Received: 1 August 2018 Revised: 20 November 2018 Accepted: 26 December 2018 DOI: 10.1002/ajpa.23778

RESEARCH ARTICLE

Quantitative genetic analyses of postcanine morphological crown variation

Christopher M. Stojanowski1 | Kathleen S. Paul1 | Andrew C. Seidel1 | William N. Duncan2 | Debbie Guatelli-Steinberg3

1Center for Bioarchaeological Research, School of Human Evolution and Social Change, Abstract Arizona State University, Tempe, Arizona Objectives: This article presents estimates of narrow-sense heritability and bivariate genetic 2Department of Sociology and Anthropology, correlation for 14 tooth crown morphological variants scored on permanent premolars, first East Tennessee State University, Johnson City, molars, and second molars. The objective is to inform data collection and analytical practices in Tennessee dental biodistance and to provide insights on the development of molar crowns as integrated 3Department of Anthropology, The Ohio State University, Columbus, Ohio structures. Correspondence Materials and Methods: African American dental casts from the Menegaz-Bock collection were Christopher M. Stojanowski, School of Human recorded for the Arizona State University Dental Anthropology System. Estimates of narrow- Evolution and Social Change, 900 S. Cady Mall, sense heritability and genetic correlation were generated using SOLAR v.8.1.1, which included Arizona State University, Tempe, AZ 85287. assessment of age, sex, and birth year as covariates. Both continuous scale and dichotomized Email: [email protected] estimates are provided. Funding information National Science Foundation Research, Grant/ Results: Heritability estimates were nonsignificant for the majority of variables; however, for Award Numbers: BCS-1063942, BCS- variables yielding significant estimates, values were moderate to high in magnitude and compa- 1750089; IRB at The Ohio State University, rable to previous studies. Comparing left and right-side heritability estimates suggests direc- Reference Number: 2012B0529 tional asymmetry in the expression of environmental variance, something not seen in anterior tooth traits. Genetic correlations were moderate among antimeres and metameres and low for different traits scored on the same tooth crown. Although several negative correlations were noted, few reached statistical significance. Results affirm some of the current data cleaning and analytical practices in dental biodistance, but others are called into question. These include the pooling of males and females and combining left and right-side data into a single dataset. Conclusions: In comparison to anterior tooth crown traits, postcanine heritabilities were more often non-significant; however, those traits with significant heritability also tended to produce higher estimates. Genetic correlations were unremarkable, in part, because they were under- powered. However, M1 results may provide insight into the complex relationship between genes, environment, and development in determining ultimate crown form.

KEYWORDS biodistance, dental morphology, heritability, pleiotropy, quantitative genetics

1 | INTRODUCTION among the distinct advantages of early mammalian taxa. For this rea- son, and due to the comparative abundance of tooth crowns in the Teeth are used as genetic proxies to reconstruct evolutionary relation- fossil and archaeological records, understanding the genetic signals ships in archaeological and paleontological contexts. Tooth morphol- manifest in patterns of dental variation is important for a number of ogy, for example, is used in bioarchaeology to infer population fields including anthropology, paleontology, and comparative mam- relationships at multiple scales of analysis. The size and morphology malogy. Researchers have used a combination of experimental, of tooth crowns are also used to infer the adaptive niches of extinct evolutionary-developmental, and quantitative genetic analyses to species, as heterodonty and the evolution of isomeric occlusion were identify the mechanisms involved in tooth crown differentiation and

606 © 2019 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/ajpa Am J Phys Anthropol. 2019;168:606–631. STOJANOWSKI ET AL. 607 to reconstruct the developmental processes responsible for the variation in this population as well as high environmental variance due observed range of variation in molar crowns (Gómez-Roblez & Polly, to the socioeconomic/living conditions of the Gullah (Guatelli-Stein- 2012; Grieco, Rizk, & Hlusko, 2013; Hlusko & Mahaney, 2003; berg, Sciulli, & Edgar, 2006; Stojanowski et al., 2018). Although our Hlusko, Maas, & Mahaney, 2004; Hlusko, Sage, & Mahaney, 2011; interest was in estimating quantitative genetic parameters that speak Jernvall, Åberg, Kettunen, Keränen, & Thesleff, 1998; Jernvall, Kettu- to the dentition's use as a proxy in evolutionary studies, the lower nen, Karavanova, Martin, & Thesleff, 1994; Koh et al., 2010; Polly, than expected heritability estimates reported in both papers are con- 2015; Polly & Mock, 2018; Salazar-Ciudad & Jernvall, 2002, 2010). sistent with the documented degree of dental asymmetry in the Gul- Developmental origins of crown variants have also been discussed lah sample (Guatelli-Steinberg et al., 2006). within a quantitative genetic framework, particularly in studies of sin- Here, we use the same sample of mid-20th century African Amer- — gle species datasets (e.g., Papio hamadryas Hlukso, Do, & Mahaney, ican individuals living on James Island, South Carolina (ethnic Gullah) — 2007; Hlusko et al., 2004; Cryptocoryne parva Polly & Mock, 2018). to generate estimates of narrow-sense heritability as well as genetic In particular, the work of Hlusko and colleagues has provided critical and phenotypic correlations among postcanine crown variants within data on patterns of modularity and integration in the primate denti- the ASUDAS (Edgar, 2017; Scott & Irish, 2017; Turner II et al., 1991). tion, focusing on features such as interconulid/interconulus presence This article has two goals. The first is to present new estimates of (Hlusko & Mahaney, 2003), enamel thickness (Hlusko, Suwa, Kono, & narrow-sense heritability and genetic correlation for postcanine mor- Mahaney, 2004), molar loph/lophid angle (Hlusko et al., 2004), molar phological crown traits. The second is to use quantitative genetic ana- cusp areas (Hlusko et al., 2007; Koh et al., 2010), and geometric mor- lyses to assess current assumptions and analytical “best practices” phometric assessments of tooth/arcade form (Hlusko et al., 2011). employed in dental biodistance research. The first goal provides foun- By comparison, quantitative genetic analyses of human dental dational knowledge about dental biology, while the second is practical data have been limited, especially concerning crown variation of the and informs data collection, data cleaning, and statistical methods in postcanine dentition. Most previous studies have focused on overall dental biodistance research. This work complements previous studies crown size (e.g., Alvesalo & Tigerstedt, 1974; Dempsey & Townsend, of the same sample (Stojanowski et al., 2017, 2018) and aims to refine 2001; Townsend & Brown, 1978a, 1978b, 1979; Townsend et al., the use of postcanine morphological variants for reconstructing bio- 1986; Stojanowski, Paul, Seidel, Duncan, & Guatelli-Steinberg, 2017) logical relationships and microevolutionary processes. or specific features such as Carabelli's trait (Alvesalo, Nuutila, & Portin, 1975; Biggerstaff, 1973; Harris & Bailit, 1980; Laatikainen & Ranta, 1996; Townsend & Martin, 1992) or cusp 5 of the maxillary molars 2 | BACKGROUND (Harris & Bailit, 1980; Townsend, Yamada, & Smith, 1986). However, comprehensive assessments of a more complete suite of postcanine Twin and family studies have been essential to exploring the genetic crown variants, such as that presented in the Arizona State University foundations of dental variation. These studies employ documented Dental Anthropology System (ASUDAS) (Turner II, Nichol, & Scott, genealogical information and (typically) casted dentitions of extended 1991) is lacking (but see Scott & Potter, 1984). pedigree members or kin pairs. For crown morphology, initial efforts In two previous papers we used quantitative genetic methods to focused on determining modes of inheritance, testing simple Mende- estimate heritability and inter-trait genetic correlations for mesiodistal lian versus complex polygenic trait models. In particular, Carabelli's tooth size and a series of anterior morphological crown variants in a trait was the focus of intensive, foundational research. Early studies sample of African American individuals from the Southeastern United showed Carabelli's trait data to fit either a dominant-recessive or States (Stojanowski, Paul, Seidel, Duncan, & Guatelli-Steinberg, 2018; autosomal codominant model, allowing for gene frequency estimation Stojanowski et al., 2017). Results presented in Stojanowski in some cases (Devoto & Perrotto, 1971; Dietz, 1944; Kraus, 1951; et al. (2017) indicated a high degree of genetic integration of mesio- Tsuji, 1958; Turner, 1967). These findings were not always corrobo- distal crown size across the dentition. While univariate heritability rated (Goose & Lee, 1971; Lee & Goose, 1972; Sofaer, 1970), suggest- estimates were lower than those reported for other human popula- ing a more complex, polygenic mode of inheritance. The fact that tions, positive estimates of genetic correlation indicated a high degree morphological characters like Carabelli's trait vary widely in their of dimensional pleiotropy compared to a hypothesized general mam- malian pattern based on previous studies of baboons and mice degree of expression has also been viewed as consistent with a multi- (Hlusko & Mahaney, 2007; Hlusko et al., 2011). In Stojanowski factorial mode of inheritance (Scott, Turner II, Townsend, & Martinón- et al. (2018), estimates of narrow sense heritability and inter-trait Torres, 2018; Sofaer, 1970). Assuming an underlying polygenic frame- genetic correlation were presented for anterior tooth crown morpho- work, subsequent studies assessed the fit of threshold or quasi- logical variants. Results indicated low but statistically significant heri- continuous trait models to pedigreed datasets as a means of exploring tabilities for most traits, strong genetic and phenotypic correlations the variable nature of discrete crown characters (e.g., Bailit, Ander- among antimeres, strong genetic correlations among traits scored son, & Kolakowski, 1974; Bailit, Brown, & Kolakowski, 1975; Harris, across different teeth, and a complex pattern of positive and negative 1977; Scott, 1973). Complex segregation analyses also provided genetic correlations among traits scored on the same tooth crown. As insight into competing genetic effects (i.e., “major genes” and “minor with the odontometric results, heritabilities for tooth crown variants genes”) and trait transmissibility (Kolakowski, Harris, & Bailit, 1980; were lower than previously reported estimates, which we interpreted Nichol, 1989). The results of this work are summarized by Scott as reflecting the combined effects of reduced additive genetic et al. (2018). 608 STOJANOWSKI ET AL.

