Received: 25 December 2020
Revised: 30 May 2021
Accepted: 13 June 2021
DOI: 10.1002/oa.3014
RESEARCH ARTICLE
Best practice for osteological sexing in forensics and
bioarchaeology: The utility of combining metric and
morphological traits from different anatomical regions
Denise U. Navitainuck1
| Werner Vach1,2
| Kurt W. Alt1,3
| Jörg Schibler1
1
Integrative Prehistory and Archeological
Science (IPAS), Department of Environmental
Sciences, University of Basel, Basel,
Switzerland
2
Basel Academy for Quality and Research in
Medicine, Basel, Switzerland
3
Center of Natural and Cultural Human
History, Danube Private University, Krems,
Austria
Abstract
This paper aims to systematically investigate the value of combining traits from different anatomical regions in osteological sexing by contrasting the utility of single
traits and established scores with those of ensembles of traits from single or multiple
anatomical regions, allowing metric and morphological traits to be combined. The
utility was defined as the fraction of the population for whom we could reach a posterior probability above 95% of being male or female. A total of 675 adult individuals
Correspondence
Denise U. Navitainuck, Integrative Prehistory
and Archeological Science (IPAS), Department
of Environmental Sciences, University of Basel,
Spalenring 145, Basel CH-4055, Switzerland.
Email: denise.navitainuck@unibas.ch
Funding information
The study was funded by a scholarship of
Studienstiftung des Deutschen Volkes.
from the sixth to eighth century AD cemetery of Mannheim Bösfeld, Germany, were
assessed, and 27 postcranial metric traits and 41 morphological traits from the pelvis,
mandible, and cranium were used. In addition, 13 metric and 3 morphological scores
were considered. Linear discriminant analysis (LDA) was used to construct rules and
cross validation to determine accuracy and utility. These parameters were determined for single traits and scores, trait groups defined by anatomical regions and/or
previously considered in the literature, and ensembles of traits defined by selecting
several promising traits from different anatomical regions. Accuracy of single traits
ranged from 0.76 to 0.94, with scores even reaching 0.97, but utility remained
around 0.2–0.4 for metric traits and up to 0.6 for morphological traits. Only scores
and ensembles combining traits from different anatomical regions reached a utility
above 0.7; that is, sex could be estimated in more than 70% of the individuals with a
posterior probability above 95%. When selecting a limited number of traits for systematic sexing in a human skeletal series, it is advisable to select traits from different
anatomical regions to obtain a reasonably reliable result in as many individuals as
possible. Large scale investigations covering all relevant anatomical regions
and involving a wide range of populations are required for more precise
recommendations.
KEYWORDS
latent class analysis (LCA), metric traits, morphological traits, sex estimation
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any
medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
© 2021 The Authors. International Journal of Osteoarchaeology published by John Wiley & Sons Ltd.
Int J Osteoarchaeol. 2021;1–14.
wileyonlinelibrary.com/journal/oa
1
NAVITAINUCK ET AL.
2
1
|
B A CKG R O U N D
The starting point of the investigation was a list of publications
on sex estimation considering various groups of traits. The traits iden-
Biological sex, alongside age at death, is among the most essential
tified in these publications were determined, when possible, in all
information required about an individual in both a forensic and bio-
adult skeletal individuals of an early medieval series. We then deter-
archaeological context. It is also a key building block for population
mined the utility of each single trait, and the previously suggested
studies. However, an accurate assessment of these parameters is highly
combinations of traits, before considering the utility of trait groups
dependent on the preservation and integrity of the human remains.
defined by anatomical regions and new ensembles of traits covering
Both metric and morphological traits have been used previously for
several anatomical regions, including both morphological and metric
skeletal sexing (e.g., Buikstra & Ubelaker, 1994; Novotny, 1975; Rösing
traits. The utility of a trait group is determined by developing a dis-
et al., 2007; Stloukal, 1982). Traditionally, metric traits have been used
criminant score specific for the series considered here; that is, we
to construct binary decision rules based on the application of a discrimi-
make no use of published sex estimation approaches.
nant function to one or several metric traits (e.g., Albanese et al., 2005;
In the Supporting Information for this article, we systematically
Alt et al., 1995; Christensen et al., 2014; Garcia-Campos et al., 2018;
compared the distribution of single traits in our population with those
Henke, 1977). Morphological traits have typically been used to arrive at
from the selected publications and investigated the distribution of the
a 3- (female, indeterminate, and male) or 5-point (female, probable
posterior probabilities obtained by the DPS2 tool in our sample.
female, indeterminate, probable male, and male) ordinal scale. A fundamental step forward was the work by Murail et al. (2005) in developing
the diagnose sexuelle probabiliste (DSP) and DSP2 (Bruzek et al., 2017)
2
|
MATERIAL AND METHODS
tools (based on classical discriminant analysis), enabling for any subset
of at least 4 out of 10 metric pelvic traits to determine the (posterior)
2.1
|
The skeletal sample
probability of a skeletal individual representing a male or a female subject, respectively. The approach behind these tools combines two basic
The basis of this study was the skeletal sample from the early medi-
principles: flexibility and cautiousness. Flexibility in that it allows the
eval cemetery of Mannheim-Seckenheim (“Hermsheimer Bösfeld”),
sex estimation of any subject with a sufficient number of traits to be
Germany, which has been previously studied (e.g., Hansen &
conducted, regardless as to how many and which traits are measurable.
Alt, 2012; Meyer et al., 2014; Meyer & Alt, 2012; Navitainuck
This is in contrast to alternative published approaches using multiple
et al., 2013). Given the number of graves and grave goods recov-
traits, as they typically require all traits to be measurable. And cautious-
ered from this cemetery, dating from the sixth to the eighth century
ness, as Murail et al. (2005) require a posterior probability of at least
AD, the skeletal sample represented a promising cohort for both
95% to be male, or of at least 95% to be female, in order to arrive at a
osteological and archeological research. More than 900 individuals
final sex estimation – an approach also used in other studies
were found at this site, and a total of 675 adult individuals form the
(e.g. Hora & Sladek, 2018; Santos et al., 2014). In this way, these
basis of this study. Age estimation was carried out according to
authors overcame the tradition of strictly binary decision rules for met-
international
ric traits and introduced an intermediate group for which the sex
Lovejoy, 1985; Miles, 1963; Nemeskéri et al., 1960; Szilvassy, 1988;
remains undetermined.
