anterior tooth lengths load most negatively and post-canine tooth crown areas load most positively on PC2, similar to the pattern observed in the phenotypic correlation matrix.

Decomposition of the arch measurement genetic correlation matrix shows a similar arch width-arch depth relationship as the phenotypic correlation matrix. The first principal component of the arch measurement genetic correlation matrix accounts for 72.4% of the total variance. All arch measurements load similarly on PC1, ranging from −0.115 to −0.202. The second principal component accounts for 13.7% of the total variance. Arch widths load most negatively and arch depths load most positively on PC2.

Discussion

Phenotypic analyses

Principal components analysis of the phenotypic correlation matrices demonstrates an overall size component, represented by the first principal component, that accounts for much of the phenotypic variance in the population. This is the case whether all measurements, only dental measurements, or only arch measurements are included. This first principal component accounts for a larger proportion of the variance when only dental traits are considered, possibly indicating a stronger overall size effect among dental traits than among arch measurements. Beyond this first principal component, a negative relationship between arch widths and arch depths is shown on the second principal component whether dental measurements are included or not. A negative relationship between incisor and canine lengths versus premolar and molar crown areas also accounts for substantial variance among dental measurements beyond the overall size component. This could indicate a degree of phenotypic independence between anterior and post-canine teeth, but it may also be influenced by the different uses of mesio-distal length measurements for the anterior teeth and crown surface areas for the post-canine teeth.

Heritability

Estimates of $h_r^2$ from the Jirel population are all significantly different from zero. Although it is generally understood that dental traits are more highly heritable than skeletal traits, heritability estimates for dental and skeletal measures are rarely collected in the same populations for comparison. Between-trait comparisons within the Jirel population indicate that post-canine crown areas occupy the upper range of overall trait heritabilities, while anterior tooth lengths are moderate (Figure 3). Estimates of $h_r^2$ from tooth lengths and crown areas are comparable to those obtained from dental measurements of other human populations (Alvesalo & Tigerstedt, 1974; Dempsey & Townsend, 2001; Stojanowski et al., 2017) and from non-human primates (Hardin, 2019a; Hlusko et al., 2002). Heritability estimates were generally greater for estimated crown areas than for mesiodistal lengths in brown-mantled tamarins (Hardin, 2019a), indicating that differences in $h_r^2$ between the anterior and post-canine dimensions could be due to differences between the linear measurements representing the anterior teeth and the crown areas representing the post-canine teeth. Arch measurements, whether anterior or post-canine, have $h_r^2$ estimates ranging from moderate to high.

Our finding that $h_r^2$ estimates are greater in post-canine dental measurements than in arch dimensions is consistent with one hypothesis for the increased prevalence of dental crowding in modern humans which states that reduced masticatory strain during jaw development negatively impacts arch size without affecting dental size (Lieberman et al., 2004). Greater environmental effects on arch measures compared to dental measures indicates the potential for masticatory strain to alter arch dimensions without affecting dental dimensions, possibly contributing to dental crowding and other dental malocclusions.

Tooth-arch genetic correlations

The full genetic correlation matrix shows an overall size component shared by dental dimensions and dimensions of the maxillary and mandibular arches on PC1. Independent of this overall size component, inverse genetic relationships are estimated between tooth size and arch width and, secondarily, between tooth size and arch depth. PC1 of the arch measurement genetic correlation matrix similarly reflects overall size, while PC2 shows an inverse relationship between arch width and arch depth. Together these results indicate the existence of a genetic component contributing to overall size, and additional genetic influences on the relative sizes of the anterior and post-canine dentition and the shape of the dental arch in the Jirel population.

When the overall size effect is removed, tooth size, arch length, and arch depth measurements are positively genetically related and are genetically independent from or negatively associated with arch width measurements. Cole et al. (2017) estimated negative genetic correlations between facial depths and facial widths in children from the Bantu peoples of Tanzania, as well as a general pattern of negative genetic correlations between orthogonal dimensions. This indicates a fairly consistent disconnect between widths and depths of the face and arch when size is removed. The tendency toward positive genetic correlations in the arch and teeth and toward negative genetic correlations in the face (Cole et al., 2017) may be rooted in greater positive genetic integration in the arch than in the face. This difference could also be an artifact of the different methods and populations used in each study, especially since an overall size effect may be less consistent in children relative to adults.

