Journal of

Anatomy

J. Anat. (2016)

doi: 10.1111/joa.12561

Quantification of anatomical variation at the atlanto-occipital articulation: morphometric resolution of commingled human remains within the repatriation documentation process J. Christopher Dudar1 and Eric R. Castillo2 1

Department of Anthropology, National Museum of Natural History, Smithsonian Institution, Washington, DC, USA Department of Human Evolutionary Biology, Harvard University, Cambridge, MA, USA

2

Abstract Within many institutional collections are skeletal and mummified human remains representing a part of our species’ adaptation and evolution to various biocultural environments. Archaeologically recovered individuals come from deep into our past, and possess information that provides insight into population history, genetics, diet, health and other questions relevant to all living peoples. Academic concerns have been raised regarding the reinterment of these collections due to the rise of the international repatriation movement, the passage of various laws and implementation of institutional policies. While all potential research questions cannot be anticipated, the proactive documentation of collections is one way to ensure primary data are maintained for future study. This paper explores developments in digitization technology that allow the archive of virtual copies of human remains, and an example of how anatomical and archaeological collections can be digitized towards pragmatic research goals. The anatomical variability of the human atlanto-occipital (AO) articular surfaces was studied using non-metric categorical shape, 2D measurement and 3D morphometric analyses to provide reference standards for the reassociation of individuals from commingled skeletal remains, such as found in some archaeological sites or forensic investigations including mass grave or mass disaster recovery scenes. Results suggest that qualitative shape observations and caliper-derived measurements of the articulating AO condyles tend to display significant sexual dimorphism and biological ancestry-related size and shape differences. Variables derived from a scanned 3D mesh, such as condylar angle and articular surface curvature, quantify biomechanical variation and display a stronger congruency within individuals. It is recommended that a two-stage approach involving initial screening and identification of possible reassociation candidates is accomplished with a linear osteometric approach, followed by 3D laser scanning of the candidate joint surfaces for morphometric analyses to confirm reassociations when destructive DNA typing is not allowed or otherwise impractical due to cost or other resource restrictions. Key words: 3D digitization; atlanto-occipital joint; atlas vertebra; commingled human remains; morphometric; occipital condyles; repatriation.

Introduction Human remains collections within museums, universities and other institutional holdings contain a wealth of information documenting our species’ evolution and adaptation to biological and sociocultural environments. However, academic concerns regarding the reinterment of these remains Correspondence J. Christopher Dudar, Department of Anthropology, National Museum of Natural History, Smithsonian Institution, Washington, DC, 20013-7012 USA. E: [email protected] Accepted for publication 11 October 2016 © 2016 Anatomical Society

have been raised due to increased international repatriation advocacy, subsequent legislation, and other government or institutional policies that otherwise support the reburial or restriction of access to remains excavated or in collections (Turner, 1986; Ubelaker & Grant, 1989; Ubelaker, 1990; Klesert & Powell, 1993; Brenton, 1994; Owsley, 1996; Rose et al. 1996; Fforde & Ormond-Parker, 2001; Westaway & Burns, 2001; Brothwell, 2004; Ousley et al. 2005; Flessas, 2008; Moshenska, 2009; Curtis, 2010; Schillaci & Bustard, 2010; Young, 2010; Parker-Pearson et al. 2011; Sayer, 2011). While many of these concerns are valid from a scientific perspective, Bray (2001), Hanna (2003), Kakaliouras (2008, 2014) and Martin et al. (2013) advocate better engagement

2 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

with the public and descendent communities to educate and foster partnerships in studies that benefit all parties. For example, Egeland et al. (2009) found that ancient human remains can shed light on past methyl mercury exposure and thus inform the diet of current indigenous people who continue to rely on traditional marine resources. Thompson et al. (2013) obtained whole body computed tomography (CT) scans of mummies from four different cultures spanning 4000 years to reveal that atherosclerosis was present in over one-third of the individuals. This suggests that a predisposition to the disease has always been present and that atherosclerosis may not be a product of the post-industrial sociocultural environment. Advances in virtual anthropology have provided a viable means by which a digital copy of human remains can be preserved and archived for future investigation. Virtual anthropology is defined as ‘computer-assisted anthropology. . . designed to allow investigations of three-dimensional morphologic structures by means of digital data-sets’ (Weber, 2001:193). Weber & Bookstein (2011:2) further characterize it as, ‘A multi-disciplinary approach to studying anatomical data, particularly that of humans, their ancestors, and closest relatives, in three or four dimensions. . .’, in other words across time and space. This study demonstrates how virtual anthropology and digitization technologies have been used at the National Museum of Natural History (NMNH), Smithsonian Institution, with the goal of archiving virtual copies of human remains subject to repatriation. In order to demonstrate the implementation of digitization within the repatriation osteological documentation process, this paper applies qualitative shape observation, quantitative caliper-based osteometric assessment and 3D laser-scanning technology to assess the anatomical and morphometric variation at the atlanto-occipital (AO) joint. This investigation was undertaken as an augmentation of the Smithsonian Institution, NMNH, Repatriation Osteology Lab’s (ROL) documentation process using the Osteoware: standardized skeletal documentation software [https://osteoware.si.edu/] in order to create a protocol for assisting in the reassociation of individual crania to postcranial remains when they are found separated within a commingled skeletal series. As such it provides a pragmatic example of a non-standard digital approach that may be undertaken to overcome commingling difficulties encountered during skeletal documentation or other investigations, and thus allows for the optimization of whole skeleton data recovered at the individual level, as well as the more culturally significant repatriation and reburial of the complete individual composing the remains.

Commingled skeletal analysis: the problem defined Cases involving mass burials and commingling of human skeletal remains are increasingly being reported in forensic

anthropology due to mass disasters, cremation litigation and human rights investigations (Ubelaker, 2008, 2014). Commingling of any skeletal series may result from a long and varied list of taphonomic factors beginning with the death of each individual composing the series and extending to the time of the most recent osteological analysis (Ubelaker, 2002). Cultural mortuary customs may involve leaving the body exposed to the environment, such as raising the corpse on a scaffold or placing a bundled infant in a tree (Sprague, 1968; Brugge, 1978), or the use of above ground charnel houses to facilitate secondary rituals (Chesson, 1999). Primary burials in the ground are often intruded upon due to intercutting of subsequent burial shafts, or in some cultures exhumation is conducted with subsequent secondary burial in community ossuaries (Pfeiffer & Fairgrieve, 1994). Over the course of documenting archaeologically recovered human remains at the NMNH, the ROL has discovered that skeletal elements of more than one individual are often found within catalog numbers from certain sites. One must also consider that the majority of North American skeletal series within most institutions were excavated during the 19th- and early 20th-centuries (Rose et al. 1996). These were the developmental years for archaeology as a discipline, and less than optimal excavation or field management protocols were exercised. For example, in the 1930s, Ales Hrdlicka (1945:212) disinterred Native Alaskan human remains in a manner he characterized as ‘exploratory incisions’, which lacked most of the archaeological control protocols developed to that point. Commingling among catalog numbers may also occur during packing for shipment, museum accession procedures, and subsequent storage and study over the decades. All of these factors are cumulative, resulting in older museum collections, or even curated forensic cases, being especially prone to commingling of individuals (Ubelaker, 2002). Commingled human remains methodology has received relatively little attention from physical and forensic anthropologists (Ubelaker, 2014). While technological advances in isotope and DNA analysis can tremendously assist in mass burial investigation (Mundorff et al. 2014; Puerto et al. 2014), the destructive nature and potential cost per sample in large skeletal series severely limits their use in museum and other budget-conscious institutions. Gonzalez-Rodriguez & Fowler (2013) investigated non-destructive XRF elemental analysis and found that the commingled remains of up to three individuals can be reliably separated; however, again the entry cost of this technology can be prohibitive for some researchers. This leaves qualitative and quantitative osteological comparison of skeletal elements to assess the degree of congruence between joint surfaces, which according to Kerley (1962) is one of the most convincing lines of evidence for reassociating bones into a single individual, also referred to as ‘individuation’ in the literature. Joint articular surfaces are known to be highly © 2016 Anatomical Society

Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo 3

constrained (Ruff et al. 1991; Lieberman et al. 2001), so once the potential pool of comparisons is culled by age and sex estimation, then assessing this congruence will assist in reassociation of skeletal elements into individuals within a commingled but closed burial environment. Whenever possible, multiple lines of evidence should be used to support any conclusion, such as common taphonomic appearance (animal scavenging, staining or sunbleaching patterns) or shared pathology like matching areas of osteoarthritic eburnation across the joint surfaces. Buikstra & Gordon (1980) and Buikstra et al. (1984) recognized that osteologists seldom approach joint congruence from the perspective of intra-individual patterning or interindividual variability. They developed quantitative osteometric standards to assess the degree of congruence between the bones of the neck in order to provide evidence in a forensic case involving the determination of individuation among cervical spinal elements. The cervical vertebrae of individuals from an anatomical collection were measured and interosseous variables were calculated to determine the normal variation in size difference between consecutive vertebrae. These ‘measures of dispersion and central tendency’ were successfully used in statistical tests to challenge the null hypothesis that the cervical vertebrae from the forensic case came from the same individual (Buikstra et al. 1984:125). This methodological approach utilizing joint congruence was implemented in the current study to assist in the reassociation of crania with their postcranial remains when found commingled at the NMNH. Anatomical variation of the AO joint was assessed by qualitative observations of articular surface shape, and quantitative 2D and 3D morphometrics of the articular surfaces and related structures.

Anatomical variation at the AO joint Reuniting commingled crania with their postcranial remains from large skeletal series can be imprecise when visually comparing qualitative aspects of the AO articular surfaces, composed of the occipital condyles (OCs) of the skull, and the superior facets of the first cervical or atlas vertebra (C1). Ubelaker (2002:333) maintains that ‘the relationship between articulating bones is especially close’, and provides as an example of this close relationship the OC and C1 facets. However, it has been shown that morphological variants of these articular surfaces, such as bipartite facets, may appear on only one element or even just one side of the AO joint (Naderi et al. 2005; Castillo & Dudar, 2010; Kalthur et al. 2014). Puerto et al. (2014) conducted subsequent DNA analysis of bones reunited by osteological methods and found that reassociations involving the AO joint are considered only moderately reliable with only 60–90% of commingled matches to the correct individual. Therefore, improvements upon traditional joint congruence analysis, involving ‘best-fit’ observations for reassociating © 2016 Anatomical Society

commingled crania and postcranial remains via the AO joint, are required. Quantitative studies of the occipital region or C1 condyles have involved investigations of anatomical variability towards understanding biomechanical function and optimizing surgical procedures (Naderi et al. 2005; Chancey et al. 2007; Kosif et al. 2007; Kalthur et al. 2014), chiropractic medicine (Briggs et al. 2008; Hart et al. 2009), and forensic sex and race estimation (Marino, 1995, 1997; Gapert et al. 2009a,b; Swenson, 2013). To our knowledge no study has been accomplished involving the qualitative or quantitative assessment of anatomical variation across the AO joint of individuals, and more specifically no investigation has addressed the morphometric assessment of AO joint congruence towards the reassociation of an individual’s cranium and postcranial elements. We hypothesize that basic qualitative observational assessment of the AO articular shape morphology, using the eight recognized ‘types’ identified by Naderi et al. (2005), will reveal a high proportion of matching condyle shape both across the joint interface (i.e. respective matching of the right and left OC with the right and left condyles of C1) and side-toside matching within the OC and C1 condyles. We further hypothesize that osteometric dimensions of the OC should display congruence with the articular facets of the matching C1 due to functional biomechanical constraints. A close, if not 1 : 1, relationship should be demonstrated. Lastly, we hypothesize that 3D digitization approaches that capture morphometric shape variables, such as surface area, condylar angle and radial curvature, will demonstrate stronger relationships of congruence and yield more robust variables for reassociating commingled remains.

Materials and methods Studies of the occipital region and C1 have revealed some statistically significant linear dimensions that can be used for sex and biological ancestry estimation when more accurate indicators are absent (Marino, 1995, 1997; Gapert et al. 2009a,b; Swenson, 2013). While the OC and C1 dimensions were shown to be of relatively limited efficacy for these purposes, any biologically meaningful difference such as sexual dimorphism must be considered in further analyses involving individuation of commingled remains at the AO joint. Therefore, skeletal remains from the Terry anatomical collection and a variety of archaeological series from the physical collections at the NMNH were chosen to include 52 females and 80 males from a range of biological ancestry: Asian (n = 27), AfricanAmerican (n = 23), European (n = 46) and Native American (n = 36), for a total of 132 individuals (see Tables 2 and 3). A diverse subsample of 36 individuals was selected for 3D laser scanning based on the preservation of the OC and C1 articular surfaces. This includes three Asian, nine African-American, 12 European and 12 Native American individuals, with 12 females and 24 males in the 3D subsample. Sixteen linear osteometric dimensions were captured per individual (to the nearest 10th of a millimetre) using Mitutoyo Series 500 digital sliding calipers. Matching OC and C1 articular surfaces were digitized using a NextEngine HDTM laser desktop scanner, which was

4 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

used to measure four surface area values (right and left OC and C1), two condylar angles (OC and C1), and four condylar radii (right and left OC and C1) per individual. In total 26 primary variables were collected, and these measurements were used to create 14 derived secondary variables to test for congruence at the AO joint. All primary variables and derived secondary variables are defined below. A small number of outliers was identified as plotting beyond the 95% confidence interval of the primary variable and investigated for possible cause. In most instances, osteoarthritic lipping or other degenerative change to the articular surface resulted in difficulty identifying the margin of the condyle, and in some cases the opposing articular surface did not display equal manifestation of osteoarthritis. In addition, two individuals often displayed outlier status; an archaeologically recovered male of European ancestry with significant scoliosis of the spine, and another European ancestry male with probable acromegly (see Jones & Ousley, 2008 and Ortner, 2003 for a discussion of these cases). The outlying data were removed from further analysis but are discussed as points of interest. Factorial ANOVA was accomplished within SYSTAT 10 with biological ancestry and sex as categorical variables. With outliers culled from the sample, no violations of the equal variance assumption were discovered as determined using the Levene test, which involves determining whether the absolute values of transformed ANOVA residuals are significant.