Todd, 1920) as part of the general anthropological study of this
However, this flexible and cautious approach can be applied to
any group of traits, including morphological ones. For any given group
standards
(Lovejoy
et
al.,
1985;
Meindl
&
cemetery (Meyer & Alt, 2012), separating subadult from adult individuals (20 years and older).
of traits, we can arrive at a posterior probability for any given sub-
The skeletal sample from the Bösfeld site is assumed to represent
group of these traits measurable in an individual using discriminant
Franconian retinue warriors and their families (Koch, 2013; Koch &
analysis. This allows us to compare different trait groups not only with
Wirth, 2005). According to the archeological findings, the connection
respect to their accuracy (as done in many published studies) but also
between the Merovingian cemetery and the settlement indicates con-
with respect to their utility for sex estimation. We define the utility of
tinuous use. Burials with weapons as grave goods are assumed to be
a trait group as the fraction of skeletal individuals for whom we can
warriors, with a total of 10 fully armed warriors and about 80 burials,
arrive at a final sex estimation, that is, at a posterior probability of at
per generation, having been identified (Koch, 2013). Together with
least 95% being either male or female. A high utility of a group of
the historical background, this forms a well-founded picture of the
traits requires both a high accuracy as well as a sufficiently high rate
composition of the sample (Koch, 2004, 2007, 2013; Link, 2003;
of measurable traits.
Wirth et al., 2007).
The aim of this paper is to systematically investigate the increase
in utility when combining several traits using this flexible and cautious
approach, based on a variety of traits that have already been
established for sex estimation in general. Both metric and morphologi-
2.2 | Traits and trait groups selected from the
literature
cal traits were considered, and several anatomical regions were
covered. The focus was to combine traits across several anatomical
Ten publications on metric traits for sex estimation and five publica-
regions, including combining morphological with metric traits.
tions on morphological traits build the basis of our investigation
NAVITAINUCK ET AL.
3
(cf. Table 1). From these publications, which covered recent
This way, 13 scores involving only the selected metric traits and
(e.g., Gapert et al., 2009) as well as traditionally used approaches
3 scores based on morphological traits were identified and included in
(e.g., Phenice, 1969), we selected 27 main metric traits that are easily
the analysis.
Tables 1–4 give an overview on the traits and scores identified in
measurable and have a high probability of preservation. The anatomical regions covered are os occipitalis, scapula, os coxae, patella, talus,
the selected publications.
and calcaneus. All 41 morphological traits from the publications were
selected, covering os coxae, mandibula, and cranium. In addition, the
literature was checked for the definition of scores, that is, explicit for-
2.3
|
Data assessment
mulas to combine the information from several traits into one number.
All the trait measurements were taken according to the description in
the cited literature using a digital sliding caliper (measuring accuracy
T A B L E 1 Metric traits considered in this study stratified by the
source publication
Source and trait
Laterality
of 0.02–0.04 mm), though for some of the pelvic measurements, a
friction divider was used (see Bruzek et al., 2017 and instructions
including pictures in the DSP2 tool). Bilateral traits were measured on
both sides. All measured values were entered into a Microsoft Access
Gapert et al. (2009) (Basicranium)
MLC: maximum length of condyle
Bilateral
MWC: maximum width of condyle
Bilateral
EHC: external hypoglossal canal openings distance
Unilateral
MxID: maximum interior distance between condyles
Unilateral
BCB: maximum bicondylar breadth
Unilateral
MnD: minimum distance between condyles
Unilateral
Helmuth and Rempe (1968) (Atlas and Axis)
database, except for the metric pelvic measurements, which were
entered into the DSP2 software provided by Bruzek et al. (2017).
All data were assessed by one observer (DN).
2.4
|
Reference standards
To determine the utility and accuracy of a trait group, we needed a
Atlasap: anterior–posterior distance
Unilateral
reference standard for the sex of the individuals. In this paper, we
Axisheight: anterior full height
Unilateral
considered three different basic approaches to obtain such a
standard:
Özer et al. (2006) (Scapula)
GCH: glenoid cavity height
Bilateral
GCB: glenoid cavity breadth
Bilateral
1. Using subjects with a posterior probability for male or female
above 0.95 based on DSP2. However, as this tool does not allow
Murail et al. (2005) (Os coxae, pelvic)
PUM: acetabulo-symphyseal pubic length
Bilateral
SPU: cotylo-pubic width
Bilateral
the combining of traits from the left and the right side, we actually
obtained two reference standards.
2. Using latent class analysis (LCA) applied to all available traits in
DCOX: innominate or coxal length
Bilateral
IIMT: greater sciatic notch height
Bilateral
ISMM: ischium post-acetabular length
Bilateral
threshold probability. LCA is a popular method to find different
SCOX: iliac or coxal breadth
Bilateral
phenotypes in multivariable data. It is based on the simple assump-
SS: spino-sciatic length
Bilateral
tion that there are classes in the population of interest that differ
SA: spino-auricular length
Bilateral
in the distribution of variables. It allows the inclusion of continuous
SIS: cotylo-sciatic breadth
Bilateral
as well as ordinal variables affected by missing values and is there-
VEAC: vertical acetabular diameter
Bilateral
fore well suited to construct a data-dependent reference standard
order to obtain a posterior probability for each subject, transforming the probabilities into a reference standard using a specific
for sex. It has already previously been used for this purpose
Bidmos et al. (2005) (Patella)
MAXH: maximum height
Bilateral
MAXB: maximum breadth
Bilateral
(e.g., Passalacqua et al., 2013).
3. Using the archeological sex provided by C. Meyer and M. Stecher
at the University of Mainz based on sex-specific grave goods typi-
Bidmos and Dayal (2003) (Talus)
TL: talar length
Bilateral
TH: talar height
Bilateral
TW: talar width
Bilateral
Introna et al. (1997) (Calcaneus)
cally
observed
in
early
medieval
(Franconian)
burials
(i.e., Brather, 2008; Koch, 1977). In this way, a sex was assigned to
267 individuals with multiple, nonconflicting pieces of information.
We, therefore, had four reference standards, none of which was
MAXL: maximum length
Bilateral
optimal. When using DSP2 as a reference to evaluate traits already
BH: body height
Bilateral
included in the DSP2, or correlated with traits included in the DSP2,
Note: For each trait, it is indicated whether it is expressed unilateral or
bilateral.
we may have been too optimistic. With respect to LCA, this applies to
all traits used; indeed, the overoptimism may even be increased as the
NAVITAINUCK ET AL.