Despite initial searches for major genes and simple modes of varied greatly. While Alvesalo et al. (1975) reported no evidence for inheritance, current perspectives acknowledge that morphological correlations among siblings in a sample of rural Finns, Scott (1973) crown traits are likely polygenic and characterized by complex modes reported intra-class correlations ranging from 0.39 to 0.57 (across sib- of inheritance. As such, dental anthropology has embraced quantita- ling and parent-offspring pairs) in Euro-Americans. In a more recent tive genetic approaches, which help ground truth the assumptions of study of South Australian twins, model-fitting approaches yielded her- biodistance analyses and enhance analytical methods for reconstruct- itability estimates of 0.90 for M1 Carabelli's trait and indicated that a ing evolutionary processes. Character-specific heritability estimates combination of additive genetic effects, shared environmental effects, inform trait selection through quantification of the relative influence and unique environmental effects best account for observed pheno- of genes on patterns of phenotypic variation; heritability is often seen typic patterns (Townsend & Martin, 1992). While no single heritability as a measure of a trait's “utility” for both biodistance and phylogenetic estimate can be applied across populations, research generally indi- research. It is also a key parameter for reconstructing population cates a moderate degree of heritability for the varying expression of structure from quantitative traits via R matrix analysis (e.g., RMET) this character, with several twin studies converging upon similar esti- (Relethford, 1994, 1996; Relethford & Blangero, 1990; Relethford, mates of ~0.40, despite using samples of diverse bioregional origins Crawford, & Blangero, 1997; Williams-Blangero & Blangero, 1989; (Boraas, Messer, & Till, 1988; Mizoguchi, 1977; Scott & Potter, 1984; reviewed in Relethford, 2007, 2016), and can inform trait weighting in Scott et al., 2018; Townsend & Martin, 1992). multivariate phenotypic distance calculations (Stojanowski & Schillaci, Heritability estimates have been reported for select postcanine 2006). Narrow-sense heritability (h2) is the parameter of interest variants beyond Carabelli's trait. Higgins, Hughes, James, and Town- because it represents the relative contribution of additive genetic vari- send (2009) reported a hypocone heritability estimate of 0.87 for M1 2 ance alone, as compared to broad-sense heritability (H ) that does not and 0.93 for M2 in a South Australian twin sample. The best-fit model distinguish between additive and nonadditive (e.g., multigene interac- incorporated only additive genetic and unique environmental effects tion, dominance) genetic effects. as contributors to hypocone variance (Higgins et al., 2009). Hughes Results of quantitative genetic analyses have shown permanent et al. (2010) also reported heritability estimates exceeding 0.75 for crown dimensions to be under moderate to strong genetic influence, several mandibular crown traits in the same sample. With few excep- with additive genetic variance accounting for over half of phenotypic tions, best-fit models included both an additive genetic and unique variance on average (e.g., Alvesalo & Tigerstedt, 1974; Dempsey & environmental term (Hughes et al., 2010). The estimates presented in Townsend, 2001; Dempsey, Townsend, Martin, & Neale, 1995; Lund- these twin studies exceed all family-based intraclass correlation coef- ström, 1948; Stojanowski et al., 2017; Townsend & Brown, 1979). By ficients reported for postcanine tooth traits by Scott (1973) (M2 hypo- comparison, morphological characters on adult teeth yield lower heri- 1 cone r = 0.40–0.55; M Carabelli's trait r = 0.39–0.57; P1/P2 lingual tability estimates, typically falling within the 0.40 to 0.80 range for the cusp number r = 0.21–0.61; M1 cusp 7 r = 0.28–0.52). Family studies mesial-most member of each tooth class (e.g., see Berry, 1978; Laati- of M1 cusp 5 in Solomon Islanders (Harris & Bailit, 1980) and Aborigi- kainen & Ranta, 1996; Mizoguchi, 1977; Townsend & Martin, 1992; nal Australians (Townsend et al., 1986) yielded fairly low sibling– Scott & Turner, 1997, p. 164). It is important to note that not all stud- sibling correlation coefficients (Solomon Islands: M1 C5 sister–sister ies employ the same analytical methods and that heritability estima- ρ = 0.32; Australia: M1 C5 ϕ = 0.04). These findings indicated a con- tion has improved in statistical rigor over the years. Initial work siderable environmental influence on cusp 5 expression. However, it derived estimates from trait concordance rates among monozygotic should be noted that a statistically significant correlation was reported and dizygotic twin pairs, familial intra-class correlation coefficients, for the deciduous second molar in the Aboriginal sample (m2 C5 and analysis of variance. Carabelli's trait, along with certain molar vari- ϕ = 0.66) (Townsend et al., 1986), and when Harris and Bailit (1980) ants, received much attention (Alvesalo et al., 1975; Berry, 1978; Big- pooled data for all Solomon Islander relatives, they obtained cusp gerstaff, 1970, 1973; Kaul, Sharma, Sharma, & Corruccini, 1985; 5 heritability estimates of 0.65 and 0.15 for M1 and M2, respectively. Laatikainen & Ranta, 1996; Mizoguchi, 1977; Scott & Potter, 1984; A more moderate sibling–sibling correlation coefficient of 0.30 was Sofaer, MacLean, & Bailit, 1972). More recently, sophisticated model- reported for M1 cusp 6 in the Aboriginal Australian sample fitting approaches have become the norm, such as path analysis and (Townsend, Yamada, & Smith, 1990). structural equation modeling (Hughes, Vo, Mihailidis, & Townsend, 2010; Townsend & Martin, 1992; Townsend et al., 1992; Trakinienė et al., 2018), as well as variance components analysis via maximum 3 | MATERIALS AND METHODS likelihood estimation (Paul, Stojanowski, Hughes, Brook, & Townsend, 2018; Stojanowski et al., 2018). Data on 14 morphological molar crown variants were collected using Considering the diversity of these analytical approaches and the ASUDAS standards (Turner II et al., 1991). The trait list includes five population-specificity of heritability, it is not surprising that reported maxillary molar traits recorded for both the M1 and M2 (metacone, values vary greatly. Molar morphology is not an exception. In a recent hypocone, cusp 5, Carabelli's trait, parastyle), one mandibular premolar review of Carabelli's trait research, Scott et al. (2018) summarized the trait collected for both the P1 and P2 (lingual cusp variation), and eight results of several twin concordance studies (e.g., Berry, 1978; mandibular molar crown variants, of which six were collected on both Biggerstaff, 1973; Scott & Potter, 1984; Skrinjaric, Slaj, Lapter, & the M1 and M2 (cusp 5, cusp 6, cusp 7, cusp number, groove pattern, Muretic, 1985), for which heritability estimates ranged from ~0.0 to protostylid) and two were scored only on the M1 (anterior fovea, 0.91 (mean h2 = 0.45) (pp. 143-144). Family-based estimates also deflecting wrinkle). Third molar data were infrequent due to the STOJANOWSKI ET AL. 609 limitations of the casting protocol. All data were scored by a single significantly different from 0.0 (complete pleiotropy), significantly differ- investigator (WND) to minimize interobserver error. We have previ- ent from 1.0 (no pleiotropy), or significantly different from both (incom- ously discussed assessment of intraobserver error for this dataset plete pleiotropy). Tests that returned two insignificant results were (Stojanowski et al., 2018), which produced estimates within an accept- considered underpowered and interpreted as a non-result. Derived phe- able range (cf., Marado, 2017; Scott, 1973). Mesiodistal dimensions notypic correlations (ρp) were subsequently estimated using the formula qffiffiffiffiffi q ffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi were recorded by CMS and are used here as markers of crown size.  ρ ¼ h2 h2 ρ + 1 − h2 ð1 − h2 ρ . Because, each pair-wise The study sample consists of ~460 dental casts of African Ameri- P 1 2 G 1 2 E can individuals living in coastal South Carolina during the early to mid- combination of variables could include multiple estimates of heritabil- 20th century (ethnic Gullah). Casts and genealogical records were col- ity (see below) bivariate analyses included traits dichotomized at lected by Rene Menegaz-Bock during her dissertation research expression breakpoints that yielded the highest univaritate heritability (Menegaz-Bock, 1968); the latter provide information on familial rela- estimate. tionships, age at time of casting, sex, and birth year. We used these Narrow-sense heritabilities and estimates of genetic, environmen- data to compile genealogies that resulted in the identification of tal, and phenotypic correlations were calculated for each variable in 22 bilineal families, including one single pedigree that included two ways. First, the variable was treated as continuous scale in recog- 313 individuals. The distribution of genealogical relationships is pre- nition of the fact that ASUDAS morphological scoring applies an ordi- sented in Supporting Information Table S1 and includes 652 individ- nal scale to what is an inherently (quasi)continuous variable (see uals inclusive of non-casted founders. All individuals were living on Hlusko & Mahaney, 2003; also Carson, 2006; Cheverud, Buikstra, & James Island, South Carolina at the onset of Menegaz-Bock's research Twichell, 1979; Corruccini, 1976; Harris, 1977; Sofaer, Niswander, project. She noted a population of approximately 3,400 individuals liv- McLean, & Workman, 1972). Data were transformed using SOLAR's ing on the island at the time, a number which slightly underestimates inorm function to mitigate the effects of distributional variance (pri- the total population size of the island and does not reflect the size of marily kurtosis) on significance testing. Analyses with kurtosis values the entire coastal South Carolina Gullah population during the mid- beyond the acceptable range were marked in our output and should 20th century. The cast sample represents ~13% of the population liv- be interpreted with caution. These results are most comparable to the ing on the island at that time. Previous studies using the reconstructed odontometric heritabilities and correlations previously reported in genealogies suggest minimal impact of recording errors (Stojanowski Stojanowski et al. (2017). Because SOLAR does not accommodate et al., 2017, 2018), although there is the potential for adoptions and ordinal scale data, we then divided each trait into a number of binary other fictive kin relationships (and half sibships) that were not cap- scale variables at different breakpoints as determined by sample fre- tured in the genealogical recording (Twining & Baird, 1991). Further quency. For example, Carabelli's trait was analyzed as a continuous details on the Gullah sample can be found in Stojanowski et al. (2017, scale variable and as a series of seven binary scale variables with 2018), which summarize the relevant details from initial work among breakpoints for trait presence defined as 1+ = present, 2+ = present, the population (Menegaz-Bock, 1968; Pollitzer, 1958, 1993, 1999; and so forth. The distribution of raw scores is presented in Supporting Pollitzer, Menegaz-Bock, Ceppellini, & Dunn, 1964), including prior Information Table S2. dental anthropological analyses (Edgar, 2000; Edgar & Sciulli, 2004; Guatelli-Steinberg et al., 2006) and assessments of genetic variation (McClean Jr. et al., 2003, 2005; Parra et al., 2001; Sale et al., 2009). 4 | RESULTS All research presented in this article was conducted under the approval of The Ohio State University IRB (2012B0529). Heritability estimates and results of covariate screening are presented We estimated narrow-sense heritability (h2) using maximum likeli- in Table 1. The covariates of birth year and age at time of casting hood variance components analysis. All estimates were derived using returned significant p-values for some variables, but these were not SOLAR v.8.1.1 (Almasy & Blangero, 1998; Blangero et al., 2016), consistent across sides or breakpoints and are likely the result of which accommodates unbalanced and complex pedigrees and pro- family-wise error. In fact, exactly 9% of tests were statistically signifi- vides more realistic estimates of trait heritability (i.e., free of overesti- cant, which is expected at the α = 0.10 level. Birth year may reflect a mation based on sibling, parent-offspring, or twin study designs). Four cohort effect or secular trends in morphological variation due to covariates were screened for significant effects: age, sex, age/sex changing environmental (i.e., lifestyle) conditions. Age, on the other interaction, and birth year. Significance of covariates was assessed at hand, likely indexes scoring error related to dental attrition; the lack of the p < 0.10 level; the total effect of all significant covariates was significance for this variable suggests scoring error has been mini- recorded. All significant covariates were fixed in subsequent bivariate mized in this sample. For the sex covariate, 17% of p-values were sta- analyses (see Boehnke, Moll, Kottke, & Weidman, 1987; Falconer, tistically significant at the α = 0.10 level, which is beyond the 1989; Hopper & Mathews, 1982; Lange, Boehnke, & Opitz, 1983). expectations of family-wise error. Many of these significant results Bivariate analyses (SOLAR v.8.1.1) were used to estimate additive were isolated and inconsistent across sides/breakpoints and likely 2 1 genetic (ρG) and environmental (ρE) correlations between pair-wise com- spurious. However, the results for RM hypocone, LM Carabelli's binations of traits (see Almasy, Dyer, & Blangero, 1997; Blangero, trait, RM2 cusp 6, and RM1 cusp 7 suggest a real phenomenon is cap- Konigsberg, & Vogler, 1991; Hlusko & Mahaney, 2007; Hlukso et al., tured. These results are consistent with previous research document- 2004; Mahaney et al., 1995). Likelihood ratio tests were then used to ing sexual dimorphism in Carabelli's trait expression in some assess whether the genetic and environmental correlations were populations (Townsend & Brown, 1981; Tsai, Hsu, Lin, & Liu, 1996), 610 STOJANOWSKI ET AL.

TABLE 1 Gullah sample heritability estimates: Postcanine crown morphology

Heritability Covariates Ageg Sexg Age*sexg Birth yearg Traita Nb Kc h2d p-valued SEe c2f p-value p-value p-value p-value

LM1 META CONT 258 0.51 0.000 0.500 — 0.008 0.108 0.952 0.561 0.092 BP 3 (99.3) 258 — 0.000 0.500 — 0.000 0.774 0.315 0.233 — BP 3.5 (97.9) 258 — 0.000 0.500 — 0.000 0.896 0.936 0.195 0.935 BP 4 (95.8) 288 — 0.474 0.261 0.810 0.000 0.191 0.962 0.237 — BP 5 (24.7) 288 — 0.095 0.273 0.175 0.000 0.330 0.819 0.956 —

RM1 META CONT 291 2.04* 0.000 0.500 — 0.000 0.502 0.712 0.873 0.522 BP 3 (99.0) 291 — 0.946 0.073 0.719 0.000 0.719 0.726 0.422 — BP 3.5 (96.9) 291 — 0.000 0.500 — 0.000 0.635 0.251 0.546 0.649 BP 4 (93.5) 291 — 0.263 0.217 0.084 0.000 0.634 0.887 0.595 0.597 BP 5 (14.8) 291 — 0.000 0.500 — 0.000 0.896 0.735 1.000 —

LM2 META CONT 94 1.04* 0.444 0.047 0.274 0.000 0.904 0.948 0.301 0.967 BP 3.5 (94.7)94 — 0.000 0.500 — 0.000 0.799 0.320 0.477 0.807 BP 4 (76.6)94 — 1.000 0.010 — 0.000 0.849 0.522 0.784 0.875 BP 5 (5.3) ———— ————— —

RM2 META CONT 90 1.90 0.146 0.265 0.251 0.001 0.390 0.226 0.017 0.483 BP 3.5 (96.1) 103 — 0.000 0.500 — 0.000 0.520 0.756 0.562 — BP 4 (79.6)90 — 0.552 0.121 0.517 <0.001 0.961 0.601 0.090 0.918 BP 5 (6.8)90— 0.000 0.500 — 0.366 0.033 0.020 0.972 —

LM1 HYPO CONT 297 0.00 0.435 <0.001 0.131 0.000 0.604 0.156 0.242 0.525 BP 3 (97.6) 268 — 0.000 0.500 — 0.018 0.892 0.328 <0.001 0.703 BP 3.5 (93.3) 267 — 0.000 0.500 — 0.006 0.909 0.061 0.043 0.632 BP 4 (68.7) 298 — 0.669 <0.001 0.219 0.000 0.669 0.159 0.964 0.605 BP 5 (14.1) 268 — 0.657 0.001 0.245 0.003 0.812 0.615 0.057 0.745

RM1 HYPO CONT 294 −0.21 0.144 0.058 0.105 0.000 0.934 0.254 0.794 0.978 BP 3 (98.6) 294 — 0.000 0.500 — 0.113 1.000 <0.001 0.747 — BP 3.5 (97.3) 294 — 0.000 0.500 — 0.000 0.789 0.539 0.594 — BP 4 (73.1) 294 — 0.230 0.062 0.117 0.000 0.825 0.488 0.168 0.797 BP 5 (18.7) 294 — 0.379 0.027 0.225 0.009 0.546 0.047 0.128 0.624

LM2 HYPO CONT 86 −0.22 0.323 0.082 0.246 0.043 0.329 0.132 0.014 0.315 BP 1 (96.8)95 — 0.000 0.500 — 0.000 0.999 0.179 1.000 — BP 2 (86.3)95 — 0.089 0.427 0.414 0.000 0.828 0.318 0.337 0.831 BP 3 (73.7)86 — 0.313 0.223 0.440 0.028 0.758 0.564 0.043 0.795 BP 3.5 (53.7)86 — 0.435 0.154 0.456 0.045 0.993 0.357 0.028 1.000 BP 4 (22.1)95 — 0.493 0.156 0526 0.000 0.419 0.966 0.194 — BP 5 (2.1)95 — 1.000 0.263 — 0.181 0.865 0.024 1.000 —

RM2 HYPO CONT 85 −0.57 1.000 <0.001 — 0.034 0.074 0.007 0.731 0.087 BP 1 (92.6)85 — 0.816 0.151 0.749 0.220 0.070 0.477 0.648 — BP 2 (80.0)95 — 1.000 <0.001 — 0.000 0.534 0.877 0.740 — BP 3 (72.6)95 — 1.000 0.004 — 0.000 0.551 0.588 0.624 0.603 (Continues) STOJANOWSKI ET AL. 611