Linear osteometric variable definitions Sixteen congruence-based dimensions were captured from the matching OC and C1 of individuals, and are illustrated in Fig. 1 and defined below. To optimize the collection of metric data the measurements were standardized with definitions that utilize more precise anatomical points of reference. In the case of the anteroposterior length, the most anterior and most posterior point along the articular surface circumference was estimated, and the condylar length was then measured between these two points rather than trying to determine a geometric ‘long axis’ of the condyle; reference to the caliper ‘jaws’ being perpendicular or parallel to a condyle axis is present only to guide the researcher in the practical aspects of orienting the measuring device. Possible sources of measurement error include the presence of osteoarthritic lipping or joint surface erosion obscuring the precise identification of the articular margin; this lipping should be excluded, and if the margin is eroded or otherwise obscured by osteoarthritis or taphonomic damage the measurement should not be taken. The calculation of secondary derived delta (Δ) variables (see Tables 2–4) is described in the respective primary measurements.

Right and left OC medial-lateral width (ROC_ML, LOC_ML) Measured from the medial point of the widest spot on the OC articular surface to the lateral point of the widest spot of the OC. The caliper ‘jaws’ are held parallel to the long axis of the condyle. The respective right and left measurements of A are congruent to B, and by subtracting B from A the derived delta variables Δ_ROCC1_ML and Δ_LOC-C1_ML are created.

Right and left C1 condyle medial-lateral width (RC1_ML, LC1_ML) Measured from the medial point of the widest spot on the C1 superior articular surface to the lateral point of the widest spot of the C1 condyle. The caliper ‘jaws’ are held parallel to the long axis of the condyle. Measurement B is congruent to A.

Fig. 1 (a,b) Congruence-based linear dimensions of the OC and C1, with letters referring to the respective definitions in this paper. Variables A, B, C and D are captured from both right and left sides for a total of 16 measurements.

Right and left OC antero-posterior length (ROC_AP, LOC_AP) Measured from the most anterior point of the OC articular surface to the most posterior point of the OC articular surface. The caliper ‘jaws’ are held perpendicular to the long axis of the condyle. The respective right and left measurements of C are congruent to D, and by subtracting D from C the derived delta variables Δ_ROCC1_AP and Δ_LOC-C1_AP are created.

Right and left C1 condyle antero-posterior length (RC1_AP, LC1_AP) Measured from the most anterior point of the C1 superior articular surface to the most posterior point of the C1 articular surface. The caliper ‘jaws’ are held perpendicular to the long axis of the condyle. Measurement D is congruent to C.

Foramen magnum antero-posterior diameter (FM_AP) Measured from the most anterior point of the foramen magnum (basion) to the most posterior point (opisthion) of the foramen magnum using the ‘internal jaws’ of a spreading caliper. Generally © 2016 Anatomical Society

Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo 5

speaking, this diameter is along the sagittal plane, but avoids any small tubercles that may be present. The measurement E is congruent to F, and by subtracting F from E the derived variable Δ_FMVF_AP is created.

Vertebral foramen antero-posterior diameter (VF_AP) Measured from the most anterior point of the vertebral foramen of C1 to the most posterior point of the vertebral foramen using the ‘internal jaws’ of a spreading caliper. Generally speaking, this diameter is along the sagittal plane, but avoid any osteoarthritic lipping present on the facet for the odontoid process of the dens by measuring from the inferior side of C1. Measurement F is congruent to E.

Foramen magnum coronal diameter (FM_CR)

magnum just posterior to the left and right condyles. These markers facilitated the auto-alignment of the three scans usually required to digitize each OC and C1; however, in some cases more scans were required to completely capture the shape of the condyles, such as those with bipartite facets or more convex or concave surface morphologies (Fig. 2). The articular surfaces were isolated by digitally trimming the 3D mesh surrounding the joint margin and then smoothing was applied within the SCANSTUDIO HDTM software (Fig. 3). The SCANSTUDIO HDTM software was used to calculate the right and left condylar surface areas (ROC_SA, LOC_SA, RC1_SA, LC1_SA) and then summed for total condylar surface areas (OC_TSA and C1_TSA), based on the number and size of the polygons of the 3D mesh for each occipital and C1 condyle. The angle of the occipital and C1 condyle (OC_CAn, C1_CAn) was calculated using the

Measured from the most lateral point of the right side to the most lateral point of the left side of the foramen magnum using the ‘internal jaws’ of a spreading caliper. Generally speaking, this diameter is along the coronal plane, but accounts for any asymmetry. The measurement G is congruent to H, and by subtracting H from G the derived variable Δ_FM-VF_CR is created.

Vertebral foramen coronal diameter (VF_CR) Measured from the most lateral point of the right side to the most lateral point of the left side of the vertebral foramen using the ‘internal jaws’ of a spreading caliper. Generally speaking, the diameter is along the coronal plane, but accounts for any asymmetry. Take the measurement from the inferior side of the C1 (as per VF_AP). Measurement H is congruent to G.

OC maximum breadth (OC_MxB) Measured from the most lateral points of the right and left OC articular surfaces. The measurement I is congruent to J, and by subtracting J from I the derived variable Δ_OC-C1_MxB is created.

Fig. 2 The resulting merged 3D mesh (prior to smoothing) for a C1 bilaterally displaying the anatomical variant bipartite facets.

C1 condyles maximum breadth (C1_MxB) Measured from the most lateral points of the right and left C1 superior articular surfaces. Measurement J is congruent to I above.

OC minimum breadth (OC_MnB) Measured from the most medial points of the right and left OC articular surfaces. This is usually at the antero-medial margins. Measurement K is congruent to L, and by subtracting L from K the derived variable Δ_OC-C1_MnB is created.

C1 condyles minimum breadth (C1_MnB) Measured from the most medial points of the right and left C1 superior articular surfaces. This is usually at the antero-medial margins. Measurement L is congruent to K.

2D and 3D morphometric variable definitions The AO articular surfaces of the OC and the superior facets of C1 were digitized using a NextEngine HDTM laser desktop scanner model 2020i with divisions set at 15, precision at macro, triangle size 0.0050″, and smoothing set at 2. Three modeling clay markers of approximately 1 mm diameter were placed near but not on the condyles being scanned; one on the anterior border of the foramen magnum, and two on the lateral borders of the foramen

© 2016 Anatomical Society

Fig. 3 The matching C1 (top) and OC (bottom) 3D mesh after digital trimming to isolate the articular surfaces. Mesh smoothing was required to reduce surface texture artifacts as seen in Fig. 2. Note that unlike the C1 of this individual, the OC does not have bipartite facets, but type 4 ‘eight-shaped’ condyles according to the Naderi et al. (2005) standards.

6 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

Statistical Analysis Software SAS/STAT procedure employed by Tocheri et al. (2007), where the third eigenvector in a principal components analysis is the normal of the least-squares plane of the 3D mesh. To estimate the radius of curvature of the OC and C1 articular surfaces, a non-linear least-squares numerical optimization function was coded in the statistical software R Project for Statistical Computing version 3.1.2 (Fig. 4; Appendix 1). This function minimized the 3D sums of squares of the best-fit sphere modeled through the point cloud of the joint articular surface, which was accomplished using the Simulated Annealing optimization algorithm, with optimization parameters set to a maximum of 10 000 iterations. The geomorph package in R used to import files and extract 3D coordinates from scans (Adams & Otarola-Castillo, 2013). A reliability test of the estimated OC and C1 radii was conducted via bootstrap resampling to determine the variance in the optimization estimate. A random subsample of articular surfaces was chosen and submitted to the optimization procedure 100 times, creating a bootstrapped distribution from which confidence intervals were calculated. This technique revealed that 90% of the resampled optimization results fell within 0.15 mm range, indicating a 90% confidence interval of
0.075 mm. The calculation of secondary derived delta (Δ) variables (see Tables 2–4) is described in the respective primary measurements.