4
TABLE 2
Scores based on metric traits considered stratified by source publication
Traits involved
Name
Formula
Cranium a
0.274 * MLC left + 0.286 * MWC right + 0.273 * MnD – 15.548
Gapert et al. (2009) (Basicranium)
MLC left, MWC right, MnD
BCB, MnD
Cranium b
0.224 * BCB + 0.191 * MnD – 15.039
MLC, MWC, BCB, MxID, MnD
Cranium c
0.238 * MLC right + 0.288 * MWC right + 0.114 * MLC left + 0.032a MWC
left 0.049a BCB + 0.016a MxID + 0.277a MnD – 16.004
MLC left, MWC right, BCB, MnD
Cranium d
0.244 * MLC left + 0.253 * MWC right + 0.042 * BCB + 0.253a MnD
BCB, MxID, MnD
Cranium e
0.198 * BCB + 0.040 * MxID + 0.193 * MnD – 15.235
MnD, MxID
Cranium f
0.278 * MnD + 0.170 * MxID – 11.705
Scapula aa
(0.143 * GCH) + (0.367 * GCB) – 14.340
Patella aa
0.223 * MAXH + 0.133 * MAXB – 14.581
Talus aa
0.256 * TL + 0.122 * TW + 0.044 * TH – 20.015
Talus ba
0.158 * TL + 0.204 * TH + 0.159 * TW – 20.103
Calcaneus aa
1.96 * MAXL + 2.42 * BH
MAXLTal (=TL), MAXWTal (=TW)
Talus ca
0.42002 * TL + 0.41096 * TW.
BHCalc (=BH), MAXLTal (=TL),
MAXWTal (=TW)
CalTal aa
0.23126 * BHCalc + 0.31859 * MAXLTal + 0.51311 * MAXWTal
16.110
Özer et al. (2006) (Scapula)
GCH, GCB
Bidmos et al. (2005) (Patella)
MAXH, MAXB
Bidmos and Dayal (2003) (Talus)
TL, TH, TW
Bidmos and Dayal (2004) (Talus)
TL, TH, TW
Introna et al. (1997) (Calcaneus)
MAXL, BH
Steele (1976) (Calcaneus and Talus)
Note: For each score, the traits involved, a name used in this publication, and the formula published to sum up the measurements are given.
Scores that can be applied separately for the left and right side.
a
TABLE 3
Morphological traits considered stratified by publication
Trait
Female expression
Male expression
Glabella (3)
Smooth
Marked to massive, prominent
Arcus superciliaris (2)
Smooth
(Very) marked, arched
Tubera frontalia and parietalia (2)
Marked
Indistinct to missing
Inclinatio frontale (1)
Vertical
(Strongly) inclined
Processus mastoideus (3)
(Very) small
(Very) large
Relief of Planum nuchale (3)
Smooth
Nuchal lines and occipital crest (with rough
surface)
Protuberantia occipitalis externa (2)
Smooth
(Very) marked
Processus zygomaticus (3)
(Very) thin, low
(Very) thick, high
Os zygomaticum (2)
(Very) low, smooth surface
(Very) high, irregular surface
Crista supramastoidea (2)
(Very) slight-present
(Very) marked
Margo supraorbitale Forma orbitae (1)
Round, (very) sharp border
Quadrangular, (very) rounded
Overall aspect (3) (Mandibula)
(Very) gracile
(Very) robust
Mentum (2)
Small, rounded
(Very) prominent
Angulus mandibulae (2)
Smooth
(Strongly) marked eminences
Margo (1)
Thin
Thick
Ferembach et al. (1980) (cranium) 5-point scale
Ferembach et al. (1980) (Mandibula) 5-point scale
Kemkes-Grottenthaler et al. (2002) (Mandibula) 5-point scale
Ramus flexure
Straight edge
Flexure at the level of the occlusal surface
of the molars
NAVITAINUCK ET AL.
TABLE 3
5
(Continued)
Trait
Female expression
Male expression
Ferembach et al. (1980) (os coxae, pelvis) 5-point scale
Sulcus praeauricularis (3)
Deep, (well) delimited
Slight-present/absent
Incisura ischiadica major (3)
(Very) wide, U-shaped
(Narrow), (very) V-formed
Angulus pubisa (2)
(Strongly) obtuse to right angled, rounded
(Strongly) acute angled, A-form
Arc composé (2)
Double curve
Single curve
Os coxae (2)
Low, broad, with expanding ala ossis and
slight muscle relief
High, narrow with stronger muscle relief
Foramen obturatum (2)
Triangular, (with sharp rims)
Oval, (rounded rim)
Corpus ossis ischii (2)
(Very) narrow, with less conspicuous Tuber
ischiadicum
(Very) broad, marked Tuber ischiadicum
Crista iliaca (1)
(Very) flat, S-formed
Accented S-form
Fossa iliaca (1)
(Very) low, broad
(Very) high, narrow
Pelvis major (1)a
(Very) broad, oval
(Very) narrow, heart shaped
Development of negative relief
(preauricular surface 1)
Deep depression well-limited (pits)
Relief smooth or very slightly negative relief
Aspect of grooves or pitting
(preauricular surface 2)
Pits or groove with closed circumference
Depression with open circumference
Development of positive relief on
preauricular surface
(preauricular surface 3)
Lack of tubercle
Tubercle present or clear protuberance
Proportion of length of sciatic notch
chords (sciatic notch1)
Posterior chord segment longer than or
equal to anterior chord
Posterior chord shorter than anterior chord
Form of contour notch chords
(sciatic notch 2)
Symmetry relative to depth in basal portion
of sciatic notch
Asymmetry relative to depth of sciatic
notch
Contour of posterior notch chord
relative to line from point a to sciatic
notch breadth (sciatic notch 3)
Outline (contour) of posterior chord does
not cross perpendicular line
Contour of posterior chord crosses
perpendicular line
Composite arch, relation between
outline of sciatic notch and outline of
auricular surface
Double curve
Single curve
Characterization of margo inferior ossis
coxae (1)
External eversion
Direct course of medial part
Absence or presence of the phallic
ridge (inferior ossis coxae 2)
Lack of the phallic ridge or presence of only
little mound
Clear presence of the phallic ridge
Ischiopubic ramus aspect (inferior ossis
coxae 3)
Gracile aspect
Robust aspect
Relation between pubis and ischium
lengths (ischiopubic proportion)
Pubis longer than ischium
Ischium longer than pubis
Ventral arc
Ventral arc on the ventral surface of the
pubis
Slight ridge on ventral aspect of the pubis
Subpubic concavity
Subpubic concavity/dorsal aspect shows
lateral recurve in the ischiopubic ramus
No concavity
Ischiopubic ramus
Medial aspect of the ischiopubic ramus
female: ridge
Broad surface
Bruzek (2002) (os coxae, pelvis) 3-point scale
Phenice (1969) (os pubis) 3-point scale
Dar and Hershkovitz (2006) (os sacrum/ilium) 4-point scaleb
SIB: sacro-iliac joint bridging
Sacro-iliac joint bridging
Note: For each trait, the anatomical name or a short description (with the name used in this paper in parantheses) and the typical expression for males and
females are given. For the publications, the reference, the bone/anatomical region involved, and the scoring scale are given; 3-point scale refers to a
coding conceptually corresponding to male–indefinite–female and 5-point scale to a coding conceptually corresponding to male–probably male–
indefinite–probably female–female. The papers may not explicitly use these labels.