The genetic relationships observed in the dental arch and teeth could allow selection for tooth size reduction to decrease arch length and depth through a correlated response to selection without a proportional decrease in arch width. The PCs of the full genetic correlation matrix reflect a secondary genetic component wherein anterior tooth size and anterior arch depth measures are positively related, but are independent from or inversely related to post-canine crown areas. Together, these components indicate that while selection on the dentition and dental arches will primarily serve to change the overall size of the dentognathic complex, the morphological relationships of arch width to tooth size and anterior arch depth to post-canine tooth size may be less genetically constrained and may therefore exhibit greater evolvability.

Genetic correlations in the dentition

Patterns of genetic correlations are similar in the right and left sides of the dentition and maxillary and mandibular arches. Genetic correlations between left-right dental antimeres approach complete pleiotropy (values close to 1.0), as has been found in previous studies of humans (Stojanowski et al., 2017) and non-human primates (Hlusko et al., 2011). Genetic correlations are especially high within the anterior dentition and within the post-canine dentition, yet moderate to high genetic correlation estimates between dental regions indicate shared genetic contributions governing tooth size across tooth types, similar to patterns observed previously in humans (Stojanowski et al., 2017) and tamarins (Hardin, 2019b). The first principal component of the dental genetic correlation matrix has consistently similar loadings across all variables, indicating that PC1 represents an overall size component. However, PC2 reflects an inverse genetic relationship between anterior tooth lengths and post-canine crown areas, indicating a negative genetic relationship between these regions of the dentition when effects of overall size are removed. Although the genetic correlations between tooth types are more positive overall in the Jirel population, the genetic relationships on PC2 are similar to the pattern of genetic modularity by tooth type observed in baboons and mice (Hlusko et al., 2011; Hlusko & Mahaney, 2009).

Evolution of the primate dentognathic complex

Heritabilities and genetic correlations can greatly impact evolutionary response to selection (Lande & Arnold, 1983; Lush, 1937). Although the genetic architecture of the craniodental complex in extinct hominin taxa cannot be studied, similarities in the genetic architecture of mandibular morphology between evolutionarily disparate taxa indicate that aspects of the genetic architecture are conserved (Willmore et al., 2009). Furthermore, evolutionary relationships among body size, brain size, cranial shape, mandibular shape, and tooth size influence broader hypotheses of hominin evolution and reflect hypothesized genetic and functional relationships between regions of the skull (Brace et al., 1987; Elton et al., 2001; Jungers et al., 2016; Plavcan & Daegling, 2006; Quam et al., 2009; Will et al., 2017). Quantitative genetic parameters from this modern human sample may therefore serve as a useful model of the genetic architecture of the craniodental complex in hominin evolution.

Strong genetic correlations between post-canine tooth crown areas and measures of arch length indicate that selection on post-canine crown areas could alter arch lengths, and vice versa, through correlated response to selection. This relationship between post-canine tooth crown area and arch length is also expected from a purely geometric perspective, since mesio-distal tooth crown lengths contribute to both arch length and tooth crown area. However, anterior mesio-distal tooth lengths are less closely genetically correlated with arch lengths. Evolutionary change in arch shape, from the straight post-canine dental rows of Australopithecus (Kimbel and Delezene, 2009) to the parabolic arch of Homo sapiens (Stelzer et al., 2019), may be a consequence of the relative genetic independence between post-canine tooth crown areas and arch widths and between arch depths and arch widths. Selection on post-canine tooth crown area would be predicted to change arch depth, through correlated response to selection, without necessarily impacting arch width. The same would be true for selection on arch depth.

Morphological integration in human and non-human primate skulls indicates close phenotypic relationships between maxillary and mandibular arch shapes (Stelzer et al., 2017). Phenotypic relationships between molar dimensions and aspects of craniofacial morphology are also represented in the literature (Plavcan & Daegling, 2006; Polychronis & Halazonetis, 2014). Loci contributing to these phenotypic relationships have been identified in mice (Workman et al., 2002), baboons (Sherwood et al., 2008), and humans (Sherwood et al., 2011). The genetic correlations estimated here support the hypothesis of close genetic relationships between the maxillary and mandibular arches. Our findings also indicate that, although overall size has the greatest impact on measures of the arch and teeth, there is a secondary pattern along PC2 that reflects a degree of independence between a genetic component influencing post-canine tooth size, arch length, and arch depth and a genetic component influencing arch widths.