Right and left OC surface area (ROC_SA, LOC_SA) Surface area is calculated based on the number and size of the polygons of the 3D mesh for each OC. By subtracting the congruent surface area of the respective right and left RC1_SA and LC1_SA from ROC_SA and LOC_SA, the derived delta variables Δ_ROC-C1_SA and Δ_LOC-C1_SA are created.

Right and left C1 condyle surface area (RC1_SA, LC1_SA) Surface area is calculated based on the number and size of the polygons of the 3D mesh for each C1 superior condyle. The respective right and left RC1_SA and LC1_SA are congruent to ROC_SA and LOC_SA.

a

OC total surface area (OC_TSA) The OC total surface area is the sum of ROC_SA and LOC_SA. By subtracting C1_TSA from OC_TSA the derived delta variable Δ_OCC1_TSA is created.

C1 condyle total surface area (C1_TSA) The C1 total surface area is the sum of RC1_SA and LC1_SA. By subtracting C1_TSA from OC_TSA the derived variable Δ_OC-C1_TSA is created.

OC angle (OC_CAn) The overall angle of the OCs is the normal of the least-squares plane of the 3D mesh. By subtracting the congruent angle C1_CAn from OC_Can, the derived variable Δ_OC-C1_CAn is created.

C1 condylar angle (C1_CAn) The overall angle of the C1 condyles is the normal of the leastsquares plane of the 3D mesh. C1_CAn is the congruent angle of OC_CAn.

Right and left OC radius (ROC_Rd, LOC_Rd) Right and left OC radii are the estimates of the radius of curvature for their articular surfaces. By subtracting the congruent condylar radius of the respective right and left RC1_Rd and LC1_Rd from ROC_Rd and LOC_Rd, the derived variables Δ_ROC-C1_Rd and Δ_LOC-C1_Rd are created.

Right and left C1 condyle radius (RC1_Rd, LC1_Rd) Right and left C1 radii are the estimates of the radius of curvature for their articular surfaces. The respective right and left RC1_Rd and LC1_Rd are congruent to ROC_Rd and LOC_Rd.

Qualitative shape definitions Naderi et al. (2005) observed the OC and classified its perimeter shape into eight different types (Fig. 5; results in Table 2); however, no other guidance or definitions were provided in their study. These eight basic shape types are defined below, and used to

b

c

Fig. 4 (a–c) From top to bottom, antero-posterior views of the OC 3D mesh from three individuals in this study: (a) catalog number 484; (b) 381320; and (c) 923; all displaying a range of condylar surface curvatures as estimated by the radius of a 3D sum of squares for the best-fit sphere. For example, 923 has a left OC with an estimated radius of 13.5 mm, but the right condyle is visibly flatter and has a radius of 27.4 mm.

Fig. 5 The eight types of articular surface shape of the OC and C1 condyles after Naderi et al. (2005). 1 is Oval-shaped; 2 is Kidneyshaped; 3 is S-shaped; 4 is Eight-shaped; 5 is Triangle-shaped; 6 is Ring-shaped; 7 is Bipartite; 8 is Deformed/other. © 2016 Anatomical Society

Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo 7

qualitatively categorize the articular surface shape of the OC and C1 condyles in this study.

Oval-shaped The condyle is longer than it is wide along the antero-posterior axis, with a smooth convex perimeter and no concave deviations of the margins.

Kidney-shaped The condyle has an overall smooth convex perimeter with a single concave deviation either on the medial or lateral margin.

S-shaped The condyle perimeter has two concave curves, one on the medial margin the other on the lateral margin, but these concave curves are not opposite each other (note arrows in Fig. 5).

Eight-shaped The condyle perimeter has two concave curves, one on the medial margin the other on the lateral margin that are opposite each other creating a ‘pinch-point’ (note arrows in Fig. 5); however, there is some vestige of continuity to the articular surface at this point.

Triangle-shaped The condyle perimeter has one end much smaller than the other, and while there are no ‘straight’ margins or angles, a rough threesided triangular shape is perceived.

Ring-shaped The condyle perimeter is nearly as wide as it is long.

Bipartite The condyle perimeter has two distinct facets with palpable discontinuity of the condylar surface between them.

Deformed/other The condyle is misshapen due to osteoarthritis, or otherwise displays a shape unlike the defined seven types.

Results Qualitative OC and C1 articular surface shape The OC and C1 condyle articular surface shape, as captured by applying the Naderi et al. (2005) shapes and the standard definitions created here, are presented in Table 1. The overall results reveal that the type 1 ‘oval-shaped’ is the most common for the OC at 35.1% for the right and 29.5% for the left side, while for the C1 the most common type is 4 ‘eight-shaped’, with the right side at 48.1% and the left at 45.1%. The least common OC and C1 type was 8 ‘deformed/Other’, which appeared on only one individual, but the next least common OC type was 7 ‘bipartite’ (right 1.5% and left 2.2%), while for C1 it was type 6 ‘ring-shaped’ (1.5%, 1.5%). Naderi et al. (2005) also found that the most common OC type was ‘oval’ at 50%, and the least common was type 7 ‘bipartite’ at 0.8% (Table 2). © 2016 Anatomical Society

Naderi et al. (2005) did not include an investigation of the C1 condyles. Using a Chi-square goodness-of-fit test, a significant difference was found between the Naderi et al. (2005) OC type frequency pattern and the OC pattern revealed here (P < 0.001, 6 dof). Type 8 ‘deformed/other’ was not included as a category as it is a rare type in this and other studies, and would thus distort the pattern and bias statistical outcomes. Significant OC and C1 type frequency pattern differences were also found between all ancestry-based subgroups in this study (P < 0.001, 6 dof). For example, the anatomical variant bipartite facets appear with a frequency of 0.8% in the Turkish sample analyzed by Naderi et al. (2005), while in the current study European-Americans display bipartite facets at 3.2% for OC and 22% for C1; in Native Americans 0% for OC and 4.1% for C1; in AfricanAmericans 4.3% for OC and 8.7% for C1; and 0% for OC or C1 in Asian-American males. The overall frequency pattern of OC type in this study is not significantly different between the right and left side using a Chi-square goodness-of-fit test (P = 0.64, 6 dof), nor is the condyle type pattern different between right and left sides of the C1 (P = 0.10). When comparing the condylar shape type within the OC of each individual, it is discovered that there is a shape match between the right and left sides 53.7% of the time, while there is a 56.2% match between the sides of the C1. Comparison of the overall condylar type frequency pattern of the respective right OC and C1 and left OC and C1 result in a significant difference (P < 0.001, 6 dof). When the condylar shape across the AO joint of each individual is compared, the respective OC and C1 match shape type only 24.8% of the time on the right side and 23% on the left side. Given the demonstrated poor correspondence between OC and C1 qualitative shape at the individual level, this variable was not included in further investigation towards reassociation of commingled remains.

Quantitive assessment: linear and morphometric variables The archaeologically recovered male of European ancestry with significant scoliosis of the spine manifests significant condylar angle asymmetry in Fig. 6 (OC_CAn, C1_CAn). In Fig. 7 the European ancestry male with probable acromegaly displays a considerably increased total condylar surface area (OC_TSA, C1_TSA). Outlying data such as these were removed from further analysis to avoid bias of reported reference standards; however, in many instances these two cases proved not to be outliers for the derived delta variables involving the subtraction of the C1 primary variable from the congruent OC value. The inter-observer technical error of measurement (TEM) and relative TEM were calculated for the linear osteometric variables according to Lewis (1999) and Perini et al. (2005) from a subset of 19 individuals. The TEM for the 3D

8 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

Table 1 Qualitative assessment of OC and C1 condyle shape type using the Naderi et al. (2005) standards, with their summary data provided in column 2. The most frequent types appear in bold.