a
These two traits were not included in our analyses, as they could be assessed in 1 or 15 cases only.
b
The 4-point scale referred conceptually to the states, m, m?, 0, 0? The trait does not allow to come to the decision that a subject is female.
NAVITAINUCK ET AL.
6
TABLE 4
Scores based on morphological traits considered stratified by source publication
Traits involved
Scoring rule
Name
All traits from Ferembach et al. (1980)
cf. Table 3
The scoring rule is based only on the traits discernible. Each single trait is
scored as 2, 1, 0, 1, or 2. The overall score is defined as the weighted sum
of the trait specific scores (weights shown in Table 1) divided by the sum of
the weights of the discernible traits.
Ferembach score
All traits from Bruzek (2002) cf. Table 3
For the three traits, preauricular surface, sciatic notch, and inferior ossis coxae,
the three subtraits are reduced to a male (1)–indefinite (0)–female ( 1)
decision based on a simple majority rule. Then a summary score is built over
of these three traits, composite arch and ischiopubic proportion.
Bruzek score
Phenice-defined traits ventral arc,
subpubic concavity, ischiopubic ramus
The three traits are each scored as 1, 0, and 1. The paper does not include an
explicit score but suggests a more informal majority rule. In the case of three
traits scored on a 3-point scale, this is however close to considering the sum
(or average) over the three traits.
Phenice score
Note: For each score, the traits involved, a description of the scoring rule, and a name used in this paper are given.
construction of the reference standard is already based on our data.
trait is measurable and the average number of measurable traits
However, LCA is based on many traits, so that the effect for a single
within the individuals with at least one measurable trait, which we
trait may be negligible. The archeological reference standard does not
refer to as the “effective number of traits.” The first aspect is depicted
suffer from this problem, as it is completely based on external
by computing an accuracy in the traditional sense: a subject is reg-
information (grave goods). Conversely, DSP2 and the archeological
arded as male if the cross-validated posterior probability is above
standard provided a sex estimation in less than 50% of all individuals
50%; otherwise, it is female. This decision is then compared with the
in our series, whereas LCA has the potential to define a reference
reference standard, and the rate of agreement is reported as accuracy.
In addition, the rate of misclassified subjects among those with a
standard for a larger number of subjects.
Consequently, we defined our final reference standard by com-
posterior probability above 95% is reported. This number serves two
bining all four reference standards. As each assigns a sex to only a
purposes. First, the misclassification rate can be much less than 5%, if
subset of all individuals, which of the four reference standards is actu-
there are many subjects with a posterior probability higher than 95%.
ally applicable to a particular individual must be taken into account.
The misclassification rate can therefore inform us about the additional
Therefore, the overall reference standard is “male,” if all reference
potential of a trait group. Conversely, the computation of a posterior
standards applicable to an individual indicate “male,” and “female” is
probability depends on the assumption of a normal distribution of the
defined in an analogous manner. The reference standard remains
discriminant score. The actual distribution may differ from a normal
undefined if none of the four reference standards is applicable or if
distribution. For example, metric traits with skewed distributions or
they result in contradicting classifications.
affected by outliers may result in a distribution with heavier tails, or
the distribution may be very discrete in the case of a single or only a
few morphological traits. Then the misclassification rate may be above
2.5
|
Computation of utilities and accuracies
5%, informing us about a violation of this assumption and the potential invalidity of the posterior probabilities. Misclassification rates are
For any group of traits, the utility is determined in the following way:
only reliable if they can be based on a sufficient number of subjects;
for each subgroup of traits appearing as measurable traits in at least
therefore, the computation is restricted to trait groups with at least
one individual, linear discriminant analysis (LDA) is applied to deter-
100 individuals with a posterior probability above 95%.
mine a new discriminant score, that is, a weighted sum of the measurements. Based on this score, the posterior probability of each
individual (with this pattern of measurable traits) to be male is com-
2.6
|
Analytic strategy
puted. We combine this with cross validation by only using the data
of the remaining individuals to determine the posterior probability for
First, we checked the validity of the final reference standard by com-
each single individual. In this way, we obtain a posterior probability
paring the agreement between the four basic reference standards.
for any individual for whom at least one trait is measurable, that is, a
We then considered the utility of single traits and scores identified in
flexible approach. The utility is then defined by the fraction of individ-
the selected literature, with the central investigation considering the
uals reaching a posterior probability above 95% or below 5%,
utility of trait groups. Trait groups defined by an anatomical region or
reflecting a cautious approach to sex estimation.
previously considered in the literature were investigated before we
The utility of a trait group depends on both the accuracy of the
finally considered ensembles of traits by selecting a few promising
traits involved and their measurable frequency. The second aspect is
traits from different anatomical regions, allowing us also to combine
depicted by reporting the number of individuals for which at least one
morphological with metric traits.
NAVITAINUCK ET AL.
7
Potential differences in population distributions when comparing
variables are measured. Correlation matrices that failed to be positive
our study population and the populations used in the selected publica-
semidefinite were replaced by the least-squares positive-semidefinite
tions are investigated in Appendix S1 for all traits. To evaluate the
approximation.
possible impact of differences in population distributions on sex esti-
We have used LDA to develop a rule for sex estimation for a
mation rules based on requiring a 95% posterior probability, the distri-
given ensemble of traits due to its popularity in this field. In fact,
bution of the posterior probabilities computed by the DSP2 tool in
a recent systematic comparison also found no distinct advantages in
our population is depicted in Appendix S2.
using alternative approaches (Nikita & Nikitas, 2020).
|
2.7
2.7.3
Details of statistical methods
|
Cross validation
All computations were performed in Stata 15.1.