TABLE 1 (Continued)

Heritability Covariates Ageg Sexg Age*sexg Birth yearg Traita Nb Kc h2d p-valued SEe c2f p-value p-value p-value p-value BP 3.5 (50.5)95 — 0.651 0.053 0.362 0.000 0.152 0.772 0.281 — BP 4 (22.1)95 — 0.898 0.037 0.310 0.135 0.966 0.003 0.532 — BP 5 (5.3)85 — 1.000 0.083 — 0.127 0.005 0.018 0.217 0.005

LM1 C5 CONT 219 −0.68 0.108 0.162 0.122 0.000 0.333 0.297 0.641 0.385 BP 1 (51.1) 197 — 0.028 0.435 0.133 0.042 0.013 0.854 0.133 — BP 2 (26.9) 219 — 0.524 0.018 0.298 0.008 0.661 0.088 0.949 0.714 BP 3 (10.5) 219 — 0.098 0.393 0.328 0.000 0.893 0.172 0.520 — BP 4 (4.6) 219 — 0.000 0.500 — 0.000 0.489 0.347 0.362 0.485 BP 5 (1.4) 219 — 0.000 0.500 — 0.000 0.875 0.764 0.830 —

RM1 C5 CONT 210 −0.01 0.074 0.188 0.093 0.000 0.619 0.893 0.462 0.592 BP 1 (57.6) 210 — 0.137 0.182 0.170 0.000 0.725 0.765 0.316 0.764 BP 2 (32.9) 186 — 0.018 0.455 0.166 0.009 0.551 0.508 0.313 <0.001 BP 3 (16.7) 210 — 0.057 0.391 0.218 0.000 0.573 0.700 0.909 0.509 BP 4 (7.6) 210 — 0.000 0.500 — 0.000 0.797 0.306 0.609 0.756 BP 5 (1.0) 210 — 0.000 0.500 — 0.190 0.873 0.144 <0.001 —

LM2 C5 CONT 69 −0.78 0.866 0.002 0.293 0.000 0.495 0.739 0.683 0.508 BP 1 (47.8)69 — 1.000 0.014 — 0.005 0.007 0.494 0.812 0.926 BP 2 (29.0)69 — 1.000 0.007 — 0.000 0.516 0.955 0.124 — BP 3 (11.6)69 — 0.000 0.500 — 0.000 0.265 0.852 0.323 — BP 4 (4.3)69 — 0.000 0.500 — 0.000 0.387 0.342 0.681 — BP 5 (2.9)63 — 0.000 0.500 — 0.200 0.088 0.783 0.950 —

RM2 C5 CONT 63 −0.89 0.145 0.388 0.499 0.149 0.005 0.488 0.952 0.006 BP 1 (45.2)73 — 0.000 0.500 — 0.000 0.131 0.233 0.378 — BP 2 (26.0)72 — 0.833 0.056 0.843 0.000 0.792 0.294 0.222 — BP 3 (15.1)72 — 0.511 0.321 0.050 0.000 0.573 0.944 0.928 — BP 4 (5.5)72 — 0.000 0.500 — 0.000 0.469 0.657 0.789 —

LM1 CTRAIT CONT 298 −0.82 0.380 <0.001 0.117 0.043 0.784 0.002 0.100 0.808 BP 1 (62.8) 333 — 0.580 <0.001 0.102 0.013 0.870 0.023 0.186 0.845 BP 2 (42.9) 333 — 0.448 <0.001 0.172 0.015 0.936 0.006 0.270 — BP 3 (36.6) 333 — 0.508 <0.001 0.133 0.008 0.531 0.030 0.283 — BP 4 (29.4) 333 — 0.410 0.001 0.164 0.007 0.953 0.044 0.191 — BP 5 (19.8) 298 — 0.847 <0.001 0.254 0.091 0.989 <0.001 0.001 0.980 BP 6 (7.8) 333 — 0.310 0.113 0.391 0.000 0.907 0.192 0.365 0.821 BP 7 (5.1) 333 — 0.000 0.500 — 0.000 0.318 0.208 0.371 0.278

RM1 CTRAIT CONT 293 −0.73 0.266 0.003 0.121 0.057 0.060 0.245 0.181 0.073 BP 1 (61.2) 293 — 0.235 0.053 0.085 0.033 0.026 0.592 0.524 — BP 2 (42.1) 293 — 0.612 <0.001 0.222 0.028 0.564 0.181 0.033 — BP 3 (36.7) 293 — 0.653 <0.001 0.225 0.027 0.517 0.606 0.051 — BP 4 (30.4) 293 — 0.598 <0.001 0.215 0.043 0.262 0.138 0.013 — BP 5 (20.9) 293 — 0.492 0.003 0.230 0.044 0.262 0.045 0.055 — BP 6 (8.4) 335 — 0.691 0.008 0.345 0.000 0.644 0.248 0.229 0.600 BP 7 (5.7) 293 — 0.000 0.500 — 0.034 <0.001 0.149 0.280 0.310 (Continues) 612 STOJANOWSKI ET AL.

TABLE 1 (Continued)

Heritability Covariates Ageg Sexg Age*sexg Birth yearg Traita Nb Kc h2d p-valued SEe c2f p-value p-value p-value p-value

LM2 CTRAIT CONT 136 0.29 0.004 0.491 0.180 0.014 0.809 0.409 0.043 0.866 BP 1 (27.1) 136 — 0.202 0.265 0.351 0.010 0.980 0.377 0.026 0.951 BP 2 (9.0) 155 — 0.000 0.500 — 0.000 0.516 0.673 0.585 0.295 BP 3 (5.8) 136 — 0.000 0.500 — 0.060 0.637 0.515 0.087 0.127 BP 4 (3.2) 136 — 1.000 0.069 — 0.141 0.284 <0.001 0.001 <0.001 BP 5 (2.6) 136 — 1.000 0.291 — 0.214 0.931 0.008 <0.001 0.001 BP 6 (0.6) 155 — 0.000 0.500 — 0.000 0.770 0.166 1.000 —

RM2 CTRAIT CONT 160 0.33 0.000 0.500 — 0.000 0.345 0.407 0.326 0.374 BP 1 (28.8) 160 — 0.235 0.053 0.085 0.033 0.026 0.592 0.524 — BP 2 (8.8) 159 — 0.000 0.500 — 0.000 0.660 0.443 0.630 0.724 BP 3 (5.6) 159 — 0.000 0.500 — 0.000 0.677 0.611 0.594 0.740 BP 4 (4.4) 159 — 0.000 0.500 — 0.000 0.908 0.960 0.540 0.831 BP 5 (3.1) 159 — 0.000 0.500 — 0.000 0.690 0.835 0.721 0.658 BP 6 (1.9) 159 — 0.000 0.500 — 0.000 0.877 0.755 0.958 —

LM1 PARA CONT 298 147.74* 0.000 0.500 — 0.000 0.573 0.930 0.799 0.601 BP 1 (0.7) 298 — 0.000 0.500 — 0.001 0.321 0.004 0.271 0.561

RM1 PARA CONT 262 63.01* 0.000 0.500 — 0.003 0.021 0.339 0.498 0.754 BP 1 (1.7) 299 — 0.000 0.500 — 0.000 0.917 0.535 0.747 0.888

LM2 PARA CONT 100 88.05* 0.000 0.500 — 0.055 0.080 0.093 0.421 0.092 BP 1 (0.9) ———— ————— —

RM2 PARA CONT 120 54.78* 0.000 0.500 — 0.025 0.321 0.096 0.243 0.280 BP 1 (1.7) ———— ————— — h LP1 LINGC CONT 1 224 −0.67 0.000 0.500 — 0.011 0.130 0.073 0.903 0.125 CONT 2 224 −0.94 0.000 0.500 — 0.000 0.323 0.149 0.918 0.321 BP 2 224 — 0.000 0.500 — 0.000 0.803 0.159 0.892 — BP 3 224 — 0.117 0.323 0.252 0.000 0.630 0.355 0.660 0.660 h RP1 LINGC CONT 1 209 −0.74 0.046 0.351 0.127 0.000 0.891 0.234 0.547 0.857 CONT 2 209 −0.88 0.000 0.500 — 0.000 0.763 0.258 0.473 0.738 BP 2 209 — 0.004 0.492 0.148 0.000 0.768 0.253 0.749 0.725 BP 3 209 — 0.000 0.500 — 0.000 0.939 0.446 0.124 0.961 h LP2 LINGC CONT 1 195 −1.14 0.052 0.337 0.130 0.000 0.155 0.396 0.606 0.179 CONT 2 195 −1.00 0.000 0.500 — 0.000 0.283 0.601 0.742 0.327 BP 2 195 — 0.000 0.500 — 0.007 0.469 0.513 1.000 0.030 BP 3 195 — 0.000 0.500 — 0.000 0.242 0.689 0.553 0.364 h RP2 LINGC CONT 1 168 −1.13 0.101 0.215 0.140 0.009 0.984 0.345 0.012 0.883 CONT 2 168 −1.13 0.147 0.126 0.147 0.002 0.978 0.431 0.020 0.828 BP 2 168 — 0.250 0.097 0.285 0.003 0.299 0.203 0.006 0.409 BP 3 191 — 0.427 0.065 0.333 0.000 0.102 0.889 0.343 — (Continues) STOJANOWSKI ET AL. 613

TABLE 1 (Continued)

Heritability Covariates Ageg Sexg Age*sexg Birth yearg Traita Nb Kc h2d p-valued SEe c2f p-value p-value p-value p-value

LM1 AFOV CONT 214 −0.35 0.338 0.001 0.139 0.030 0.046 0.899 0.429 0.051 BP 1 (99.1) 214 — 0.000 0.500 — 0.176 0.821 0.063 0.096 — BP 2 (96.2) 235 — 0.000 0.500 — 0.000 0.622 0.415 0.138 — BP 3 (65.1) 235 — 0.260 0.054 0.188 0.000 0.827 0.950 0.993 — BP 4 (16.6) 235 — 0.721 <0.001 0.247 0.000 0.333 0.966 0.540 —

RM1 AFOV CONT 221 −0.34 0.428 <0.001 0.142 0.000 0.635 0.108 0.775 0.668 BP 1 (99.5) 222 — 0.000 0.500 — 0.000 0.986 0.150 0.995 — BP 2 (95.9) 222 — 0.000 0.500 — 0.000 0.679 0.134 0.592 — BP 3 (62.9) 222 — 0.509 0.004 0.240 0.016 0.531 0.023 0.996 0.572 BP 4 (15.8) 222 — 0.806 0.002 0.180 0.000 0.710 0.937 0.730 0.697

LM1 C5 CONT 199 −0.56 0.292 0.007 0.143 0.000 0.862 0.417 0.302 0.861 BP 3 (98.0) 199 — 0.000 0.500 — 0.000 0.241 0.355 0.651 — BP 4 (83.9) 199 — 0.530 0.012 0.247 0.000 0.470 0.464 0.946 — BP 5 (33.7) 199 — 0.226 0.133 0.230 0.012 0.499 0.036 0.308 0.501

RM1 C5 CONT 209 −0.47 0.149 0.118 0.142 0.000 0.610 0.207 0.567 0.643 BP 1 (99.5) 209 — 0.188 0.469 2.113 0.000 0.131 0.612 0.510 — BP 2 (99.0) 210 — 0.676 0.340 1.240 0.000 0.175 0.836 0.739 — BP 3 (97.6) 210 — 0.190 0.449 1.354 0.000 0.491 0.471 0.927 — BP 4 (81.8) 210 — 0.147 0.309 1.592 0.000 0.893 0.787 0.370 — BP 5 (30.6) 210 — 0.177 0.157 0.205 0.017 0.990 0.034 0.407 0.958

LM2 C5 CONT 90 −0.94 0.106 0.325 0.245 0.000 0.812 0.818 0.851 0.787 BP 1 (68.9)78 — 1.000 0.002 — 0.076 0.004 0.991 0.778 — BP 2 (64.4)90 — 0.810 0.019 0.383 0.000 0.188 0.896 0.543 — BP 3 (43.3)90 — 0.328 0.212 0.497 0.000 0.584 0.970 0.881 0.593 BP 4 (23.3)90 — 0.000 0.500 — 0.000 1.000 0.805 1.000 — BP 5 (6.7)78— 0.000 0.500 — 0.077 0.144 0.639 0.494 0.017

RM2 C5 CONT 85 −0.95 0.391 0.039 0.246 0.000 0.722 0.408 0.429 0.691 BP 1 (64.7)85 — 0.355 0.180 0.409 0.000 0.823 0.177 0.492 0.747 BP 2 (62.4)85 — 0.303 0.174 0.343 0.000 0.712 0.137 0.480 0.638 BP 3 (38.8)85 — 0.632 0.061 0.420 0.000 0.608 0.757 0.188 0.602 BP 4 (22.4)85 — 0.683 0.050 0.422 0.000 0.374 0.678 0.452 — BP 5 (4.7)85 — 0.841 0.160 0.776 0.000 0.506 0.906 0.736 —

LM1 C6 CONT 153 0.56 0.428 0.002 0.166 0.007 0.230 0.622 0.084 0.261 BP 1 (20.4) 153 — 0.556 0.032 0.343 0.016 0.270 0.437 0.059 — BP 2 (13.8) 167 — 0.869 0.001 1.115 0.000 0.184 0.578 0.164 — BP 3 (9.0) 167 — 0.840 0.006 0.467 0.000 0.924 0.363 0.150 —

RM1 C6 CONT 174 0.40 0.111 0.212 0.155 0.000 0.679 0.150 0.715 0.688 BP 1 (73.6) 174 — 0.415 0.086 0.350 0.000 0.945 0.550 0.598 0.926 BP 2 (16.7) 174 — 0.035 0.449 0.291 0.048 0.699 0.005 0.554 — BP 3 (4.6) 174 — 0.000 0.500 — 0.084 0.367 0.025 — 0.344 (Continues) 614 STOJANOWSKI ET AL.