The third principal component of the full genetic correlation matrix expresses a degree of independence between post-canine tooth crown areas with negative loadings on PC3, and anterior tooth dimensions and anterior arch depths with positive loadings on PC3. This pattern is similar to the morphology expressed by robust australopiths, in which expansion of the post-canine teeth is accompanied by reduction in the anterior dentition and a flattening of the anterior dental arch (Wood and Constantino, 2007). These findings suggest a potential role of correlated response to selection on the suite of morphological traits characteristic of the robust australopiths.

Evolution of the genetic correlation matrix

Reduced morphological covariation between regions of the human masticatory apparatus has been hypothesized to stem from the less mechanically challenging diet of modern humans compared to other hominoids (Stelzer et al., 2018). Although the evolution of the genetic architecture itself is, as yet, poorly understood (Agrawal & Stinchcombe, 2009; Cheverud, 1988b; Griswold, 2006; Melo & Marroig, 2015; Wagner, Pavlicev, & Cheverud, 2007; Watson et al., 2014), the pattern of genetic integration in the human craniodental complex may be closely related to large-scale evolutionary changes seen in the hominin skull. Low genetic correlations between specific dimensions could decrease evolutionary constraint on regions of the skull under opposing selection pressures, allowing, for example, molar size to decrease without impacting arch width through correlated response to selection. Differential environmental effects on dental and skeletal traits, as indicated by the greater $h_t^2$ of dental measurements compared to arch measurements, also serve to decrease the morphological integration of these components without requiring reduced genetic integration. These environmental effects and reduced genetic integration between functionally integrated structures, such as the maxillary and mandibular arches, likely increase the potential for dental crowding and other biomechanical insufficiencies in the human dentognathic complex (Enlow et al., 1969).

Integrated quantitative genetic analyses of craniofacial and dental characters from phylogenetically diverse taxa will inform hypotheses regarding the evolution of the genetic architecture itself. The powerful pedigree of the Jirel population of Nepal provides an opportunity to precisely estimate genetic influences on dental and orofacial morphology in humans. Combined analyses of dental and skeletal measurements in additional populations and species will generate a more complete picture of genetic relationships throughout the body and their potential evolutionary outcomes.

Conclusions

This study presents heritability and genetic correlation estimates from across the human dentognathic complex to illustrate the genetic relationships between dental and skeletal features that contribute to the shape of this complex in the Jirel population of Nepal. Traits were moderately to highly heritable and nearly all genetic correlations were significantly different from zero. We observed that 1) dental measurements were highly heritable and were closely genetically correlated across tooth types; 2) heritabilities were greater in dental measurements than in arch measurements; and 3) genetic correlations were not always stronger within dental or arch measurements than between dental and arch measurements.

The results demonstrate several potential influences on malocclusion, including differences in dental and skeletal heritabilities and incomplete pleiotropy between dental arch lengths and widths. In addition to the overall size impact that is indicated by the positive genetic correlations throughout the dentognathic complex, patterns are observed in the principal components of the genetic correlation matrix. All genetic correlations between dental measurements are positive, similar to those observed in humans and tamarins (Hardin, 2019a; Stojanowski et al., 2017), yet genetic correlations are greater within the anterior and post-canine dentition as has been observed in cercopithecoids and mice (Hardin, 2020; Hlusko et al., 2011; Hlusko & Mahaney, 2009). Close genetic correlations between dental arch lengths and post-canine tooth crown areas indicate the potential for genetic constraints on the evolution of the human dentognathic complex. Likewise, weaker genetic correlations with arch widths indicate potential evolvability in the shape of the dental arch.

Further quantitative genetic analyses of both dental and skeletal features will demonstrate how these genetic relationships vary phylogenetically. It remains to be seen whether the pattern of genetic correlations observed in the Jirel population of Nepal is typical of other human populations. These results provide clear evidence of genetic relationships between dental and skeletal components of the human dentognathic complex, and will serve as a useful model for understanding the evolution of this functionally integrated complex.