A 10-fold cross validation was used.
2.7.1 |
standard
3
Use of LCA to construct a reference
|
3.1
RE SU LT S
|
Measurements
All unilateral and bilateral metric traits and all morphological traits
were used as input to the LCA. Because LCA assumes conditional
Out of the 675 adult individuals, at least one of the metric traits was
independence of the input variables used given the true sex, all bilat-
measurable in 534, and at least one morphological trait was measur-
eral traits entered this analysis once using the average of the two
able in 597. In 621 individuals, at least one metric or one morphologi-
measurements if both are available. Nevertheless, the resulting poste-
cal trait was measurable. Information on the distribution of the single
rior probabilities may be too optimistic, as we still have to expect cor-
traits can be found in the Tables S4 and S5.
relations among the traits beyond what we can explain by sex. To
take this into account, threshold probabilities of 0.999 and 0.001,
respectively, were used. The two classes obtained by LCA were com-
3.2
|
Construction of reference standards
pared with the archeological reference standard, and the class with
the higher frequency of males (according to the archeological sexing)
The application of LCA with the number of classes fixed to two
obtained the label “male.”
resulted in estimated class prevalences of 49.7% and 50.3%,
corresponding with the expectation that the classes should represent
sex. A total of 473 individuals obtained a posterior probability above
2.7.2
|
Linear discriminant analysis
0.999 or below 0.001, respectively. Table 5 shows the distribution of
the two sexes according to the different basic reference standards
Metric traits entered the LDA with their actual measurements. Mor-
and the agreement between the four basic reference standards. The
phological traits entered the LDA after recoding to
1, 0, 1, 2 or
agreement was nearly perfect. The final overall reference standard
1, 0, 1. Bilateral traits entered with both measurements if they
identified 253 males and 263 females (cf. Table S6). DSP2 identified
were available. In computing correlation matrices, as input to the LDA,
more males than females, whereas the archeological sexing
the available pair approach is used, that is, each single correlation
identified more females than males. The first reflects the higher popu-
between two variables is based on all subjects for whom both
lation variation in males than in females in the reference sample used
to
2,
T A B L E 5 The number of males and females identified according to the different reference standards (left part) and the agreement between
the reference standards (right part)
Number of
DSP right
Agreement
Females
Males
50
113
DSP right
DSP right
DSP left
LCA
Archeological
100%
98.1%
98.5%
99.3%
100%
DSP left
58
88
DSP left
92/92
LCA
238
235
LCA
158/161
144/145
Archeological
160
107
Archeological
66/67
62/62
99.6%
222/223
Note: The agreement is expressed as a percentage in the upper triangle and as the absolute number of agreeing individuals related to the absolute number
of individuals for whom both reference standards could be applied in the lower triangle.
Abbreviations: DSP, diagnose sexuelle probabiliste; LCA, latent class analysis.
NAVITAINUCK ET AL.
8
to develop the DPS2 tool. This implies that large measurements are
This reflects the discrete nature of these traits, which implies a poor
more reliable in pointing to males than small measurements in
normal approximation to the discriminant score distribution. To
pointing to females. The second probably indicates that females tend
evaluate the utility of these traits in a more specific manner, Table 9
to more often have a distinct, sex-specific pattern in their grave goods
presents the exact posterior probabilities for those traits with an accu-
than males.
racy above 0.8 and a utility of at least 0.2, according to Table 7. All
traits assigned a posterior probability above 95% to some individuals,
but only for incisura ischiadica major this was the case for more than
3.3 |
scores
The utility of previously considered traits and
250 individuals. Two further traits (Arcus superciliaris, sciatic notch 3)
assigned a posterior probability above 90% to more than 250 individuals, and this holds for three further traits (Arc compose, Glabella, sci-
A complete list of the utilities for all traits is provided in Table S1.
None of the unilateral traits reached an accuracy above 0.8, and
all the utilities stayed below 0.05, reflecting the maximally moderate
atic notch 2) when using a threshold of 85%. This underlines the high
utility of these traits, at least when lowering the limit of a 95% posterior probability, which is very demanding for a single, discrete trait.
accuracy and/or the low number of individuals in which the trait was
Table 10 shows the results for the three existing morphological
measurable. The highest utility of 0.04 was reached for the height of
scores. All three scores have a high accuracy, and two have a remark-
the second cervical vertebra (Axisheight), which was measurable in
able high utility above 0.4. The high utility of the Ferembach and
more than a third of the adult individuals with an accuracy of 0.78.
Bruzek scores reflects that these do not require all traits to be
In contrast, several bilateral traits with accuracies above 0.8 were
measurable—they just use the information available.
identified, and in three cases, a utility above 0.2 was reached; that is,
the sex was estimated in more than 20% of the individuals with a posterior probability above 95% (see Table 6). These are two measure-
3.4
|
The utility of trait groups
ments from the scapula (glenoid cavity height [GCH] and glenoid
cavity breadth [GCB]) and one pelvic measurement, the vertical ace-
Table 11 shows the utility of some trait groups. We started by consid-
tabular diameter (VEAC). These more favorable results for bilateral
ering the different single skeletal regions covered by our traits and
traits reflect the higher degree of accuracy, as well the necessity for
observed the highest utility for the morphological traits of the cranium
only one measurement from a single side to perform a sex estimation.
(0.62) and the pelvis (0.59) and for the metric traits of the pelvis
Table 7 shows the results for the metric trait scores. In spite of
(0.47). These trait groups showed accuracies above 0.90; however,
accuracies close or above 0.8, we always observed rather low utilities.
the high utilities are additionally due to the fact that we were able to
All these scores required several traits to be measurable, and for most
determine at least some of the traits of each group in many individ-
scores, this was fulfilled in less than 100 individuals. The most promi-
uals. This point is nicely illustrated by the four scapula traits, which
nent exception is the score Scapula a, applicable in nearly 200 subjects
enabled to define a rule with an accuracy of 0.92. However, it was
and reaching a utility above 0.2.
Table 8 shows the results for those single morphological traits
that reached an accuracy of 0.8 and above, with some reaching a utility above 0.4. Many of the traits are part of either the Bruzek (2002)
approach or the Ferembach et al. (1980) score. However, we also
observed that the misclassification rates were often above 0.05.