TABLE 1 (Continued)

Heritability Covariates Ageg Sexg Age*sexg Birth yearg Traita Nb Kc h2d p-valued SEe c2f p-value p-value p-value p-value

LM2 C6 CONT 85 1.52* 0.000 0.500 — 0.000 0.788 0.146 0.163 0.733 BP 1 (18.8)73 — 0.000 0.500 — 0.007 0.037 0.134 0.108 0.821 BP 2 (17.6)85 — 0.000 0.500 — 0.045 0.124 0.078 0.144 — BP 3 (8.2)85 — 0.437 0.266 0.766 0.000 0.544 0.510 0.724 0.577

RM2 C6 CONT 69 1.29* 0.094 0.392 0.346 0.161 0.049 0.075 0.306 0.059 BP 1 (17.7)79 — 0.792 0.135 0.683 0.045 0.132 0.032 0.915 — BP 2 (13.9)79 — 0.000 0.500 — 0.066 0.104 0.046 0.944 — BP 3 (8.9)79 — 0.000 0.500 — 0.049 0.316 0.048 0.267 — i LM1 C7 CONT 192 −1.06 0.142 0.136 0.144 0.015 0.310 0.628 0.008 0.259 BP 1 (40.0) 192 — 0.039 0.430 0.226 0.009 0.475 0.460 0.024 0.411 BP 2 (35.3) 192 — 0.145 0.255 0.220 0.009 0.267 0.806 0.006 0.206 BP 3 (21.4) 192 — 0.306 0.100 0.277 0.007 0.727 0.961 0.016 0.598 BP 4 (13.5) 192 — 0.198 0.252 0.317 0.017 0.354 0.856 0.028 0.300 i RM1 C7 CONT 216 −0.70 0.070 0.239 0.107 0.012 0.670 0.071 0.470 0.686 BP 1 (38.9) 215 — 0.169 0.167 0.210 0.000 0.798 0.394 0.506 0.803 BP 2 (29.6) 215 — 0.214 0.120 0.211 0.012 0.899 0.045 0.588 — BP 3 (21.3) 118 — 0.000 0.500 — 0.013 0.377 0.026 0.193 0.196 BP 4 (11.6) 118 — 0.000 0.500 — 0.000 0.603 0.459 0.197 0.918 i LM2 C7 CONT 100 2.33* 0.238 0.152 0.243 0.000 0.750 0.815 0.361 0.718 BP 1 (17.0) 100 — 0.440 0.205 0.567 0.000 1.000 0.823 0.413 1.000 BP 2 (14.0) 100 — 0.933 0.024 0.433 0.000 0.792 0.501 0.776 0.802 BP 3 (9.0) 100 — 0.760 0.102 0.510 0.000 0.317 0.634 0.426 — BP 4 (5.0)85 — 0.839 0.234 1.043 0.069 0.075 0.609 0.329 — i RM2 C7 CONT 118 2.84* 0.311 0.056 0.209 0.000 0.982 0.705 0.773 0.959 BP 1 (16.1) 103 — 1.000 0.009 — 0.015 0.026 0.944 0.696 0.862 BP 2 (7.6) 118 — 0.000 0.500 — 0.000 0.991 0.602 0.561 0.888 BP 3 (4.2) 118 — 0.000 0.500 — 0.013 0.379 0.026 0.193 0.196 BP 4 (2.5) 118 — 0.000 0.500 — 0.000 0.603 0.459 0.197 0.918 j LM1 CNO BP 6 168 — 0.278 0.155 0.312 0.000 0.332 0.319 0.102 — j RM1 CNO BP 6 174 — 0.419 0.099 1.364 0.000 0.743 0.378 0.596 0.728 j LM2 CNO CONT 85 −1.07 0.284 0.151 0.300 0.000 0.212 0.677 0.479 0.177 BP 5 73 — 0.868 0.049 0.514 0.057 0.072 0.305 0.875 — BP 6 73 — 0.000 0.500 — 0.006 <0.001 0.167 0.148 0.694 j RM2 CNO CONT 80 −1.04 0.247 0.212 0.340 0.000 0.396 0.199 0.976 0.415 BP 5 80 — 0.100 0.402 0.427 0.000 0.893 0.351 0.998 0.866 BP 6 71 — 0.688 0.170 0.709 0.027 0.571 0.053 0.807 —

LM1 DWRINK CONT 188 −0.87 0.081 0.236 0.121 0.000 0.872 0.126 0.159 0.828 BP 1 (37.8) 188 — 0.096 0.295 0.566 0.000 0.632 0.407 0.333 0.640 (Continues) STOJANOWSKI ET AL. 615

TABLE 1 (Continued)

Heritability Covariates Ageg Sexg Age*sexg Birth yearg Traita Nb Kc h2d p-valued SEe c2f p-value p-value p-value p-value BP 2 (29.3) 188 — 0.185 0.190 0.226 0.000 0.977 0.330 0.338 0.972 BP 3 (13.8) 168 — 0.323 0.149 0.354 0.065 0.139 0.010 0.037 —

RM1 DWRINK CONT 173 −1.43 0.000 0.500 — 0.000 0.324 0.214 0.728 0.396 BP 1 (48.0) 173 — 0.000 0.500 — 0.000 0.368 0.516 0.416 0.454 BP 2 (39.9) 173 — 0.000 0.500 — 0.000 0.241 0.325 0.823 0.284 BP 3 (23.1) 173 — 0.122 0.318 0.273 0.030 0.284 0.039 0.197 0.423 k LM1 GROOVE BP X (12.1) 214 — 0.151 0.269 0.275 0.000 0.509 0.649 0.748 0.527 BP Y (84.1) 214 — 0.295 0.099 0.260 0.000 0.626 0.554 0.725 0.625 BP + (3.7) 214 — 0.000 0.500 — 0.000 0.970 0.352 0.413 0.980 k RM1 GROOVE BP X (20.7) 208 — 0.000 0.500 — 0.000 0.789 0.457 0.826 0.811 BP Y (65.9) 208 — 0.030 0.441 0.209 0.000 0.988 0.965 0.831 0.997 BP + (13.5) 208 — 0.139 0.334 0.123 0.000 0.803 0.356 0.656 0.849 k LM2 GROOVE BP X (15.6) 109 — 0.683 0.107 0.556 0.058 0.374 0.041 0.538 — BP Y (23.9) 109 — 0.387 0.186 1.412 0.000 0.862 0.785 0.389 0.801 BP + (60.6) 109 — 0.505 0.082 0.491 0.000 0.119 0.181 0.379 — k RM2 GROOVE BP X (13.0) 108 — 0.000 0.500 0.001 0.000 0.819 0.240 0.243 — BP Y (20.4) 108 — 0.173 0.359 0.489 0.000 0.641 0.562 0.587 0.672 BP + (66.7) 108 — 0.560 0.102 0.999 0.000 0.327 0.228 0.946 —

LM1 PROTO CONT 238 9.29* 0.123 0.078 0.101 0.000 0.676 0.415 0.375 0.750 BP 1 (8.0) 238 — 0.432 0.057 0.204 0.000 0.722 0.563 0.515 0.781

RM1 PROTO CONT 243 12.09* 0.070 0.167 0.080 0.000 0.766 0.413 0.711 0.642 BP 1 (6.6) 243 — 0.301 0.136 0.316 0.000 0.919 0.476 0.778 0.832

LM2 PROTO CONT 128 15.14* 0.094 0.329 0.227 0.000 0.971 0.539 0.646 0.962 BP 1 (5.5) 128 — 0.380 0.305 0.534 0.000 0.974 0.491 0.713 0.981

RM2 PROTO CONT 131 8.49* 0.360 0.020 0.214 0.000 0.424 0.774 0.789 0.404 BP 1 (8.4) 131 — 1.000 0.017 — 0.000 0.489 0.854 0.931 0.467 a L = left; R = right; P = premolar; M = molar. Maxillary and mandibular traits indicated by superscript and subscript, respectively. META = metacone; HYPO = hypocone; C = cusp; CTRAIT = Carabelli's trait; PARA = parastyle; LINGC = lingual cusp variation; AFOV = anterior fovea; CNO = cusp num- ber; DWRINK = deflecting wrinkle; GROOVE = groove pattern; PROTO = protostylid; CONT = trait treated as a continuous variable; CONT 1 = premo- lar lingual cusp variation treated as a continuous variable across all possible ASUDAS grades; CONT 2 = premolar lingual cusp variation treated as a continuous variable based on lingual cusp number (1 cusp, 2 cusp, or 3 cusp); BP = dichotomization breakpoint when trait treated as a binary variable. Monomorphic breakpoints and traits/breakpoints with extremely low frequencies (see Supporting Information Table S2) were omitted from the analyses. Presence/absence trait frequencies are presented in italics and parentheses for each breakpoint. Dashes are associated with incalculable parameter esti- mates. Models whose entire set of parameters are marked with dashes failed to converge. b N = sample size for heritability estimation. c K = model kurtosis value. Asterisks indicate a violation of kurtosis assumptions. These model results should be interpreted with caution. d h2 = total heritability estimate (MLE). All significant heritability estimates (p−value < 0.050) and associated probability value estimates are bolded. e SE = standard error estimate (MLE). f c2 = total covariate estimate (MLE). g All significant probability value estimates (p-value < 0.100) for the covariates of age, sex, age/sex interaction, and birth year are bolded. h Grade 1 interpreted as missing data for premolar lingual cusp variables. For the quantitative genetic analyses, breakpoints for this trait were basedon cusp number only. For this reason, frequency data are not presented. See Supporting Information Table S2 for frequencies based on dichotomized ASU- DAS scores. i Grade 1A interpreted as missing data for cusp 7 variables. j See mandibular molar cusp 5 and 6 frequencies. k Molar groove pattern was treated as three separate presence/absence traits (Y versus non-Y, X versus non-X, + versus non-plus). 616 STOJANOWSKI ET AL. and suggest that the expression of other cusp variants is sexually of which were not significantly different from zero. This is in sharp con- dimorphic. This may require reconsideration of the pooling of sexes in trast to the genetic correlations among antimeres for mesiodistal dental biodistance analyses, but even in this sample the effect was dimensions (Stojanowski et al., 2017) and anterior tooth crown variants not consistent across antimeres. (Stojanowski et al., 2018). The same is true for the phenotypic correla- Heritabilities were moderate in magnitude and generally compa- tions which were, on average, 0.628 for postcanine traits (inclusive of rable to previously reported estimates based on analyses of other M2s), 0.708 for anterior tooth crown traits (Stojanowski et al., 2018), populations, contrary to results reported for anterior tooth crown data and 0.799 for mesiodistal dimensions (Stojanowski et al., 2017). That in the Gullah (Stojanowski et al., 2018). The best index of comparison postcanine morphology demonstrates the least antimeric symmetry and is Carabelli's trait, which returned significant heritability estimates at overlap in additive genetic contribution might suggest a greater poten- nearly all breakpoints with the maximum left (0.847) and right (0.691) tial effect of environmental variance on trait expression. side estimates comparable to previous studies of European and Asian Genetic correlations for metameres are presented in Table 3 for samples (reviewed in Scott et al., 2018). Average heritability by tooth those traits scored on both the M1 and M2. The small sample sizes for type for all statistically significant estimates was: M1 = 0.621, observable M2s significantly limits the utility of these analyses, how- 2 M = 0.882, M1 = 0.707, M2 = 0.870. The average for all statistically ever. Significant p-values are infrequent but suggest complete pleiot- significant estimates across tooth types and arcades was 0.748. The ropy for some hypocone and M1 cusp 5 comparisons. In general, the M2 (both maxillary and mandibular) heritabilities are likely spuriously correlations are positive, many equaling or approaching 1.0, which sug- high, resulting from small sample sizes. As such, these results should gests the same genes are implicated in the formation and size of pri- be considered preliminary and provide limited basis for comparing M1 mary and secondary cusps of the first and second maxillary molar and M2 estimates. We note that all molar averages are considerably crowns. The lack of consistency across sides and breakpoints indicates higher than those we previously reported for anterior tooth crown caution is needed; results should not be over interpreted. None of the variants, which averaged ~0.340 across all statistically significant esti- observed negative correlations are significantly different from zero and mates (Stojanowski et al., 2018). These differences are unlikely to be should be considered spurious until confirmed with additional data. statistically different given the large standard errors associated with In Table 4 we present the results of the genetic correlation ana- these estimates. A number of molar traits are also characterized by lyses for traits scored on the same tooth crown. These data test the heritabilities that were not significantly different from 0.0 for any assumption of trait independence, which is now generally recognized breakpoint (M1 metacone, M2 Carabelli's trait, M1 parastyle, M2 para- as problematic given our understanding of multicuspid crown devel- * style, P1 lingual cusp number, P2 lingual cusp number, M2 cusp 6 ,M1 opment. Following standard protocol, the issue of genetic redundancy cusp 7, M1 cusp number, M1 deflecting wrinkle, M1 groove pattern, is instead ameliorated through the use of key teeth for ASUDAS data * * M2 groove pattern, M1 protostylid ; indicates kurtosis violation), in collection or through trait omission based on post hoc phenotypic cor- contrast with the anterior dentition for which only three traits failed relations (Scott et al., 2018; Turner et al., 1991). Unfortunately, sample to produce statistically significant heritability estimates (Stojanowski sizes for the M2s were too small to produce interpretable results. In et al., 2018). This difference could reflect variation in the way the addition, parastyle data were removed, because the trait was molar traits are scored and the limited variation that results from the extremely infrequent in this dataset, rendering most results meaning- scoring protocol. For example, it is rare to have an M1 metacone less. Comparing left-side M1 crown traits to the mesiodistal dimension scored less than four, thus compressing the range of variation to only indicates that cusp 5 and Carabelli's trait are not genetically correlated two scores (4 and 5) for most individuals. Regardless, scoring scale with molar crown length; the underpowered metacone results suggest does not explain all traits that returned zero heritability estimates (for a similar interpretation. Mesiodistal diameter and hypocone size are example LM1 cusp 6 and 7). incompletely pleiotropic, which is as expected given that mesiodistal Another difference between the postcanine morphology and length is, in part, determined by hypocone presence and size. In other anterior morphology results was the degree of asymmetry in the post- words, there is some overlap in the genes responsible for mesiodistal canine heritability estimates. There were many traits for which at least tooth size, the size of primary molar cusps, and the presence and size one left-side estimate was significantly different from zero and the of secondary molar cusps. None of the right-side comparisons pro- corresponding right-side estimates were not (M2 metacone*,M1 cusp duced significant p-values, which we interpret as reflecting a higher 2 * 5, M cusp 5, M1 cusp 5, M1 cusp 6, M2 cusp number; indicates kur- than expected degree of asymmetry in this sample. tosis violation). For traits for which both sides returned a significant Genetic correlations among maxillary morphological traits heritability estimate, there was also a tendency for the left-side esti- returned two significant p-values, indicating complete pleiotropy mate to be higher than the corresponding right-side estimate (M1 between metacone and Carabelli's trait and between hypocone and 1 hypocone [left higher], M Carabelli's trait [left higher], M1 anterior Carabelli's trait. Other trait comparisons returned moderate to high * fovea [right higher], M2 cusp 5 [left higher], M2 cusp 7 [right higher] ; positive genetic correlations; however, p-values were not significant, *indicates kurtosis violation). Given that additive genetic variance is which in most cases indicated a lack of power. These results call into held constant for these comparisons, the reduction in heritability on question the assumption of genetic independence for these traits. Once the right-side suggests an environmental effect is evident, which rep- again, none of the right-side comparisons produced a significant p-value. resents directional asymmetry in this dataset. The greater number of traits scored on mandibular molars makes Asymmetry among antimeres is also indicated by estimates of interpreting these results more challenging. Comparisons involving genetic correlation (Table 2), which were not uniformly high and many the M1 mesiodistal dimension and crown features returned significant STOJANOWSKI ET AL. 617