Condyle type

Naderi et al. (2005) N = 202

Right OC n (%)

Left OC n (%)

Right C1 n (%)

Left C1 n (%)

1 2 3 4 5 6 7 8

50.0% 3.5% 23.2% 4.2% 9.0% 4.0% 0.8% 5.5%

46 23 15 27 14 6 2 0

39 19 18 30 14 9 3 0

15 28 4 64 6 2 13 1

9 35 10 60 3 2 15 1

Oval Kidney ‘S’ ‘Eight’ Triangle Ring Bipartite Deformed/other

(35.1) (17.3) (11.3) (20.3) (10.5) (4.5) (1.5)

(29.5) (14.3) (13.5) (22.6) (10.5) (6.8) (2.2)

(11.3) (21.1) (3.0) (48.1) (4.5) (1.5) (9.8) (0.8)

(6.8) (26.3) (7.5) (45.1) (2.2) (1.5) (11.3) (0.8)

C1, first cervical or atlas vertebra; OC, occipital condyle.

Table 2 Overall sample (in bold), male (♂) and female (♀) summary statistics, and from the AO joint. Linear variables

N

Mean

SD

95% CI

Δ_ROC-C1_AP ♂ ♀ Δ_ROC-C1_ML ♂ ♀ Δ_LOC-C1_AP ♂ ♀ Δ_LOC-C1_ML ♂ ♀ Δ_OC-C1_MxB ♂ ♀ Δ_OC-C1_MnB ♂ ♀ Δ_FM-VF_AP ♂ ♀ Δ_FM-VF_CR ♂ ♀

126.00 75.00 51.00 130.00 78.00 52.00 127.00 76.00 51.00 129.00 78.00 51.00 129.00 78.00 51.00 127.00 75.00 52.00 128.00 77.00 51.00 125.00 76.00 49.00

0.73 0.91 0.47 0.66 0.76 0.52 0.66 0.70 0.61 0.86 0.94 0.73 1.28 1.30 1.26 0.86 0.99 0.67 5.39 5.65 4.98 1.92 2.35 1.25

1.71 1.55 1.91 1.43 1.48 1.36 1.72 1.79 1.62 1.31 1.35 1.24 1.45 1.57 1.26 1.51 1.40 1.64 2.00 2.13 1.73 2.01 1.98 1.88

1.03 1.26 0.99 0.91 1.08 0.89 0.96 1.10 1.06 1.08 1.24 1.07 1.53 1.65 1.60 1.12 1.31 1.11 5.73 6.13 5.45 2.27 2.80 1.78

to to to to to to to to to to to to to to to to to to to to to to to to

0.43 0.56 0.06 0.41 0.43 0.15 0.36 0.29 0.17 0.63 0.64 0.39 1.03 0.95 0.91 0.52 0.68 0.22 5.04 5.18 4.50 1.57 1.90 0.72

ANOVA

results for derived delta (Δ) linear osteometric variables

results

95% CI Size

Pearson’s r

ANOVA

0.60 0.70 1.05 0.49 0.66 0.74 0.60 0.81 0.89 0.45 0.60 0.68 0.50 0.70 0.69 0.52 0.64 0.89 0.69 0.95 0.95 0.71 0.89 1.06

0.74 0.71 0.64 0.47 0.41 0.54 0.78 0.63 0.81 0.55 0.48 0.61 0.89 0.87 0.92 0.82 0.85 0.78 0.50 0.33 0.77 0.58 0.57 0.64

By ancestry P = 0.004

No significant difference

By ancestry P = 0.031

No significant difference

By ancestry P < 0.001

No significant difference

By ancestry P = 0.016

By sex P = 0.002 and ancestry P = 0.029

Derived variable calculations are described in the definition of the respective primary measurements in the Materials and methods section.

morphometric variables is not considered here, but will be explored in future studies. All linear variable TEMs (range 0.16–1.07) and most relative TEMs (range 0.60–6.13%) arguably fall within the acceptable inter-observer error range for variables of this order of magnitude. Of particular note, all variables with relative TEM approaching or exceeding 5% involve medial-lateral dimensions of the OC (4.45– 6.13%) and C1 condyles (5.40–5.41); variables that demonstrate the weakest congruency relationships between

respective dimensions. Kouchi et al. (1999) maintain that this may be a function of the difficulty faced by observers interpreting definitions and discerning landmarks, such as the maximum medial-lateral condylar dimensions in this study. It is recommended that the medial-lateral condylar variables be avoided unless damage to the remains requires their utilization. The results of the linear and 3D morphometric analysis of the occipital and first cervical vertebra are shown in © 2016 Anatomical Society

Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo 9

Fig. 6 Plot of the estimated OC and C1 condylar angles (OC_CAn, C1_CAn) for n = 34 individuals in blue diamond symbols. The calculated linear regression is y = 0.51x + 70.59 with R2 = 0.50. The open circle represents the individual with scoliosis (314297), and the open triangle represents the case with diagnosed acromegaly (227508), both identified as statistical outliers.

Fig. 7 Plot of the estimated OC and C1 total surface areas (OC_TSA, C1_TSA) for n = 31 individuals of different biological ancestry. The calculated linear regression is y = 0.75x + 88.41 with R2 = 0.87. The open triangle in the upper right represents the individual with diagnosed acromegaly (227508), and is identified as a statistical outlier.

Tables 2–4. The derived delta variables are calculated differences between congruent primary condylar dimensions across the AO joint, and display a range in the strength of their correlation coefficients of between 0.45 and 0.89, as calculated between the OC and matching C1 primary measurements composing the derived variable. The lowest Pearson’s r-values of 0.45 and 0.49 involve the right and left mediolateral width of the OC-C1 condyles (Δ_ROC-C1_ML and Δ_LOC-C1_ML). The foramen magnum/vertebral foramen antero-posterior and coronal diameters (Δ_FM-VF_AP © 2016 Anatomical Society

and Δ_FM-VF_CR) have a Pearson’s r of 0.50 and 0.58, and display statistically significant ancestry differences with the latter also displaying sexual dimorphism, although less than 2 mm between subsamples. The antero-posterior lengths of the condyles (Δ_ROC-C1_AP and Δ_LOC-C1_AP) displays an improved correspondence, as seen by Pearson’s r of 0.74 and 0.78, but also significant differences by ancestral group (P = 0.004) of less than 2 mm. The strongest correlations among the linear variables are the congruent measurements involving the inter-condylar breadth dimensions across the AO joint (Δ_OC-C1_MxB and Δ_OC-C1_MnB). These inter-condylar maximum and minimum breadths also display among the smallest standard deviations (1.31 and 1.45, respectively) and 95% confidence interval sizes (0.50 and 0.52 mm), but the Δ_OC-C1_MxB also displays significant difference by ancestry (P < 0.001), again on the order of less than 2 mm between groups. Given that five out of the eight derived linear variables display significant sexual dimorphism and/or ancestry effects, summary statistics are provided by sex in Table 2 and by ancestry in Table 3 for use in testing reassociation from commingled skeletal remains. With the exception of the derived condylar angle (Δ_OCC1_CAn), with a Pearson’s r of 0.70, the remainder of the 2D and 3D morphometric variables have correlation coefficients ranging between 0.87 and 0.95. While the 2D condylar surface area variables display significant sexual dimorphism, the other 3D variables did not demonstrate statistically significant differences by sex or ancestry. The estimated OC and C1 radii, which measure curvature of the articular surface, show strong correlation, yet in a two-way ANOVA (radius ~ side + joint), the OC were significantly more curved (smaller radius) than the matching C1 articular surfaces (P = 0.03). Similarly, the right and left articular surface areas of the OC are significantly larger than the matching C1 (P = 0.029). These results may be explained from a biomechanical perspective where the OCs are the articular surface in motion (relative to the atlas vertebra) and must glide over and ‘nest’ within the C1 condyles that support the head, yet maintain a suitable articular surface contact area to transfer weight.