TABLE 6
Trait
TABLE 7
Utilities of all metric scores
Score
Utility
N
Accuracy
Misclassification rate
Unilateral scores
Cranium a
0.01
72
0.76
-
Cranium b
0.02
69
0.77
-
Utilities of all metric traits with an accuracy over 0.8
Cranium c
0.01
38
0.84
-
Utility
Missclassification rate
Cranium d
0.01
57
0.81
-
Cranium e
0.02
53
0.87
-
0.02
57
0.85
-
N
Accuracy
GCH
0.23
265
0.91
0.01
GCB
0.24
249
0.91
0.03
Cranium f
Bilateral scores
SPU
0.14
143
0.94
0.01
DCOX
0.03
75
0.85
-
Scapula a
0.21
191
0.93
0.03
0.02
63
0.78
-
ISMM
0.17
164
0.93
0.03
Patella a
VEAC
0.28
349
0.91
0.02
Talus a
0.02
59
0.86
-
0.02
59
0.79
-
MAXB
0.05
138
0.83
-
Talus b
TL
0.13
295
0.87
0.04
Talus c
0.05
116
0.81
-
-
Calcaneus a
0.04
92
0.80
-
CalTal a
0.02
63
0.85
-
TH
0.01
89
0.81
Note: See Table S1 for complete table of results. N: number of individuals
for whom the trait was measurable.
Note: N: number of individuals for whom the score could be computed.
NAVITAINUCK ET AL.
9
T A B L E 8 Utilities of morphological
traits with an accuracy above 0.8
Trait
Utility
N
Accuracy
Misclassification rate
Glabella
0.31
358
0.87
0.06
Arcus superciliaris
0.60
412
0.92
0.08
Forma orbitae
0.15
360
0.83
0.12
Ventral arc
0.20
137
0.91
0.09
Sciatic notch 1
0.42
288
0.89
0.11
Sciatic notch 2
0.42
288
0.90
0.10
Sciatic notch 3
0.42
286
0.91
0.09
Composite arch
0.03
428
0.85
-
Sulcus praeauricularis
0.40
406
0.85
0.06
Incisura ischiadica major
0.40
389
0.90
0.03
Corpus ossis ischia
0.27
182
0.91
0.08
Arc composé
0.23
427
0.85
0.05
Preauricular surface 1
0.25
409
0.86
0.05
Preauricular surface 2
0.20
396
0.85
0.03
Preauricular surface 3
0.13
271
0.81
0.01
Note: See Table S2 for complete list of all traits. N: number of individuals for whom the trait was
measurable.
TABLE 9
Exact frequencies of the traits shown in Table 6 and the associated empirical posterior probabilities
Trait
Result
Absolute frequency
PP (female)
Result
Glabella
f
62
0.98
m
18
0.95
f/f?
164
0.85
m/m?
120
0.92
f
45
0.98
m
33
1.00
f/f?
184
0.91
m/m?
156
0.93
f
9
1.00
m
8
1.00
f/f?
71
0.91
m/m?
92
0.92
f
95
0.97
m
52
0.93
f/f?
177
0.85
m/m?
165
0.85
Incisura ischiadica major
f
99
0.98
m
33
1.00
f/f?
182
0.86
m/m?
155
0.96
Sciatic notch 1
f
120
0.89
m
128
0.88
Sciatic notch 2
f
120
0.92
m
133
0.89
Sciatic notch 3
f
125
0.91
m
126
0.91
Preauricular surface 1
f
152
0.95
m
182
0.78
Preauricular surface 2
f
128
0.97
m
179
0.77
Sulcus praeauricularis
f
47
1.00
m
96
0.94
f/f?
151
0.94
m/m?
179
0.79
Arcus superciliaris
Corpus ossis ischia
Arc compose
Absolute frequency
PP (male)
Note: “Result” refers to the sex assigned according to the expression of the trait. The posterior probabilities are the fractions of individuals with the correct
given sex among those with the result shown.
Abbreviation: PP, posterior probability.
TABLE 10
Utilities of all morphological scores
Score
Utility
N
Number of traits
Effective number of traits
Accuracy
Missclassification rate
Ferembach et al. (1980)
0.73
597
25
9.8
0.95
0.01
Bruzek (2002)
0.42
283
11
4.0
0.97
0.03
Phenice (1969)
0.18
121
3
0.6
0.97
0.03
Note: N: number of individuals for whom the score was computable.
NAVITAINUCK ET AL.
10
TABLE 11
Utilities of metric and morphological trait groups and trait ensembles
Utility
N
Number
of traits
Effective number
of traits
Accuracy
Misclassification
rate
Cranium (morph)
0.62
530
11
6.8
0.90
0.05
Os occipitale (metric)
0.08
358
8
3.7
0.66
0.12
Mandibula (morph)
0.01
484
5
3.5
0.71
-
Cervical vertebra (metric)
0.07
290
2
1.5
0.80
0.04
Scapula (metric)
0.30
315
4
2.3
0.92
0.01
Trait groups
Region specific trait groups
Pelvis (metric)
0.47
415
20
7.4
0.91
0.01
Pelvis (morph)
0.58
455
22
10
0.92
0.04
Patella (metric)
0.08
155
4
1.8
0.86
-
Talus (metric)
0.14
308
6
2.3
0.85
0.05
Calcaneus (metric)
0.08
203
4
2.0
0.77
-
Ferembach
0.55
450
8
3.8
0.92
0.03
Bruzek
0.53
443
11
6.0
0.89
0.05
Phenice
0.22
149
3
2.6
0.94
0.06
Cranium (morph) + Pelvis (morph) + Mandibula (morph)
(Original proposal of Ferembach et al., 1980)
0.72
598
24
11.7
0.95
0.02
Subsets of morphological pelvis traits
Ensembles of selected traits from different regions
Cranium (morph) + Pelvis (morph)
0.70
544
6
4.0
0.95
0.02
Cranium (morph) + Pelvis (morph) + Mandibula (morph)
0.73
597
16
9.9
0.95
0.01
Cranium (morph) + Pelvis (morph) + Pelvis (metric)
0.71
556
12
7.0
0.95
0.01
Cranium (morph) + Pelvis (morph) + Scapula (metric)
0.74
561
14
7.3
0.95
0.02
Cranium (morph) + Pelvis (morph) + Pelvis (metric)
+ Scapula (metric)
0.74
563
16
8.2
0.96
0.01
Cranium (morph) + Pelvis (morph) + Scapula (metric)
+ Talus (metric)
0.74
574
16
7.9
0.95
0.01
Cranium (morph) + Pelvis (morph) + Mandibula (morph)
+ Scapula (metric)
0.74
583
16
8.5
0.95
0.01
Cranium (morph) + Pelvis (morph) + Pelvis (metric)
+ Scapula (metric) + Talus (metric)
0.72
568
19
8.1
0.97
0.01
Cranium (morph) + Mandibula (morph) + Pelvis (morph)
+ Pelvis (metric) + Scapula (metric)
0.75
590
17
8.8
0.96
0.01
All morphological traits
0.73
598
29
12.9
0.94
0.02
All metric traits
0.56
534
48
13.0
0.93
0.02
All metric and morphological traits
0.76
616
77
23.8
0.98
0.01
Large ensembles
Note: See Table S3 for the traits included in each trait group. N: number of individuals for whom at least one trait of the trait group was measurable.
applicable in only about 50% of all subjects, resulting in a utility of just
0.30.