TABLE 2 Gullah sample antimeric (left–right) variance components correlations: Crown morphology

Genetic Environmental Phenotypic a b c d d e d f Trait (BP) N; Cov/K ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP

M1 META (4) 332; K 0.776 ± 0.612 0.368 0.359 −0.092 ± 0.960 0.919 0.339

M2 META (4) 116; A*S 0.582 ± 0.528 0.069 0.284 −0.053 ± 1.039 1.000 0.411

M1 HYPO (4) 340; K 1.000 ± —** <0.001 — 1.000 ± — 0.004 0.880

M1 HYPO (5) 300; A*S, S 0.781 ± 0.272** 0.028 0.217 0.643 ± 0.307 0.113 0.684

M2 HYPO (4) 126; S 1.000 ± —** 0.018 — −0.277 ± 1.326 0.913 0.829

M1 C5 (2) 243; B, S 1.000 ± — 0.073 — 0.367 ± 1.065 0.323 0.504

M2 C5 (C) 88; A, B 1.000 ± — 0.065 — −0.407 ± 0.884 0.560 0.323

M2 C5 (2) 101 1.000 ± —** 0.001 — −1.000 ± — 0.159 0.574

M1 CTRAIT (C) 326; A, S 1.000 ± —** <0.001 — 0.659 ± 0.055 <0.001 0.766

M1 CTRAIT (5) 326; A*S, S 1.000 ± —** <0.001 — 0.624 ± 1.007 0.228 0.829

M2 CTRAIT (1) 162; A, A*S 0.179 ± 0.936 1.000 1.000 0.616 ± 0.117 0.021 0.616

M1 PARA —— ——— ——

M2 PARA —— ——— ——

P1 LINGC —— ——— ——

P2 LINGC (C1) 211; A*S 1.000 ± — 0.139 — 0.475 ± 0.096 0.003 0.543

M1 AFOV (C) 244; A, B 0.734 ± 0.218** 0.011 0.084 0.405 ± 0.139 0.026 0.527

M1 AFOV (4) 271 0.576 ± 0.713* 0.027 0.012 1.000 ± — 0.254 0.672

M1 C5 (C) 225 1.000 ± —** 0.036 0.413 0.288 ± 0.108 0.023 0.413

M1 C5 (4) 256 1.000 ± —** 0.027 0.457 0.156 ± 0.323 0.649 0.457

M2 C5 (C) 120 1.000 ± — 0.213 — 0.799 ± 0.083 <0.001 0.775

M2 C5 (2) 120 0.962 ± 0.513 0.140 0.471 1.000 ± — 0.029 0.961

M1 C6 (1) 202; A*S 0.618 ± 0.836 0.127 0.084 1.000 ± — 0.297 0.700

M2 C6 —— ——— ——

M1 C7 (2) 231; A*S, S 1.000 ± —** 0.020 — 0.393 ± 1.161 0.236 0.609

M2 C7 (1) 123; A, K 0.896 ± 0.999 0.201 0.451 1.000 ± — 0.566 0.661

M1 CNO (6) 225 1.000 ± — 0.143 — 0.061 ± 4.005 0.774 0.251

M2 CNO (C) 114 1.000 ± — 0.599 — 0.709 ± 0.221 0.004 0.627

M2 CNO (5) 97; A 1.000 ± — 0.127 — 1.000 ± — 0.111 0.994

M1 DWRINK (3) 206; A*S, S −0.621 ± 1.002 0.566 0.422 1.000 ± — 0.007 0.607

M1 GROOVE (Y) 260 1.000 ± — 0.559 — 0.246 ± 0.866 0.317 0.301

M2 GROOVE (Y) 148 1.000 ± — 0.280 — 0.626 ± 0.606 0.209 0.764

M2 GROOVE (+) 148 0.823 ± 0.459 0.143 0.352 0.837 ± 0.549 0.219 0.825

M1 PROTO (1) 284, K 1.000 ± —** 0.029 — 0.631 ± 0.404 0.123 0.774

M2 PROTO (1) 168, K 1.000 ± —** 0.047 0.511 −1.000 ± — 0.442 0.511 a P = premolar; M = molar. Maxillary and mandibular traits indicated by superscript and subscript, respectively. META = metacone; HYPO = hypocone; C = cusp; CTRAIT = Carabelli's trait; PARA = parastyle; LINGC = lingual cusp variation; AFOV = anterior fovea; CNO = cusp number; DWRINK = deflecting wrinkle; GROOVE = groove pattern; PROTO = protostylid; BP = dichotomization breakpoint when trait treated as a binary variable; C = trait treated as a continuous variable; C1 = premolar lingual cusp variation treated as a continuous variable across all possible ASUDAS grades. Dashes are associated with incalculable parameter estimates. Models whose entire set of parameters are marked with dashes had no comparable breakpoints to compare across antimeres (i.e., breakpoint h2 estimates for the left and/or right-side are 0.0). b N = correlation analysis sample size; Cov = significant covariates (fixed in the correlation analyses); K = kurtosis violation, results should be interpreted with caution; A = age; B = birth; A*S = age/sex interaction; S = sex. c Maximum-likelihood estimate of genetic correlation. Cases of incomplete pleiotropy indicated by a single asterisks. Cases of complete pleiotropy indi- cated by two asterisks. d Probability of hypothesis (as indicated in parentheses) being true given pedigree structure with values p < .050 bolded. e Maximum-likelihood estimate of environmental correlation. f Maximum-likelihood estimate of derived phenotypic correlation. p-values only for cusp 5, indicating complete pleiotropy. Results for y accessory cusps but cause opposing phenotypic effects. In other groove pattern, anterior fovea, and deflecting wrinkle were also posi- words, genes that increase tooth size decrease the presence or size of tive, though underpowered. The most surprising result was the consis- accessory, but not primary, cusps. Comparison among morphological tent finding of negative genetic correlations between tooth size and features affirms this result. All correlations involving cusp 5 (at two cusp 6, cusp 7, and cusp number. Although these correlations were different break point values) returned negative genetic correlations, also underpowered, the negative correlations suggest the same genes including significantly negative correlations in the case of cusp 6. That underlie the expression of crown length and the presence of is, the same genes that increase the size of cusp 5 work to reduce the 618 STOJANOWSKI ET AL.

TABLE 3 Gullah sample metameric homologue variance components correlations: Crown morphology

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP METACONE

LM1 (4)

LM2 (4) 300 −0.401 ± 3.952 0.581 0.350 1.000 ± — 0.384 0.059 a*s RM1 (4)

RM2 (4) 268 1.000 ± — 0.073 — −0.760 ± 1.045 0.409 0.282 HYPOCONE

LM1 (4) LM2 (4) 307 1.000 ± —** 0.038 — −1.000 ± — 0.078 0.022 a*s, s LM1 (5)

LM2 (5) 276 1.000 ± —** 0.036 — −0.449 ± 1.362 0.970 0.822 s RM1 (4)

RM2 (4) 307 1.000 ± —** 0.007 — −1.000 ± — 0.299 0.213 a, b, s RM1 (5)

RM2 (5) 271 1.000 ± — 0.155 — −1.000 ± — 0.201 0.155 CUSP 5

LM1 (C)

LM2 (C) 236 1.000 ± —** 0.023 — −0.226 ± 0.388 0.499 0.187 s LM1 (2)

LM2 (2) 236 1.000 ± —** 0.018 — −1.000 ± — 0.307 0.395 a,b RM1 (C)

RM2 (C) 202 1.000 ± — 0.101 — −0.394 ± 0.149 0.345 −0.051 b RM1 (2)

RM2 (2) 202 1.000 ± — 0.138 — −1.000 ± — 0.204 −0.038 CARABELLI'S TRAIT a*s, s LM1 (C)

LM2 (C) 308 0.572 ± 0.776 0.439 0.404 0.507 ± 0.119 <0.001 0.468 a*s, s LM1 (1)

LM2 (1) 308 0.632 ± 0.552 0.291 0.335 0.612 ± 0.246 0.040 0.593 a*s, b, s LM1 (4)

LM2 (4) 308 1.000 ± —** 0.035 — 1.000 ± — 0.216 0.993 a*s, b, s LM1 (5)

LM2 (5) 308 1.000 ± —** 0.009 — 1.000 ± — 0.699 0.986 a RM1 (1)

RM2 (1) 308 1.000 ± — 0.078 — 0.389 ± 1.000 0.101 0.519 CUSP NUMBER a LM1 (6)

LM2 (5) 186 −0.123 ± 0.992 0.879 0.269 1.000 ± — 0.159 0.446

RM1 (6)

RM2 (5) 215 −1.000 ± — 0.822 — 0.135 ± 0.339 0.635 0.095 GROOVE PATTERN

LM1 (Y)

LM2 (Y) 260 0.281 ± 0.765 0.712 0.227 −0.032 ± 0.437 0.943 0.075 s LM1 (X)

LM2 (X) 260 0.005 ± 0.852 0.996 0.215 0.601 ± 0.697 0.366 0.305

RM1 (Y)

RM2 (Y) 258 1.000 ± — 0.588 — −0.216 ± 7.523 0.539 −0.090

RM1 (+)

RM2 (+) 258 1.000 ± — 0.204 — −0.444 ± 1.141 0.526 0.134 (Continues) STOJANOWSKI ET AL. 619

TABLE 3 (Continued)

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP PROTOSTYLID

LM1 (1)

LM2 (1) 285 1.000 ± —** 0.040 — −0.680 ± 0.877 0.331 0.156

RM1 (1)

RM2 (1) 297 0.236 ± 1.004 0.703 0.127 1.000 ± — 0.130 0.575 CUSP 5

LM1 (C)

LM2 (C) 241 0.551 ± 0.909 0.456 0.379 −0.077 ± 0.226 0.732 0.034

RM1 (2)

RM2 (2) 249 −1.000 ± — 0.405 — −1.000 ± — 0.444 −0.998 CUSP 6

LM1 (3)

LM2 (3) 206 0.626 ± 0.831 0.171 0.248 1.000 ± — 0.410 0.691 s RM1 (1)

RM2 (1) 216 0.568 ± 0.494 0.281 0.195 −0.240 ± 1.570 0.848 0.273 CUSP 7 a*s LM1 (2)

LM2 (2) 223 0.539 ± 0.801 0.526 0.301 0.596 ± 0.503 0.248 0.551 a*s LM1 (3)

LM2 (3) 223 1.000 ± — 0.390 0.214 1.000 ± — 0.116 0.813 a RM1 (1)

RM2 (1) 236 0.635 ± 1.005 0.292 0.301 0.912 ± — 0.831 0.314 a RM1 (2)