Discussion This investigation of the anatomical and morphometric variation at the AO joint was undertaken within the repatriation documentation process in order to create a protocol to assist in the reassociation of crania to postcranial remains found within commingled skeletal series. This protocol will allow for the optimization of whole skeleton data recovered at the individual level, as well as the more culturally significant repatriation and reburial of the complete individual composing the remains. While Ubelaker (2002:333) maintains that, ‘the relationship between articulating bones is especially close’ and uses the AO joint as an example, it

10 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

Table 3 Summary statistics of derived delta (Δ) linear variables from the AO joint by biological ancestry and sex as indicated by Table 1).

Linear variables Δ_ROC-C1_AP Mean/SD 95% CI CI size Δ_ROC-C1_ML Mean/SD 95% CI CI size Δ_LOC-C1_AP Mean/SD 95% CI CI size Δ_LOC-C1_ML Mean/SD 95% CI CI size Δ_OC-C1_MxB Mean/SD 95% CI CI size Δ_OC-C1_MnB Mean/SD 95% CI CI size Δ_FM-VF_AP ♂ Mean/SD ♂ 95% CI ♂ CI size ♀ Mean/SD ♀ 95% CI ♀ CI size Δ_FM-VF_CR ♂ Mean/SD ♂ 95% CI ♂ CI size ♀ Mean/SD ♀ 95% CI ♀ CI size

ANOVA

results (see

Asian-American n = 27♂ 0♀

African-American n = 12♂ 11♀

European-Americans n = 18♂ 26♀

Native American n = 23♂ 14♀

1.22/1.34 1.76 to 0.69 1.08

-0.20/2.0 0.62 to 1.02 1.64

0.26/1.47 0.81 to 0.29 1.1

1.52/1.55 2.03 to 1.0 1.03

1.22/1.17 1.67 to 0.78 0.88

0.85/1.45 1.44 to 0.25 1.19

0.40/1.47 0.89 to 0.09 0.97

0.34/1.48 0.83 to 0.15 0.98

-0.16/1.77 0.58 to 0.90 1.48

0.58/1.49 1.07 to 0.09 0.99

1.45/1.56 1.96 to 0.93 1.03

1.14/1.64 1.78 to 0.50 1.28

0.96/1.19 1.45 to 0.47 0.98

0.78/0.98 1.10 to 0.45 0.65

0.82/1.42 1.28 to 0.36 0.92

1.61/1.06 2.02 to 1.20 0.82

0.62/1.45 1.24 to 0.00 1.24

0.66/1.26 1.08 to 0.24 0.84

2.18/1.31 2.60 to 1.76 0.84

0.79/1.41 1.33 to 0.25 1.08

0.43/1.71 1.13 to 0.27 1.4

0.72/1.44 1.19 to 0.25 0.95

1.30/1.61 1.85 to 0.75 1.1

6.33/2.11 7.13 to 5.53 1.59

5.16/1.68 6.16 to 4.17 1.99 5.23/1.50 6.11 to 4.34 1.78

5.40/2.10 6.86 to 3.94 2.91 4.39/1.41 4.92 to 3.85 1.07

5.81/2.21 6.76 to 4.87 1.89 5.99/2.06 7.12 to 4.87 2.25

2.92/2.00 3.69 to 2.15 1.54

1.15/1.41 1.97 to 0.34 1.64 1.37/1.50 2.21 to 0.54 1.67

1.96/2.12 3.44 to 0.49 2.95 1.17/2.25 2.03 to 0.30 1.73

2.29/2.21 3.23 to 1.34 1.9 1.31/1.46 2.14 to 0.48 1.65

0.32/2.00 1.11 to 0.46 1.57

Derived variable calculations are described in the definition of the respective primary measurements in the Materials and methods section.

has been shown that the Naderi et al. (2005) shape types of the respective right and left OC and C1 articular surfaces are congruent within individuals less than 25% of the time. This result may partially contribute to an explanation of why Adams & Byrd (2006) contend that the cranium/atlas yields only moderately confident matches. Puerto et al. (2014) also found that forensic anthropologists’ reassociations at the AO joint should only be considered moderately reliable (in the range of 60–90% correct) when they subsequently tested osteological reassociations with DNA typing of the bones. Possible reasons for such poor confidence at so important a joint interface include unknown

morphological and unquantified osteometric variation within and between individuals; something not addressed prior to this study. The Chi-square goodness-of-fit test revealed a significant difference between the Naderi et al. (2005) OC type frequency pattern, derived from a Turkish population in their study, and the overall OC pattern found in this study derived from anatomical collections and archaeologically recovered Asian-Americans, African-Americans, EuropeanAmericans and Native Americans. While the subsamples are limited in size, further tests of the OC and C1 frequency pattern by biological ancestry also revealed statistical © 2016 Anatomical Society

Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo 11

differences between all groups in this study, possibly indicating that there are multifactorial population genetic and environmental differences expressed in the morphology of the AO joint. This supposition is supported, for example, by published OC frequencies for bipartite facets, or ‘type 7’ in the Naderi et al. (2005) standards. Naderi et al. (2005) report 0.8% bipartite facets for 404 OCs (202 crania) from a Turkish population, while Kalthur et al. (2014) report 4.9% for 142 OC from 71 crania of unreported biological ancestry. In this study, African-Americans display 4.3% OC bipartite facets, European-Americans 3.2%, and Native Americans and Asian-American males 0%. In comparison, published frequencies for bipartite facets on C1 range from 5.5% for 200 atlases ‘from different sources’ (Singh, 1965:565), to 20.8% for 500 atlases from French anatomical collections of unreported ancestral composition (Le Minor & Koritke, 1992; Billmann et al. 2007). In this study, AfricanAmericans display C1 bipartite facets with a frequency of 8.7%, European-Americans 22%, Native Americans 4.1%, and 0% for Asian-American males. The finding of statistical differences between overall biological ancestry group condyle type patterns is reflected in the ANOVA results of Tables 2 and 4, where significant differences by ancestry subsample were discovered for five of the eight derived linear variables. Significant sexual dimorphism was also discovered for the three derived condylar surface area variables (Δ_ROC-C1_SA, Δ_LOC-C1_SA, Δ_OC-C1_TSA) and the derived variable involving the coronal (side-to-side) diameter difference between the foramen magnum and vertebral foramen (Δ_FM-VF_CR).