An essential step, however, may be to consider rules combining
different regions, as we can then increase the likelihood of measuring
The trait groups with a high utility already consist of 10 or more
at least some traits in numerous individuals. Ferembach et al. (1980)
traits; therefore, it is of interest to find subsets with fewer traits but
already suggested combining morphological traits from the pelvis, the
still with a high utility. Bruzek (2002), Ferembach et al. (1980), and
cranium, and the mandible within an ensemble. Indeed, for this
Phenice (1969) included subsets of pelvic traits in their proposal. The
ensemble, we obtained a utility of 0.72 based on 24 traits. We tried to
first subset allowed us to still reach a utility of 0.52 involving only
extend this idea to various combinations of metric and morphological
11 traits, and the second 0.55 based on eight traits. The three traits
traits from different anatomical regions, with the traits within each
considered by Phenice are not sufficient to reach a high utility.
anatomical region being selected based on their accuracy. In these
NAVITAINUCK ET AL.
11
ensembles, we observed utilities from 0.70 up to 0.75. (The traits
single trait is measurable. Consequently, they may have a high accu-
selected for each ensemble are listed in Table S3.)
racy but nevertheless a limited utility.
Finally, to explore the maximum utility to be reached, we
considered all the metric, all the morphological, and all the traits
together as ensembles, giving us utility totals of 0.76 (all traits), 0.73
4.2
|
Generalizability and limitations
(all morphological traits), and 0.55 (all metric traits).
The maximal utility of 0.76 implies that for a quarter of the skeletal
Our results on the utility are based on one series of archeological skele-
individuals, no sex estimation was possible. It is interesting to note that
tons from a fully excavated early medieval site dating from the sixth to
among the corresponding 160 individuals, only in 59 were all traits
eighth century AD and the computation of posterior probabilities using
immeasurable. A total of 43 were measurable in traits from only one of
data from this site. We can expect similar results if we consider other
the 10 anatomical regions considered in Table 11 and 17 in two
series, if the traits in such a series have a similar accuracy and a similar
regions. However, even 41 were measurable in traits from at least three
rate of being measurable, and if the series is large enough to develop a
different regions and therefore had a sound basis for a sex diagnosis.
series specific reference standard, for example, based on a LCA.
To summarize, we observed that when combining between
With respect to determining the utility of trait groups, we made
12 and 19 traits from three or more anatomical regions in one ensem-
use of a rather simple statistical approach to compute posterior prob-
ble, we came very close to the optimal utility reachable when consid-
abilities, namely, LDA. It cannot be excluded that, in particular in the
ering all traits.
case of large trait groups, further improvements are possible by using
more sophisticated techniques. For the single traits, we did not investigate aspects like the intra- and interobserver variability or the influ-
4
|
DISCUSSION
ence of age at death in detail, which would be essential when
discussing the value of single traits for sex estimation. Instead, we
To the best of our knowledge, this is the first paper presenting a sys-
focused on the utility of their combined use in daily practice.
tematic investigation of the utility of combining metric and morpho-
The numerical values of the utility depend on the threshold used
logical traits from different anatomical regions. In order to assess the
for the posterior probability—in our case, the value of 95%. Other
utility (or usefulness) of an ensemble of traits, we considered a simple
choices will lead to different values, but it is unlikely that this will
measure: the probability of arriving at a sex estimation with a poste-
change the overall results. Recently, Jerkovic et al. (2020) suggested
rior probability above 95%. In our investigation, we initially studied
working with lower thresholds to increase the number of individuals
the utility of a variety of morphological and metric traits and several
with a sex estimation and to aim for an overall accuracy of 95% at a
scores suggested in the literature before we started investigating
population level, instead of at an individual level. This would imply
ensembles of traits built across different anatomical regions and/or
a different definition of utility resulting in higher numerical values.
combining morphological and metric traits.
4.1 | The benefits of using traits from different
anatomical regions
4.3 | Using rules developed in external reference
populations
Nonetheless, if we are interested in single individuals or small series,
Our investigation corroborates the simple expectation that combining
we are still confronted with the question of how well a rule developed
traits from different anatomical regions increases the chance in
in one series will act in another series (Bašic et al., 2017; Sierp &
obtaining a definitive sex estimation: If several regions are involved,
Henneberg,
the likelihood in observing a sufficient number of traits in an individual
(cf. Bruzek & Murail, 2006), is not addressed by our considerations on
increases. In our specific situation, we already achieved the maximally
the utility of ensembles of traits; however, our additional investiga-
possible utility of 0.76 when combining traits from three regions. Sin-
tions presented in Appendices S1 and S2 do shed some light on this
gle traits rarely reach such high utilities. This also holds for many pub-
question.
2015).
This
question,
regarding
external
validity
lished scores combining several traits. When considering traits from
First, we systematically investigated population differences
single anatomical regions, the maximum utility was 0.47 for metric
between our population and those used in the original publications.
traits and 0.62 for morphological traits. Overall, these results can be
For some metric and morphological traits, we observed a nearly per-
seen as an extension of a recent finding by Nikita and Nikitas (2020),
fect match. However, the most frequent pattern was a general shift in
who observed a substantial increase in accuracy when combining pel-
the population distribution, that is, a difference in the mean values
vic and cranial traits.
affecting both sexes to a similar degree. The direction of the shift was,
Making efficient use of combining traits from different regions
in the majority of cases, more towards “male” phenotypes compared
requires to use flexible rules that assign a sex estimate also if some of
with the original population. This may point to a generally more robust
the traits are not measurable. This is the basic limitation of several
anatomy of the Mannheim population when measured against
published scores based on several traits, as they require that each
populations in the original publications, which were mainly from
NAVITAINUCK ET AL.