RM2 (2) 236 1.000 ± — 0.141 — −0.451 ± 1.086 0.413 0.029 a L = left; R = right; M = molar. Maxillary and mandibular traits indicated by numbered superscript and subscript, respectively. BP = dichotomization breakpoint when trait treated as a binary variable; C = trait treated as a continuous variable. Dashes are associated with incalculable parameter estimates. Superscript abbreviations indicate fixed covariates in the model. A = age; A*S = age/sex interaction; B = birth; S = sex. b Maximum-likelihood estimate of genetic correlation. Cases of incomplete pleiotropy indicated by a single asterisks. Cases of complete pleiotropy indi- cated by two asterisks. c Probability of hypothesis (as indicated in parentheses) being true given pedigree structure with values p < .050 bolded. d Maximum-likelihood estimate of environmental correlation. e Maximum-likelihood estimate of derived phenotypic correlation. size of cusp 6 (and to a lesser extent cusp 7). Remaining comparisons cusps, and the presence of most accessory crown features. That is, the were all underpowered, and any significant p-values are associated genes responsible for a y configuration work to reduce the presence of with genetic correlations of 1.0, which are suspect. all other minor anatomical variants, including accessory cusps, while the There is, however, a potentially significant relationship between genes responsible for a + configuration work in concert to produce a groove pattern and other crown features. Because we used the variant more architecturally complex, cuspidate molar crown. Though under- that yielded the highest univariate heritability estimate for subsequent powered, univariate tests support this interpretation, with y form crowns exhibiting significantly lower cusp number (p = 0.011) and smal- genetic correlation analyses, left M1 comparisons were made between ler cusp 6s (p = 0.053) when compared to + and x form crowns, as well the presence of a y configuration and other crown traits, while right M1 comparisons were made between the presence of a + configuration as + form crowns exhibiting significantly higher cusp number and other crown traits. For the left-side comparisons, all minor crown (p = 0.019) and larger cusp 6s (p = 0.001) when compared to y and x variants, including accessory cusps, returned negative genetic correla- form crowns. Comparisons for cusp 5, cusp 7, and protostylid generally followed the same patterns, although p-values were not significant. tions. The magnitudes varied considerably. Some were quite low and unlikely to achieve statistical significance with increased sample size (anterior fovea and, to some extent, cusp 7 and protostylid). However, 5 | DISCUSSION the negative correlations between y groove pattern and both cusp

6 and deflecting wrinkle were large in magnitude and likely to be signifi- In this article we have presented new estimates of heritability and cant with a larger sample size. Interestingly, the right-side comparisons genetic correlation for a series of dental morphological traits scored in against + groove pattern were all positive and mostly large in magni- the postcanine dentition using ASUDAS standards. Despite decades tude. This suggests a relationship between overall crown form, of prior work on the heritability of specific postcanine crown features reflected in a y or + cusp configuration among the four earliest forming (for a recent review see Scott et al., 2018), we believe this is the first 620 STOJANOWSKI ET AL. article to present heritability estimates for a nearly complete series of War and abolition of slavery (Opala, 1987; Pollitzer, 1999; Twining & postcanine crown features using maximum likelihood variance compo- Baird, 1991), with little reported out- or in-migration for the Sea Island nents analysis, a statistically robust, model-fitting approach. Limita- communities of the South Carolina coast until very recently (but see tions of the article include the small sample size for second molars and Matory, 2008). As such, the cultural and linguistic ties to West Africa the high degree of asymmetry in the results. As such, we focus our are still apparent, leading some to conclude that the Gullah are the discussion primarily on the first molar data from the left-side only least acculturated African American ethnic group. This is also reflected (except where asymmetry is the focus). We interpret the results with in patterns of genetic variation. The Gullah show the lowest levels of respect to two distinct, yet overlapping areas of inquiry: (a) the impli- Euro-American admixture among African American communities (but cations of these quantitative genetic analyses for the practice of den- not Afro-Caribbeans/South Americans) (Parra et al., 1998, 2001). Esti- tal biodistance, and (b) the implications of these analyses for mates of Euro-American admixture average around 3–4% and Native understanding patterns of variation and development in the human American admixture around 2–3% (McClean Jr. et al., 2003, 2005; dentition. The latter directly relates to existing dental developmental Parra et al., 2001; Pollitzer, 1999). Even within South Carolina African models (i.e., the patterning cascade model—Jernvall (2000), Jernvall & American communities, the low level of European admixture is note- Thesleff (2000)) and previous research using other primates & mam- worthy with 80% of ethnic Gullah exhibiting <10% European admix- malian model organisms (Hlusko & Mahaney, 2003, 2007; Hlusko et ture as compared with ~50% of African Americans from the al., 2004, 2011; Koh et al., 2010). surrounding low country and Columbia environs (Parra et al., 2001). However, a low level of admixture is not necessarily the same as 5.1 | Implications for dental biodistance reduced additive genetic variance. The Gullah are clearly linked to West African populations, specifically to those in Sierra Leone and Many postcanine traits scored in the Gullah sample were not herita- populations living along the “rice coast” of West Africa (McClean ble. In fact, more than half (12 of 21) of the features typically recorded Jr. et al., 2003, 2005; Stefflova et al., 2011). Therefore, as an African- in the ASUDAS returned heritabilities not significantly different from derived population, internal genetic variation is actually considerably 0.0 (including premolar traits—cf., Ludwig, 1957; Lundström, 1963; higher in the Gullah than in European populations (mtDNA haplotype Wood & Green, 1969) (Table 1). Some of these results can be diversity: Gullah = 0.8768, European American = 0.6280 per McClean explained by small sample size (most of the M2 traits) and some can Jr. et al., 2005). Observed levels of haplotype diversity in the Gullah be explained by low sample frequency. However, low frequencies are also comparable to other African and African American popula- cannot explain all of the nonsignificant results. M1 Carabelli's trait tions. How patterns of mtDNA or Y chromosome haplotype diversity (sample frequency = 20–63%), hypocone (14–69%) and cusp 5 (27%) map onto dental phenotypes is difficult to predict. We note, however, all returned positive heritabilities (see Supporting Information Tables 1 that previous quantitative genetic studies of Gullah biomedical data and S2). However, metacone and parastyle did not, and while the low failed to find evidence of bias due to population structure (Divers frequency of parastyles (1%) in this sample likely explains the trait's lack of observed heritability, metacone frequencies varied between et al., 2010). Thus, there is no clear rationale for assuming a causal 4 and 25% across different breakpoints. The upper range matches fre- relationship between the isolation and endogamy of the Gullah and quencies of molar traits that returned positive heritabilities, and we the low heritability estimates reported here and in our previous arti- suspect the metacone results reflect an issue with the compressed cles. Furthermore, we argue the pedigree structure of this sample bet- scoring scale with respect to this feature's range of variation. The ter represents the realities of research on phenotypic variation using same pattern was evident for the mandibular first molar. Traits with the archaeological record, as compared with single-generation twin or positive heritability included hypoconulid (sample frequency = 84%), sibling studies. cusp 6 (9–20%), and anterior fovea (17%), while traits that returned 5.1.1 | Effect of breakpoints on heritability estimates 0.0 heritability included cusp 7 (sample frequency = 40%), protostylid (8%), and groove pattern (4–84%). As such, there is no clear relation- Dental morphological data are typically dichotomized in a distance ship between trait frequency and heritability that might reflect an ana- analysis. There are two reasons for this. Dichotomization minimizes lytical artifact. observer error and allows for the calculation of sample frequencies We previously attributed low heritabilities in the Gullah sample to and the Mean Measure of Divergence, the most commonly used both reduced genetic variance due to isolation and endogamy, as well population-level distance statistic in dental biodistance research. as increased environmental variance due to suboptimal socioeconomic While trait dichotomization reduces the observed range of variation conditions (Guatelli-Steinberg et al., 2006; Stojanowski et al., 2017, in a dataset, results presented here justify the approach. For exam- 2018). As such, the results reported for the Gullah may not reflect ple, treating the traits as continuous variables almost always pro- broader patterns among human populations. That is, while previous duced lower heritability estimates than treating the traits as binary twin studies may over-estimate heritability due to study design, our (presence/absence) variables. The average heritability for continuous results may under-estimate heritability due to the demographic and scale analyses was ~0.38, while the average heritability for binary socioeconomic history of the study sample. However, we may have traits were nearly double that when the maximum dichotomization over-stated the case for reduced trait heritability in our previous breakpoint was used (~0.69). Whether this reflects the effects of papers. It is widely recognized that the Gullah were isolated from sur- observer error or a real biological phenomenon is difficult to rounding communities for an extended period of time after the Civil determine. STOJANOWSKI ET AL. 621

TABLE 4 Gullah sample within-element variance components correlations: Crown morphology

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP LMI1 MD DIMENSION (C)s META (4) 298 0.725 ± 0.642 0.130 0.372 −0.157 ± 0.172 0.350 0.077 HYPO (4) 304 0.496 ± 0.210* 0.035 0.003 −0.028 ± 0.195 0.886 0.220 C5 (2)s 261 −0.019 ± 0.306 0.950 0.020 0.067 ± 0.194 0.731 0.029 CTRAIT (5)a*s, s 303 0.374 ± 0.220 0.103 <0.001 0.180 ± 0.625 0.792 0.317 PARA (1)s 307 −1.000 ± — 0.328 — 0.128 ± 0.162 0.431 0.000 META (4) HYPO (4) 306 0.700 ± 0.463 0.166 0.351 0.382 ± 0.762 0.726 0.590 C5 (2)s 289 −0.112 ± 0.881 0.903 0.351 −0.587 ± 0.553 0.297 −0.404 CTRAIT (5)a*s, s 305 1.000 ± —** 0.040 — −1.000 ± — 0.127 0.198 PARA (1)s 308 1.000 ± — 0.781 — 1.000 ± — 0.262 −0.967 HYPO (4) C5 (2)s 298 0.432 ± 0.347 0.198 0.087 −0.333 ± 0.412 0.426 0.096 CTRAIT (5)a*s, s 307 0.859 ± 0.236** 0.002 0.270 −0.841 ± 0.839 0.151 0.340 PARA (1)s 316 1.000 ± — 0.277 — 1.000 ± — 0.084 0.941 C5 (2)s CTRAIT (5)a*s, s 300 0.666 ± 0.473 0.084 0.281 −1.000 ± — 0.060 0.023 PARA (1)s 303 −1.000 ± — 0.358 — −1.000 ± — 0.127 −0.960 CTRAIT (5)a*s, s PARA (1)s 305 −1.000 ± — 0.444 — 1.000 ± — 0.080 0.248 RM1 MD DIMENSION (C)s META (3) 293 −0.073 ± 0.573 0.898 0.106 0.077 ± 0.105 0.460 0.056 HYPO (5)s 297 0.108 ± 0.574 0.855 0.156 0.189 ± 0.134 0.181 0.174 C5 (1) 244 −0.086 ± 0.757 0.909 0.196 0.273 ± 0.141 0.057 0.214 CTRAIT (6) 339 0.275 ± 0.437 0.539 0.070 0.432 ± 0.423 0.301 0.316 PARA (1) 305 1.000 ± — 0.804 — −0.004 ± 0.103 0.967 0.015 META (3) HYPO (5)s 305 1.000 ± — 0.576 — 1.000 ± — 0.112 0.959 C5 (1) 293 −1.000 ± — 0.398 — −1.000 ± — 0.063 −0.999 CTRAIT (6) 347 1.000 ± — 0.132 — 1.000 ± — 0.369 0.998 PARA (1) 315 1.000 ± — 0.405 — 1.000 ± — 0.560 0.881 HYPO (5)s C5 (1) 296 0.075 ± 0.799 0.923 0.202 −0.185 ± 0.247 0.461 −0.120 CTRAIT (6) 346 0.673 ± 0.450 0.149 0.243 −0.133 ± 0.437 0.769 0.268 PARA (1) 321 −1.000 ± — 0.496 — 0.376 ± 0.728 0.485 0.019 C5 (1) CTRAIT (6) 341 −0.107 ± 0.551 0.852 0.165 0.551 ± 0.567 0.221 0.223 PARA (1) 304 0.998 ± — 0.646 1.000 −0.445 ± 0.545 0.147 −0.311 CTRAIT (6) PARA (1) 344 −1.000 ± — 0.307 — −1.000 ± — 0.081 −0.927 LM2 META (4) HYPO (4) 104 1.000 ± — 0.057 — −1.000 ± — 0.265 0.303 C5 (2) 95 −0.194 ± 0.739 0.457 0.051 1.000 ± — 0.901 −0.161 CTRAIT (1)a*s 139 0.225 ± 0.784 0.757 0.299 −1.000 ± — 0.481 −0.119 PARA —— ————— HYPO (4) C5 (2) 95 −0.026 ± 0.528 0.961 0.146 −1.000 ± — 0.605 −0.201 (Continues) 622 STOJANOWSKI ET AL.