Kalthur et al. (2014) compared the condylar shape type within each individual, and found that 62% of their sample of 71 crania displayed an OC shape match from right to left side. The current study similarly discovered that the right and left sides of the OC match 53.7% of the time, and that there is a 56.2% side-to-side type match for the C1 condyles. Of particular interest, this study found that condylar shape types of the respective right and left OC and C1 articular surfaces are congruent within individuals less than 25% of the time. This frequency of bilateral and across-joint matching within individuals may be explained if the growth and development of the condyles and condylar shape is similar to that observed for non-metric cranial traits. In these instances, unilateral trait expression is produced if the developmental instability variance is relatively constant across the range of liability of expression, then the number of individuals with unilateral expression will compose a larger proportion of those expressing a trait with low overall frequency (Hallgrı́ msson et al. 2005). It is recognized that forensic and physical anthropologists are not relying on simple OC and C1 condylar shape matching. They are visually observing and mentally comparing multiple dimensions and curvatures of the OC and C1 articular surfaces to deduce whether the overall ‘fit’ of the joint comparison is acceptable, all in order to resolve potential reassociations between commingled individuals. However, these observations and more subjective evaluations have proven to be poor proxies (Puerto et al. 2014) and would not meet the Daubert standards in the USA forensic science evidence admissibility law (Christensen, 2004).

Table 4 Overall sample (in bold), male (♂) and female (♀) summary statistics, and ables from the AO joint.

ANOVA

3D variables

N

Mean

SD

95% CI

95% CI size

Pearsons r

ANOVA

Δ_ROC-C1_SA ♂ ♀ Δ_LOC-C1_SA ♂ ♀ Δ_OC-C1_TSA ♂ ♀ Δ_OC-C1_CAn ♂ ♀ Δ_ROC-C1_Rd ♂ ♀ Δ_LOC-C1_Rd ♂ ♀

34 19 15 33 18 15 31 17 14 34 19 15 29 16 13 33 19 14

15.88 20.89 9.89 17.67 22.45 11.94 32.72 41.27 22.33 9.16 9.11 9.23 0.61 0.72 0.47 1.21 1.64 1

14.72 11.74 11.74 17.5 13.89 12.15 19.53 17.27 17.36 7.19 8.36 5.65 1.17 0.97 1.41 1 0.9 1.11

20.90 26.17 15.61 22.89 28.86 18.09 39.59 49.48 31.42 11.57 12.87 12.09 1.04 1.20 1.24 1.55 2.05 1.58

11.01 12.65 10.56 11.44 12.83 12.3 13.75 16.42 18.18 4.83 7.52 5.72 0.85 0.95 1.54 0.68 0.81 1.16

0.9 0.92 0.88 0.92 0.9 0.92 0.95 0.95 0.93 0.7 0.6 0.77 0.87 0.88 0.84 0.92 0.92 0.93

By sex, P = 0.011

to to to to to to to to to to to to to to to to to to

10.85 15.61 10.56 11.45 16.03 5.80 25.84 33.06 13.24 6.74 5.53 6.37 0.18 0.24 0.30 0.87 1.23 0.42

results for derived delta (Δ) 2D and 3D morphometric vari-

results

By sex, P = 0.029

By sex, P = 0.005

No significant difference

No significant difference

No significant difference

Derived variable calculations are described in the definition of the respective primary measurements in the Materials and methods section. © 2016 Anatomical Society

12 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

A quantitative osteometric approach to commingled remains reassociation at the AO joint is needed, and this requires exploration of the quantitative anatomical variability. Olivier (1975:507) published summary statistics for 30 occipital bone measurements captured from 125 ‘French skulls’ from a dissecting room context of unreported biological ancestry. He provided means and standard deviations by sex for the length and breadth of the foramen magnum and OCs, and these dimensions are comparable to the primary osteometric variables captured in the current study. Olivier’s (1975) four measurements were found to be statistically different to one or more of the biological ancestry and/or sex subsamples in this study; Native-American male and females display significantly smaller foramen magnum dimensions (P-values range between 0.027 and 0.002); European-American males display larger foramen magnum dimensions (P = 0.007 to < 0.001); and African-American females display significantly shorter and broader condyles as a group (P = 0.026 and 0.003). However, none of Olivier’s measurements was found to be statistically different when compared with the overall summary statistics of this study when ancestry was not considered. This suggests that osteometric approaches used to reassociate commingled skeletal remains should implement biological ancestry-specific standards when warranted by the study context, such as an archaeological site or forensic investigation involving a closed sample of individuals with known ancestry. This recommendation coincides with the Buikstra et al. (1984) case study where they collected cervical vertebrae osteometric data only from African-American females in the Terry anatomical collection to assess the reassociation potential of a known African-American female skeleton with a skull at the C3/C4 joint interface. While the samples are small and necessitate cautious interpretation, significant differences by ancestry subsample were discovered for five of the eight derived linear variables (Δ_ROC-C1_AP, Δ_LOC-C1_AP, Δ_OC-C1_MxB, Δ_FMVF_AP, Δ_FM-VF_CR), and significant sexual dimorphism was revealed for the derived coronal diameter difference of the foramen magnum and vertebral foramen (Δ_FMVF_CR). In addition, the derived 2D condylar surface areas (Δ_ROC-C1_SA, Δ_LOC-C1_SA, Δ_OC-C1_TSA) display significant sexual dimorphism; however, the variables derived from 3D laser scans of the OC-C1 condyles that measure condylar angle and curvature display no ancestry or sexual dimorphism, and have among the highest correlations between congruent OC and C1 variables. Weber & Bookstein (2011:8) maintain that the collection of ‘high-density data’, such as achieved by CT or laser scanning, improves our ability to quantify spatial structure and measurements of form. When these data are processed with morphometric tools, a more reliable and accurate assessment of morphological variation is produced than traditional landmark distance and angle measurements. In the current study, traditional linear measurements of the condyles are shown

to be more labile to size, proportion and other shape difference ‘noise’ across the AO joint, as epitomized by the < 75% mis-match frequency of the OC and C1 condyle shape type for individuals. It is maintained that the measurements derived from ‘high-density’ laser scans, including surface area, least-squares normal of the articular surface, and condyle curvature, are variables with more biomechanically canalized requirements that are independent of overall condylar perimeter shape. Buikstra et al. (1984) assert that the utilization of secondary variables (those derived from subtracting congruent measurements across a joint) that show the lowest standard deviation and smallest 0.95 confidence interval will minimize the chance of a Type II error, or the incorrect reassociation of skeletal elements into an individual that actually come from two people. The overall derived OC-C1 variables in this study fall in the mid- to upper range of ‘dispersion’ compared with those derived by Buikstra et al. (1984:129), who were attempting to reassociate individuals separated at cervical vertebrae 3 and 4, 5 and 6. Their standard deviations ranged between 0.36 and 1.04, and confidence interval sizes between 0.26 and 0.73 for their African-American female sample. In comparison, Byrd & LeGarde (2014:189) present summary statistics standards for commingled postcranial bones across selected joints (shoulder, elbow, hip, knee and ankle); their standard deviations range between 1.67 and 2.85. This may lead one to infer that the axial skeleton, especially the cervical vertebrae, may be under tighter growth and developmental constraints than the appendicular skeleton; however, the Byrd & LeGarde (2014:170) summary data include ‘multiple populations and both sexes’ to handle commingled cases where ancestry and sex is unknown. Within this context involving skeletal elements from individuals with unknown biological characterization, they maintain that osteometric comparisons of two bones at an articular interface should conservatively probe the evidence against an association, and therefore they provide reference standards without consideration of ancestry or sex. In this study quantifying the variability of the AO joint, our summary reference data are provided to handle both commingled contexts; where the remains are from a closed group of known ancestry, and for remains where ancestry and sex are not known or cannot be estimated. The osteometric test for reassociation of two bones sharing a joint articulation should minimally involve the comparison of the difference in size of linear osteometric dimensions to published reference data. It is then proposed that possible matches revealed by this first round of osteometric evaluations then be challenged by subsequent comparisons of surface area, angle (sum of the least squares plane), and/or an estimation of the curvature of the articulating portions as derived from laser scanning. For example, testing the reassociation of a cranium to an atlas/C1 could compare the OC-C1 condylar antero-posterior lengths or, © 2016 Anatomical Society

Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo 13

depending on the preservation of the bones, any combination of the other derived variables calculated from congruent measurements provided in this study. By subtracting the measurement of one bone from the congruent measurement of the other bone and comparing this difference (delta, or Δ) to the reference data mean provided, then the deviation of this difference divided by the reference data standard deviation (Std Dev) can be evaluated for significance: t ¼ ðD variable  reference data mean DÞ= reference data D Std Dev The resulting t value is consulted for the two-tailed t-distribution with n  1 degrees of freedom, where n is equal to the sample size of the reference standard to obtain a P-value. The null hypothesis tested is that the two bones are of similar enough size to be consistent with coming from one individual. A statistically significant P-value (using the alpha value chosen by the investigator 0.90–0.95) rejects the null hypothesis, in other words the size difference between the two bones is large (or small) enough that it is more likely they are from two individuals. Byrd & LeGarde (2014) recommend a more conservative 0.10 significance level, thus rejecting more comparisons and avoiding Type II errors, though the chosen significance level should be context- and case-dependent. Within the context of investigating certain archaeological sites with commingled remains, such as the burial rooms of Pueblo Bonito (Mulhern et al. 2006), ancestry may be regarded as relatively homogenous. A more stringent significance level could be chosen if regionally specific osteometric standards are created from skeletal remains recovered in primary burial contexts, where the articulation of skull and postcranial elements confirm the bones are from the same individual. This methodological approach is currently being investigated on commingled archaeologically recovered museum collections by the ROL at the NMNH.

Conclusions Repatriation legislation in the USA and/or law and policies in other countries can produce alliances between indigenous peoples and physical anthropologists, stimulating innovative research and making significant contributions to bioarcheology (Bray & Killion, 1994; Rose et al. 1996; Brownlee & Syms, 1999; Hanna, 2003; Young, 2010). Skeletons that were untouched for decades have now been, or are in the process of being, documented in response to repatriation requests. Osteological analyses are now more comprehensive and comparable due to standardized data collection efforts, and emerging 3D digitization technologies are being explored to create and share virtual skeletal remains such as the Digitized Diseases website (http:// www.digitiseddiseases.org/alpha/). On the negative side, © 2016 Anatomical Society

improvements in the ethical study of human remains have not removed osteological study or resulting data from the political process, but arguably have in some ways increased the politicization of conducting osteology (Clark, 1999). While the custody of skeletal collections remains important, so does the control over data and interpretations, especially if cultural affiliation of human remains has implications for the ownership or control over resources, such as in traditional land claims/disputes. One aspect of documenting human remains, in archaeological excavations, museum collections or forensic investigations, involves resolving commingled skeletal series in order to maximize the representation and biological characterization of individuals. While DNA sequence typing will remain the ‘gold standard’ for reassociations by positive genetic identification of the individual’s component elements, it is destructive, expensive, time-consuming and prone to contamination from non-endogenous sources. Therefore, a physical/forensic anthropological screening and evaluation for possible matches has become a standard approach (Ubelaker, 2014). The shortcomings of using a qualitative-only shape assessment of the AO joint for reassociations have been revealed; within individuals the overall condyle perimeter shape across the AO joint matches less than 25% of the time. In addition, it was shown that the OC surface area is significantly larger, and is significantly more curved, than the matching C1 condyle within individuals, perhaps further obscuring a qualitative observational approach to reassociating commingled crania and postcranial remains. These metric differences are likely due to the requirement of the head to rotate on the transverse axis while articulating with, and yet maintaining biomechanical support by, the atlas vertebra. A quantitative osteometric approach should instead be utilized by capturing landmark-based linear dimensions that are congruent for each bone across the joint. This permits the calculation of derived variables based on the difference of the two measurements that can then be compared with AO reference standards, as provided here. If time and resources allow, this linear osteometric comparison can act as a screen to identify possible reassociations for further osteometric assessment by 3D laser scanning with the derived variables of surface area, condylar angle and articular surface curvature. Osteometric reference standard summary statistics for commingled remains analysis have been published for the major joints of the postcranial appendicular skeleton, but currently exist only for contexts involving unknown biological ancestry and sex (Byrd & LeGarde, 2014). While the sex and biological ancestry subsamples in the current study are limited, and caution must be used in their interpretation, statistically significant sexual dimorphism and biological ancestry differences were shown to exist on the axial skeleton at the AO joint. Therefore, two sets of derived OC-C1 summary statistics are provided to address commingled

14 Variation at the atlanto-occipital joint, J. C. Dudar and E. R. Castillo

contexts where these variables are known and unknown. It is recommended that the future creation of additional reference standards should consider the use of study samples with balanced subgroup distributions by ancestry and sex, and that overall and group-specific summary statistics should be provided to cover all recovery contexts. Practitioners of other disciplines that may utilize the osteological and morphometric characterization of the AO joint reported here, such as surgeons conducting trans-condylar approach to remove tumors, are also advised to consider the biological variation discovered in this study. However, not all variables displayed significant sexual dimorphism or ancestry differences; those derived from the geomorphometric processing of ‘high-density’ laser scan data, such as condylar angle and curvature/radius, appear to characterize or isolate individual variation at a biomechanical level that may be more constrained and less subject to background developmental noise. The future investigation of these ‘higher-order’ variables may be fruitful not only for commingled remains resolution but for other approaches or analyses where the characterization of joint anatomical variation and function are critical.

Acknowledgements The authors would like to acknowledge the constructive comments of the two anonymous reviewers, and the assistance and support of Dr Matthew Tocheri, Dr David Hunt, Dr William Billeck, Tyler Cargill, rola-Castillo and Dr Daniel Lieberman. Erik Ota

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This code utilizes non-linear least-squares numerical optimization to estimate the radius of curvature of the articular surfaces of the right and left occipital condyles and right and left C1 superior articular facets by computing the best-fit sphere or partial sphere.

Appendix 1 R-code to estimate the radius of curvature of an articular surface

#Radius of curvature

#Extract x, y, and z coordinates x < - data$xpts y < - data$ypts z < - data$zpts

#Optimization function to estimate radius of curvature rad.fit <- function(par) { x.center = par[1] y.center = par[2] z.center = par[3] rhat = par[4] r < - sqrt( (x-x.center)^2 + (y-y.center)^2 + (z-z.center)^2 ) sum((r-rhat)^2 ) }

#Conduct optimization procedure out <- optim(c(mean(x),mean(y),mean(z),diff (range(y)/2)), method=SANN, control=list (maxit=10000, trace=T), rad.fit)

out$par[4]

The following R code is modified from http://stats.stackexchange.com/questions/20628/estimate-center-and-radius-of-a-sphere-frompoints-on-the-surface by E.R. Castillo.

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