12
Europe or had at least a European ancestry (South African Whites).
traits as their assessment is more subjective, potentially counter-
Alongside population specificity of sexual dimorphism, which depends
balancing the higher utility (cf. Santos et al., 2019; Sierp &
on environmental factors (Bejdov
a et al., 2013), temporal consistency
Henneberg, 2015). Nevertheless, our population comparisons rev-
is a crucial factor, because secular trends highly impact on the skeletal
ealed no basic difference between metric and morphological traits
morphology (i.e., Guyomarc'h et al., 2016; Walker, 2008).
with respect to the probability of arriving at a match between the
Such population differences, however, need not reflect true dif-
actual and original population. Because we considered a skeletal pop-
ferences in phenotypes as they may be due to differences in the appli-
ulation with a relatively good state of preservation, we may, however,
cation of the measurement methods. For example, the observer of
have overestimated the value of morphological traits. Metric traits are
this study (DN) tended to regard fewer individuals as indefinite for
often seen as extending the possible range of estimation in poorly
many of the morphological traits than in the original publications.
preserved individuals, but this was not necessary in many of the indi-
Second, we investigated the robustness of the posterior probabili-
viduals in our population.
ties computed by DSP2. In contrast to our study, DSP2 was developed based on a population pooled from many different samples, also
taking into account interpopulation differences.
Consequently, the standard deviations used should be larger than
4.5 | Can we estimate the sex of all skeletal
individuals?
those in any single population. We could corroborate this expectation
with respect to our population: for all of the 16 single traits covered
A very poor state of preservation will always limit the possibility of
by DSP2, the population standard deviation in our sample was smaller
performing sex estimations with a high degree of confidence. That
than in the original sample, and the average reduction was 18.3%. The
said, our investigations suggest that even for a small fraction of indi-
combination of a cautious rule with such artificially increased popula-
viduals (here about 40 out of 675), sex estimation may remain uncer-
tion standard deviations should limit the likelihood of achieving false
tain, in spite of the sound basis provided by the availability of traits
sex estimations in spite of population differences for the single traits.
from several anatomical regions.
Indeed, we observed this robustness for the DSP2: in spite of popula-
Of course, the number of uncertain individuals also depends on
tion differences (all in the same direction) for four out of the eight
the threshold used for posterior probability. The alternative
bilateral traits covered by DSP2, we observed few misclassifications.
approaches mentioned above will hence lead to different values.
However, whether this property of DSP2 holds in general requires
further investigations.
|
4.6
4.4
|
Which traits should be used?
Outlook
We have provided clear evidence that combining traits from different
anatomical regions and allowing the combination of morphological
The desirable features of traits to be used for sex estimation like ade-
and metric traits is a useful strategy to allow sex estimation in as many
quate population variability, low intra- and interobserver variation,
individuals as possible with high confidence and limited efforts; how-
validity over a wide age-at-death range, and nondestructive and
ever, the question remains about which regions should be preferred
objective assessment have been widely discussed in the literature
and how we can arrive at sex estimation methods applicable across a
(Boldsen et al., 2015; Bruzek & Murail, 2006; Ferembach et al., 1980;
wide range of populations. The ranking of anatomical regions and the
Inskip et al., 2019; Krüger et al., 2017; Rösing et al., 2007, etc.). By
ranking of traits within regions would be helpful to transfer
considering the traits proposed in previous publications, we implicitly
the insights from this investigation into concrete guidance for future
assumed that they fulfilled such basic requirements. Indeed, the focus
practice. In the absence of a large population enabling the develop-
of our paper was less on single traits and more on the utility of com-
ment of population-specific discriminant scores, there is a need to
bining traits from different anatomical regions. However, our investi-
determine the most suitable traits for sex estimation across
gation is limited by the a priori selection of specific anatomical
populations and to develop tools similar to DPS2 to allow posterior
regions, which do not cover all regions with an established value for
probabilities for any measurable subset of these traits to be com-
sex estimation. For example, some traditional measurements, such as
puted. These tasks require access to large-scale anthropological data-
the joints of the long bones (e.g., femur), were intentionally not cov-
bases covering multiple populations and a broad range of traits. As
ered in order to focus on less frequently used features. Within the
shown in this investigation, it might not be necessary for the sex of
metric traits considered, the pelvis and the scapula showed
the individuals to be known.
the highest utility. Within the morphological traits considered, the cranium and the pelvis showed the highest utility.
One remarkable result of this investigation was the higher utility
5
|
CONC LU SION
of morphological compared with metric traits. Though the value of
morphological traits for sex estimation is widely recognized among
Assessing biological sex—one of the most important pieces of infor-
anthropologists, they are often regarded as less valuable than metric
mation about an individual—in human skeletons is a crucial step within
NAVITAINUCK ET AL.
13
forensic and bioarchaeological research. When selecting a limited
number of traits for systematic sex estimation in a series of skeletal
remains, it is advisable to select traits from different anatomical
regions in order to obtain a reasonably sure result in as many individuals as possible. In our approach, the maximally possible utility of 0.76
was reached when combining traits from three anatomical regions,
whereas single traits never reach such high utilities.
The development of more precise recommendations about the
choice of regions and the applicability of rules developed in external
reference populations requires large scale investigations, covering all
relevant anatomical regions and involving a wide range of
populations.
ACKNOWLEDGMENTS
The study was funded by a scholarship of Studienstiftung des
Deutschen Volkes. The authors thank the reviewers for their helpful
comments.
CONF LICT OF IN TE RE ST
The authors declare that there is no conflict of interest.
DATA AVAI LAB ILITY S TATEMENT
Data available on request from the authors
ORCID
Denise U. Navitainuck
Werner Vach
Kurt W. Alt
Jörg Schibler
https://orcid.org/0000-0002-6082-0778
https://orcid.org/0000-0003-1865-8399
https://orcid.org/0000-0001-6938-643X
https://orcid.org/0000-0003-2290-3553
RE FE R ENC E S
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SUPPORTING INF ORMATION
Additional supporting information may be found online in the
Supporting Information section at the end of this article.
How to cite this article: Navitainuck, D. U., Vach, W., Alt, K.
W., & Schibler, J. (2021). Best practice for osteological sexing
in forensics and bioarchaeology: The utility of combining
metric and morphological traits from different anatomical
regions. International Journal of Osteoarchaeology, 1–14.
https://doi.org/10.1002/oa.3014