TABLE 4 (Continued)

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP CTRAIT (1)a*s 139 −0.409 ± 1.130 0.690 0.345 0.170 ± 0.670 0.797 −0.034 PARA —— ————— C5 (2) CTRAIT (1)a*s 138 0.584 ± 0.725 0.321 0.296 −1.000 ± — 0.660 0.147 PARA —— ————— CTRAIT (1)a*s PARA —— — — — — — RM2 META (4)a*s HYPO (2) 95 0.929 ± 1.885 0.223 0.483 −1.000 ± — 0.145 0.024 C5 (2) 92 −0.932 ± 0.960 0.236 0.476 1.000 ± — 0.252 −0.057 CTRAIT (1)a 140 1.000 ± — 0.880 — −0.274 ± 1.025 0.615 −0.103 PARA —— ————— HYPO (2) C5 (2) 98 0.229 ± 0.392 0.475 0.111 −1.000 ± — 0.811 0.152 CTRAIT (1)a 138 1.000 ± — 0.131 1.000 ± — 0.744 0.445 PARA —— ————— C5 (2) CTRAIT (1)a 138 −1.000 ± — 0.622 — 1.000 ± — 0.130 0.254 PARA —— ————— CTRAIT (1)a PARA —— — — — — —

LM1 MD DIMENSION (C)s C5 (4) 208 1.000 ± —** 0.022 — 0.039 ± 0.166 0.818 0.266 C5 (C) 208 1.000 ± —** 0.030 — 0.155 ± 0.150 0.347 0.343 C6 (2) 180 −1.000 ± — 0.135 — 0.776 ± 0.852 0.131 0.016 C7 (3)a*s 202 −0.229 ± 0.918 0.796 0.294 0.235 ± 0.255 0.333 0.140 CNO (6) 182 −1.000 ± — 0.165 — 0.575 ± 0.251 0.012 0.220 AFOV (4) 249 0.294 ± 0.609 0.616 0.263 0.005 ± 0.162 0.974 0.063 DWRINK (3)a*s, s 194 0.592 ± 1.151 0.553 0.392 0.070 ± 0.181 0.702 0.137 GROOVE (Y) 224 1.000 ± — 0.271 — −0.278 ± 0.136 0.056 −0.122 PROTO (1) 247 −1.000 ± — 0.194 — 0.426 ± 0.227 0.097 0.119 C5 (4) C6 (2) 202 −0.919 ± 0.399** 0.023 0.418 −0.814 ± 0.504 0.149 −0.864 C7 (3)a*s 209 −0.493 ± 0.435 0.281 0.145 0.325 ± 0.535 0.500 −0.085 CNO (6) 201 −1.000 ± — 0.137 — −0.698 ± 0.216 0.040 −0.734 AFOV (4) 258 −0.356 ± 0.350 0.326 0.037 0.261 ± 0.724 0.696 −0.137 DWRINK (3)a*s, s 206 −0.015 ± 0.661 0.982 0.134 −0.457 ± 0.552 0.479 −0.228 GROOVE (Y) 227 0.519 ± 0.517 0.328 0.195 0.229 ± 0.371 0.559 0.339 PROTO (1) 250 −0.150 ± 0.512 0.762 0.106 0.502 ± 0.559 0.368 0.195 C5 (C) C6 (C)a*s 186 −0.779 ± 0.242 0.054 0.165 −0.528 ± 0.125 0.006 −0.605 C7 (C)a*s 209 −0.601 ± 0.513 0.164 0.281 0.272 ± 0.146 0.058 0.055 AFOV (C)a,b 234 −0.081 ± 0.357 0.821 0.005 −0.010 ± 0.169 0.955 −0.034 DWRINK (C) 228 −0.886 ± 0.655 0.145 0.436 0.039 ± 0.144 0.784 −0.117 PROTO (C)k 250 0.272 ± 0.467 0.554 0.108 −0.172 ± 0.119 0.147 −0.083 C6 (2) C7 (3)a*s 200 0.267 ± 0.489 0.589 0.100 0.570 ± 2.855 0.722 0.245 CNO (6) 171 1.000 ± —** 0.009 — 1.000 ± — 0.024 0.941 (Continues) STOJANOWSKI ET AL. 623

TABLE 4 (Continued)

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP AFOV (4) 254 −0.079 ± 0.334 0.813 0.001 0.230 ± 1.191 0.844 −0.016 DWRINK (3)a*s, s 196 0.483 ± 0.412 0.306 0.137 0.784 ± 1.066 0.475 0.492 GROOVE (Y) 219 −0.713 ± 0.405 0.112 0.275 0.218 ± 0.919 0.798 −0.309 PROTO (1) 246 −0.201 ± 0.431 0.640 0.070 0.751 ± 1.189 0.452 0.093 C7 (3)a*s CNO (6) 200 1.000 ± —** 0.034 — −0.552 ± 0.721 0.121 0.062 AFOV (4) 232 1.000 ± — 0.063 — −0.797 ± 0.977 0.121 0.092 DWRINK (3)a*s, s 209 1.000 ± —** 0.050 — −0.620 ± 1.086 0.114 0.005 GROOVE (Y) 209 −0.133 ± 0.599 0.825 0.108 0.028 ± 0.328 0.930 −0.024 PROTO (1) 225 −0.203 ± 0.820 0.801 0.248 0.250 ± 0.354 0.476 0.128 CNO (6) AFOV (4) 253 −0.224 ± 0.529 0.668 0.187 0.457 ± 0.517 0.377 0.116 DWRINK (3)a*s, s 196 0.163 ± 0.757 0.842 0.201 0.281 ± 0.376 0.470 0.243 GROOVE (Y) 220 −0.293 ± 0.763 0.709 0.230 −0.108 ± 0.342 0.757 −0.159 PROTO (1) 246 −0.480 ± 0.962 0.557 0.334 0.542 ± 0.387 0.198 0.221 AFOV (4) DWRINK (3)a*s, s 220 −0.812 ± 1.253 0.165 0.422 1.000 ± — 0.139 0.000 GROOVE (Y) 256 −0.039 ± 0.478 0.933 0.104 0.387 ± 0.478 0.449 0.155 PROTO (1) 259 0.384 ± 0.401 0.378 0.093 0.383 ± 0.561 0.542 0.360 DWRINK (3)a*s, s GROOVE (Y) 204 −0.654 ± 0.591 0.289 0.284 0.619 ± 0.578 0.211 0.100 PROTO (1) 225 −1.000 ± — 0.151 — 0.267 ± 0.610 0.566 −0.129 GROOVE (Y) PROTO (1) 251 −0.185 ± 0.581 0.759 0.091 −0.147 ± 0.388 0.717 −0.160

RM1 MD DIMENSION (C)s C5 (2) 219 0.834 ± 0.730 0.189 0.419 −0.268 ± 0.269 0.274 0.093 C6 (1) 190 0.114 ± 0.649 0.866 0.169 0.224 ± 0.363 0.550 0.182 C7 (2)s 224 1.000 ± — 0.066 — 0.028 ± 0.906 0.908 0.290 CNO (6) 187 −1.000 ± — 0.648 — 0.181 ± 0.184 0.251 0.080 AFOV (4) 239 1.000 ± — 0.113 — −0.944 ± 0.924 0.053 −0.053 DWRINK (3)s 209 1.000 ± — 0.119 — −0.075 ± 0.897 0.745 0.164 GROOVE (+) 221 0.179 ± 1.510 0.909 0.342 0.086 ± 0.351 0.815 0.102 PROTO (1) 251 −0.121 ± 0.847 0.883 0.294 −0.107 ± 0.301 0.725 −0.109 C5 (2) C6 (1) 212 0.126 ± 1.614 0.934 0.392 −0.630 ± 1.283 0.659 −0.271 C7 (2)s 235 1.000 ± — 0.309 — 1.000 ± — 0.046 0.999 CNO (6) 212 −0.913 ± 1.965 0.751 1.000 0.056 ± 0.988 0.934 −0.102 AFOV (4) 253 −1.000 ± — 0.224 — −1.000 ± — 0.462 −0.992 DWRINK (3)s 234 1.000 ± — 0.507 — 1.000 ± — 0.095 1.000 GROOVE (+) 232 1.000 ± — 0.308 — 1.000 ± — 0.177 0.996 PROTO (1) 255 1.000 ± — 0.427 — −1.000 ± — 0.061 −0.415 C6 (1) C7 (2)s 222 0.238 ± 0.674 0.725 0.156 −0.037 ± 0.319 0.906 0.045 CNO (6) 179 0.268 ± 1.003 1.000 1.000 0.900 ± 0.996 0.004 0.655 AFOV (4) 242 −0.129 ± 0.512 0.793 0.146 0.802 ± 0.765 0.271 0.208 DWRINK (3)s 216 0.686 ± 1.026 0.431 0.401 −0.285 ± 0.380 0.428 −0.039 GROOVE (+) 224 0.994 ± 0.827 0.230 0.497 −0.221 ± 0.491 0.607 0.180 PROTO (1) 252 0.109 ± 0.668 0.867 0.130 0.160 ± 0.425 0.694 0.140 (Continues) 624 STOJANOWSKI ET AL.

TABLE 4 (Continued)

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP C7 (2)s CNO (6) 221 −1.000 ± — 0.676 — 0.055 ± 0.263 0.774 −0.008 AFOV (4) 252 0.685 ± 0.523 0.169 0.294 −0.397 ± 0.584 0.441 0.118 DWRINK (3)s 233 1.000 ± — 0.161 — −0.109 ± 1.098 0.650 0.128 GROOVE (+) 233 0.405 ± 0.986 0.701 0.329 −0.031 ± 0.302 0.918 0.059 PROTO (1) 254 −0.450 ± 1.095 0.630 0.344 0.140 ± 0.321 0.670 0.005 CNO (6) AFOV (4) 242 −1.000 ± — 0.523 — 0.479 ± 0.499 0.203 0.101 DWRINK (3)s 217 0.124 ± 3.071 0.967 0.467 −0.071 ± 0.205 0.719 −0.061 GROOVE (+) 220 1.000 ± — 0.514 — −0.040 ± 0.826 0.846 0.070 PROTO (1) 252 −1.000 ± — 0.679 — 0.070 ± 0.230 0.762 −0.007 AFOV (4) DWRINK (3)s 228 −0.213 ± 0.733 0.778 0.322 −0.080 ± 0.540 0.885 −0.101 GROOVE (+) 245 1.000 ± — 0.129 — −0.292 ± 1.598 0.638 0.259 PROTO (1) 259 −0.030 ± 0.636 0.963 0.212 −1.000 ± — 0.027 −0.577 DWRINK (3)s GROOVE (+) 223 0.311 ± 1.335 0.826 0.338 −0.247 ± 0.330 0.431 −0.161 PROTO (1) 250 −1.000 ± — 0.389 — −0.053 ± 0.397 0.889 −0.223 GROOVE (+) PROTO (1) 252 1.000 ± — 0.199 — −0.564 ± 1.291 0.101 −0.185

LM2 C5 (1) C6 (3) 91 1.000 ± —** 0.025 — 1.000 ± — 0.553 0.990 C7 (2) 110 −0.108 ± 0.783 0.748 0.041 1.000 ± — 0.628 0.008 CNO (5)a 79 1.000 ± —** 0.003 — 1.000 ± 1.900 0.983 1.000 GROOVE (X)s 114 −0.158 ± 1.113 0.712 0.146 1.000 ± — 0.257 0.141 PROTO (1) 134 1.000 ± — 0.409 — 1.000 ± — 0.169 0.687 C6 (3) C7 (2) 108 −0.067 ± — 0.936 0.319 1.000 ± — 0.491 0.288 CNO (5)a 75 1.000 ± — 0.052 — 1.000 ± — 0.557 0.991 GROOVE (X)s 114 1.000 ± — 0.428 — −1.000 ± — 0.062 0.376 PROTO (1) 133 1.000 ± — 0.315 — −1.000 ± — 0.127 −0.287 C7 (2) CNO (5)a 93 0.207 ± 0.998 0.733 0.097 1.000 ± — 0.313 0.513 GROOVE (X)s 123 −1.000 ± — 0.068 — 1.000 ± — 0.161 −0.211 PROTO (1) 136 −1.000 ± —** 0.043 — −1.000 ± — 0.508 −0.991 CNO (5)a GROOVE (X)s 93 −0.646 ± 1.045 0.330 0.370 1.000 ± — 0.100 0.119 PROTO (1) 115 1.000 ± — 0.109 — 1.000 ± — 0.374 0.992 GROOVE (X)s PROTO (1) 138 1.000 ± — 0.111 — −1.000 ± — 0.147 0.080

RM2 C5 (5) C6 (1)s 86 −1.000 ± — 0.244 — −1.000 ± — 0.437 −1.000 C7 (1)a 109 −0.138 ± 1.003 0.819 0.165 1.000 ± — 0.826 0.197 CNO (6)s 87 −1.000 ± — 0.284 — −1.000 ± — 0.325 −1.000 GROOVE (+) 119 0.117 ± 0.652 0.284 — −0.266 ± 2.866 0.911 0.027 C6 (1)s C7 (1)a 105 0.728 ± 0.502** 0.009 0.225 −1.000 ± — 0.674 0.589 (Continues) STOJANOWSKI ET AL. 625

TABLE 4 (Continued)

Genetic Environmental Phenotypic a b c c d c e Trait (BP) N ρG P(ρG =0) P(|ρG|=1) ρE P(ρE =0) ρP CNO (6)s 83 1.000 ± — 0.203 — 1.000 ± — 0.603 1.000 GROOVE (+) 116 −1.000 ± — 0.060 — 0.206 ± 1.162 0.832 −0.558 C7 (1)a CNO (6)s 108 0.711 ± 0.331** 0.010 0.219 −1.000 ± — 0.715 0.578 GROOVE (+) 112 −0.389 ± 0.697 0.382 0.066 −1.000 ± — 0.741 −0.424 CNO (6)s GROOVE (+) 117 −1.000 ± — 0.099 — 0.014 ± 0.816 0.987 −0.555 a L = left; R = right; M = molar. Maxillary and mandibular traits indicated by superscript and subscript, respectively. META = metacone; HYPO = hypocone; C = cusp; CTRAIT = Carabelli's trait; PARA = parastyle; AFOV = anterior fovea; CNO = cusp number; DWRINK = deflecting wrinkle; GROOVE = groove pattern; PROTO = protostylid; MD = mesial-distal crown dimension; C = trait treated as a -inorm transformed, continuous variable; BP = dichotomization breakpoint when trait treated as a binary variable. Dashes are associated with incalculable parameter estimates. Models whose entire set of parameters are marked with dashes failed to converge. Superscript abbreviations indicate fixed covariates in the model. A = age; A*S = age/sex interaction; B = birth; S = sex. b Maximum-likelihood estimate of genetic correlation. Cases of incomplete pleiotropy indicated by a single asterisks. Cases of complete pleiotropy indi- cated by two asterisks. c Probability of hypothesis (as indicated in parentheses) being true given pedigree structure with values p < .050 bolded. d Maximum-likelihood estimate of environmental correlation. e Maximum-likelihood estimate of derived phenotypic correlation.

A related question is whether the standard breakpoints identi- observed in the Gullah sample (if any). For example, I1 double fied in Scott and Irish (2017), which are used widely in the dental shoveling returned a 0.0 heritability using a breakpoint of 2. Reducing biodistance literature, are optimized for evolutionary inferences. the breakpoint to 1 produces a significant heritability estimate of 0.34 Table 5 summarizes heritabilities presented here and in Stojanowski and the sample frequency of expression increases from 20.9 to 57.5%. et al. (2018) at the breakpoints specified by Scott and Irish (2017). Data in Table 5 indicate that any analysis of the Gullah sample using Of note, the final column presents additional data for those traits the breakpoints specified in Scott and Irish (2017) would include nine with nonsignificant estimates, in particular, the breakpoint and sam- traits with significant positive heritability and 12 traits with 0.0 herita- ple frequency at which a statistically significant heritability is bility. Shifting the breakpoint scale does little to ameliorate this; there is

TABLE 5 Estimated heritability of ASUDAS traits at specified breakpoints in the Gullah sample

Trait Breakpointa h2 Freqb Significant h2 (%) bpc UI1 winging 1+ 0.00d Continuous None UI1 labial curvature 2+ 0.13 17.8% UI1 shoveling 2/3 0.26/0.26 50.3%/7.3% UI1 double shoveling 2 0.11d 20.9% 0.34 (57.5%) bp = 1 UI2 tuberculum dentale 2 0.10d 41.2% 0.40 (24.4%) bp = 3 UI2 peg form 1 0.18 7.3% UC mesial ridge 1 0.12d 23.1% None UC distal accessory ridge 2 0.31 76.2% UM2 hypocone 3 / 4 0.31d/0.49d 73.7%/22.1% None UM1 cusp 5 1 0.03d 51.1% 0.52 (26.9%) bp = 2 UM1 Carabelli's trait 2/5 0.45/0.85 42.95/19.8% UM1 parastyle 2 0.00d 0.7% None LC distal accessory ridge 2 0.24 46.2% LP2 cusp number 2 0.00d NA None LM1 anterior fovea 3 / 4 0.26/0.72 65.1%/16.6% LM1 protostylid 2 0.00d 8.0% None LM1 cusp 6 1 0.56 20.4% LM1 cusp 7 1 0.04d 40.0% None LM1 deflecting wrinkle 2 0.19d 29.3% None LM2 groove pattern Y 0.39d 23.9% None LM2 cusp number 4- 0.89 - a Breakpoint based on Scott and Irish (2017). b Sample frequency of expression of trait at specified breakpoint. c This column presents a significant heritability estimate and the sample frequency at which the estimate was observed for the reported breakpoint. d Not significant at the 5% level. Bold entries are significant at the Scott and Irish (2017) breakpoint. 626 STOJANOWSKI ET AL. almost no correlation between positive heritability and sample fre- 5.1.3 | Sexual dimorphism in trait expression quency. For example, traits with positive heritability at the Scott and The influence of sex on the expression of morphological traits is Irish (2017) breakpoint varied in frequency from 7.0 to 76.2%, while debated. As Scott et al. (2018, pp. 105–106) note, “…given the nature traits with 0.0 heritability varied from 0.7 to 73.7%. Therefore, it does of sampling distributions, reports of significant sex differences for not seem possible to use trait frequency as a guide toward generating traits vary from one sample to another…. When differences are found, project-specific breakpoints based on regional patterns of dental mor- they are usually inconsistent among samples and low-order in magni- phological trait expression. Rather, adjustments during the data collec- tude. For this reason crown and root traits…can be pooled to estimate tion phase may be required if ASUDAS standards fail to capture population frequencies.” Our results corroborate this, for the most underlying genetic signals. part. We were able to replicate the results of numerous studies sug- gesting Carabelli's trait expression is sexually dimorphic in certain populations (e.g., Durner, 2011; Kondo & Townsend, 2006; Scott, Pot- 5.1.2 | Selecting between antimeres for analysis ter, Noss, Dahlberg, & Dahlberg, 1983; Townsend & Brown, 1981; Although data may be collected for both antimeres, the estimation Tsai et al., 1996), although here only the left-side data produced con- of distances based on dental morphological variables does not use sistent results (but these were the most consistent for any variable). In data from both sides of the dentition. Most often the side with the addition to Carabelli's trait, sex was a significant covariate for para- maximum degree of expression is used; however, other options style expression, and in the mandible, cusp 6 and cusp 7 expression. include using left or right-side data only with antimere substitution All of these traits are accessory cusps of the molar crown. It is often in the case of missing data. Here we provide genetic correlations assumed that dental morphological traits (with the exception of canine for antimeres that were generally significantly positive (Table 2), distal accessory ridge) are not sexually dimorphic. Although our ana- which indicates that antimeres are highly genetically correlated and lyses leave the biological mechanism unexplained, the results suggest should not be double counted. However, further complicating the that care is needed in ascertaining the sex composition of pooled sam- issue is the degree of asymmetry noted in postcanine trait heritabil- ples in archaeological contexts. Indeed, targeted association studies of ities and genetic correlations. Right-side estimates of heritability single nucleotide polymorphisms and dental morphology have also were inconsistent and more often nonsignificant than left-side esti- documented significant sex effects for several postcanine dental traits mates. This is difficult to explain in any other way than to assume (Kimura et al., 2015). that environmental variance components were higher for the right- 5.1.4 | Trait independence side of the dentition, although a biological explanation for this is unknown. Additionally, antimere genetic correlations were much A basic assumption of biological distance analysis is that the traits lower than those observed for odontometric (Stojanowski et al., used to estimate phenotypic similarity are genetically independent of 2017) and anterior morphological variables (Stojanowski et al., one another. ASUDAS protocol dictates that each trait be represented 2018), with derived phenotypic correlations being lower than by data collected on a single tooth, as supported by previous research on phenotypic correlation among metameres (Scott et al., 2018). expected based on previous studies of dental asymmetry (Baume & Based on thousands of samples, Turner and his students have identi- Crawford, 1979, 1980; Bollini, Rodriguez-Florez, & Colantonio, fied what they call “key teeth” for each trait that best reflect patterns 2009; Marado, Silva, & Irish, 2017; Mayhall & Saunders, 1986; of variation (reviewed in Scott & Irish, 2017). Mizoguchi, 1990; Moskona, Vainder, Herschkovitz, & Kobyliansky, Quantitative genetic analyses of metameric variation directly 1996; Noss, Scott, Potter, & Dahlberg, 1983; Saunders & Mayhall, assess the independence assumption. While small M2 sample size for 1982). Interpreting the entirety of the pattern is difficult, but the Gullah prevents a comprehensive evaluation, data presented in results seem to suggest that the postcanine dentition experiences Table 3 generally support it. Most genetic correlations among meta- greater directional asymmetry in the expression of dental morpho- meres demonstrate large, positive correlations that are statistically dif- logical variants. This may be related to differences in developmen- ferent from 0.0. Note that even large negative correlations validate tal timing across antimeres (Harris, 1992) that are potentially using only one tooth per trait in biodistance analyses, because a nega- exaggerated in later-forming tooth crowns, such as the premolars tive correlation reflects the action of the same genes operating to pro- and second molars. Guatelli-Steinberg et al. (2006) previously docu- duce the opposite phenotypic effects. For example, the consistent mented fluctuating and directional asymmetry for Gullah crown negative correlations between metameres for mandibular cusp num- size. Although permanent molars were not included in their study, ber simply reflects the tendency for cusp number to decrease as one results presented here are consistent with their findings. Similarly, moves distally in the tooth row. Still, many p-values were not signifi- Riga, Belcastro, and Moggi-Checci (2014) documented increased, cant, and additional data are needed to fully evaluate the metameric directional variation in molar cusp number and size in a stressed correlations. (vs. nonstressed) sample, indicating that environment can act The assumption of trait independence does not only apply to “ ” nonrandomly on developmental parameters throughout crown metameric scoring of morphological traits. A more foundational formation. Our results suggest caution is needed in selecting which assumption of the ASUDAS is that each trait itself is genetically inde- side to use in dental biodistance analyses. pendent of all other traits recorded, including those located on the same tooth crown. Here, the results are less conclusive (Table 4), with STOJANOWSKI ET AL. 627 many comparisons returning non-significant p-values for tests of both crown formation, as negative genetic correlations are often complete pleiotropy and complete genetic independence. Many of expected when characters arise as the result of the subdivision of the significant correlations were also spuriously high, suggesting an “developmental precursors” (Norry et al., 2000, p. 177; see also issue with model convergence. The one significant maxillary result Atchely, 1987; Riska, 1986). It seems the expression of M1 cusp suggests that hypocone score and Carabelli's trait are genetically cor- 5 and cusp 6, in particular, are impacted by overlapping genes but related, but this was found only on the left-side. None of the right- in opposite directions, as limited biological resources are allocated side correlations were significantly different from 0 or 1, which is throughout crown development or epithelial “partitioning” interpreted as a nonresult. In the mandible, cusps 5, 6, and 7 demon- (Bochdanovits & de Jong, 2004). A functional explanation for this strate limited evidence for complete pleiotropy (Table 4). Although relationship is not readily apparent. inconclusive, the results suggest more research with larger sample It is unclear why the patterns of within-crown genetic correlation sizes is warranted, especially in consideration of evolutionary develop- were so different for the maxillary and mandibular molars. It is possi- mental research suggesting integration of molar crown morphology ble that genetic correlations between M1 isomeric cusp areas or through iterative enamel knot signaling. crown shape would reveal these distinct morphological patterns to be the residual outcome of higher-level partitioning of the dentition into 5.2 | Implications for understanding dental variation maxillary and mandibular occlusal units (or modules) (Gómez-Roblez & Polly, 2012). Indeed, the functional role of the M1 in mastication Quantitative genetic research has, until recently, failed to explore pat- makes this scenario plausible (Cheverud, 1996; Gómez-Roblez & Polly, terns of pleiotropy in an effort to identify hierarchically-structured 2012; Yound & Hallgrímsson, 2005), and analyzing continuous mor- morphological modules across the human dentition (but see Stoja- phological variation between isomeres represents a crucial next step nowski et al., 2018). Thus, a comprehensive study of postcanine vari- in exploring hierarchical modularity in Gullah dentitions. Importantly, ants in a sample of complex pedigree structure—especially one results are specific to this sample and confirmation of these patterns employing model-fitting approaches to estimate both heritability and in other populations is required before we can obtain a complete pic- genetic correlation—is timely. This work complements a rich body of ture of the genetic architecture of the human dentition, as well as the research on Cercopithecoid dental traits (e.g., Hlusko & Mahaney, potential contribution of small-scale modularity and negatively (genet- 2003, 2007, 2009; Hlusko, Schmitt, Monson, Brasil, & Mahaney, ically) correlated traits to the exceptional morphological diversity that 2016; Hlusko et al., 2004, 2007, 2011) and evo-devo models of mam- characterizes our species. malian postcanine tooth form (Hunter, Guatelli-Steinberg, Weston, Finally, this research bolsters recent molecular genetic research Durner, & Betsinger, 2010; Jernvall, 2000; Jernvall & Thesleff, 2000; on the pleiotropic effects of gene variants among the components of Moormann, Guatelli-Steinberg, & Hunter, 2013; Ortiz, Bailey, Schwartz, Hublin, & Skinner, 2018) in an attempt to map genotype– ectodermally derived structures such as hair, mammary glands, and phenotype pathways in the dentition. Unfortunately, given M2 sample teeth (e.g., Hlusko et al., 2018). While the bulk of these studies have size limitations, as well as a dearth of homologous ASUDAS crown examined the correlation between specific EDAR and PAX9 polymor- features scored across arcades, regions of the dentition, and postca- phisms and incisor shoveling (Kimura et al., 2009; Lee et al., 2012; nine tooth classes (premolars and molars), we were unable to evaluate Park et al., 2012), molar morphology has also been examined. For higher-level modularity in the Gullah sample. However, we did eluci- example, Park et al. (2012) reported a marginally significant relation- date differential patterns of modularity at the within-crown scale, ship between the Asian-specific EDAR 370A variant and M2 cusp 5 or 1 hypoconulid presence; this, despite minimal phenotypic correlation especially for the later-forming and accessory cusps of the M /M1 crowns. between hypoconulid expression and incisor shoveling—another char- That a pleiotropic relationship was shared between M1 Cara- acter associated with the EDAR genotype. Kimura et al. (2015) also belli's trait and (a) metacone, and (b) hypocone meets expectations reported associations between a single nucleotide polymorphism in 1 outlined by the patterning cascade model, as the size and presence WNT10A and variation in (a) P2 distolingual cusps, (b) M cusp 5, and of these three later-forming cusps are (to some degree) governed (c) M2 cusp 5. These studies inform our understanding of microevolu- by the configuration of the earlier forming protocone and paracone. tionary processes and migration histories in Homo sapiens, yet their These results suggest an overlap in the genes that regulate distal capacity to identify true “causation” and/or targets of selection are and accessory cusp expression, which is perhaps complexly related limited due to the effects of linkage disequilibrium and pleiotropy. to the activation, inhibition, and protein signaling mechanisms func- Outlining the genetic architecture of the human dental complex pro- tioning at the level of the molar crown as a “developmental unit.” vides insight into the overall potential for morphological characters to

However, the negative genetic correlations between M1 cusp 5 and be impacted by the same genes or sets of genes, even when they are (a) cusp 6 and (b) cusp 7 indicate that the mandibular molar is fun- not phenotypically correlated. damentally different in its genetic architecture, at least with regard to its later forming cusps. Interestingly, it is hypothesized that neg- ative genetic correlations are the hallmark of resource competition ACKNOWLEDGMENTS across processes, for example in life history traits (Atchely, 1987; The authors would like to thank the Associate Editor and the anony- Norry, Vilardi, & Hasson, 2000). Here, the resource in play may be mous reviewer for providing valuable commentary to improve the the cellular real estate and developmental energy expended in manuscript. 628 STOJANOWSKI ET AL.

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