Sex Estimation From The Calcaneus and Talus 2019

Archaeological and Anthropological Sciences (2019) 11:4927–4946
https://doi.org/10.1007/s12520-019-00855-y
ORIGINAL PAPER
Sex estimation from the calcaneus and talus using discriminant

function analysis and its possible application in fossil remains
Carmen Alonso-Llamazares 1 & Adrián Pablos 2,3,4
Received: 25 September 2018 / Accepted: 8 May 2019 / Published online: 31 May 2019
# Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
Foot bones have been shown to be sexually dimorphic and they are frequently used for sex estimation. In this study, we estimated
the sex based on the calcaneus and the talus of a modern North American population obtained from the Hamann-Todd
Osteological Collection, housed at the Cleveland Museum of Natural History (Ohio, USA). A total of 164 calcanei (84 males
and 80 females) and 162 tali (83 males and 79 females) were studied. Several univariate discriminant functions were obtained,
with accuracy ranging from 70.2 to 90.2%. The best variable for sex estimation in this sample is the talar length. Multivariate
discriminant functions were also obtained. The accuracy (83.3 to 96.4%) was generally higher than that obtained with the
univariate discriminant functions. The best multivariate equation is the one that uses all the variables measured in the talus.
Discriminant functions previously reported in other studies were tested on the Hamann-Todd collection to verify their validity
outside the population for which they were made. In addition, together with the equations reported here, they were applied on data
from fossil remains belonging to three different groups (Homo neanderthalensis, hominins from the Sima de los Huesos, and
anatomically modern Homo sapiens) in order to find some discriminant functions that allow for a valid determination of sex in
this type of fossil populations. Several equations yielded good correct allocation percentages in fossil populations thus facilitating
the estimation of sex for 16 fossil specimens of previously unknown sex.
Keywords Sex determination . Discriminant functions . Calcaneus . Talus . Foot . Hamann-Todd collection . Fossils
Introduction fundamental step in the process, along with other biolog-

ical characteristics, such as age, stature, ancestry, or the
When studying skeletal remains, both in an archeological presence of certain anomalies and pathologies (Bidmos
and forensic context, determining individuals’ sex is a and Asala 2005; Pablos et al. 2013a; Rodríguez et al.
2013; Ruff 2002). All these traits allow us to build a
Electronic supplementary material The online version of this article biological profile which, in forensic cases, aid in deter-
(https://doi.org/10.1007/s12520-019-00855-y) contains supplementary mining the identity of the victim (Ahmed 2013; Cattaneo
material, which is available to authorized users.
2007). In those cases, definitively determining the sex
increased the likelihood of matching the identification of
* Carmen Alonso-Llamazares
karmen.hbc@gmail.com the remains (Robinson and Bidmos 2011; Scheuer 2002).
In ancient populations, the study of skeletal remains al-
1
lows us to learn more about the paleobiology of fossil
Área de Antropología Física, Departamento de Biología de
Organismos y Sistemas, Universidad de Oviedo, c/ Catedrático
individuals. Ascertaining the sex certainly helps us to es-
Valentín Andrés Álvarez, s/n, 33006 Oviedo, Spain tablish the demographic profile of these populations.
2
Centro Nacional de Investigación sobre la Evolución Humana
Sex determination is based on the existence of sexual di-
(CENIEH), Paseo Sierra de Atapuerca s/n, 09002 Burgos, Spain morphism, which is the morphological and size differentiation
3
Centro Mixto UCM-ISCIII de Investigación sobre Evolución y
between sexes. This is due to genetic and environmental dif-
Comportamiento Humanos, c/Monforte de Lemos, 5, ferences that shape the human skeleton during its growth.
28029 Madrid, Spain These differences are mainly evident starting in puberty, when
4
Área de Antropología Física, Departamento de Ciencias de la Vida, sexual hormones begin to function, making it possible to dis-
Universidad de Alcalá, 28871 Alcalá de Henares, Madrid, Spain tinguish between men and women using just a few bones
4928 Archaeol Anthropol Sci (2019) 11:4927–4946
(Ahmed 2013). This sexual dimorphism is essentially fossil remains, at least with respect to a certain sex assignation.
manifested in two forms. Firstly, in general, male bones are If existing populations present a degree of variability such that
larger and more robust than female bones. Secondly, the shape the discriminating equations that work well in one do not in
of the pelvis differs, since the male responds only to adapta- another, it would be expected that they do not offer reliable
tions to bipedalism, and the female pelvis must offer a birth results in fossil populations whose forms and proportions are
canal wide enough for the passage of the fetal head, without to some extent unknown. Nevertheless, in some cases, apply-
losing the locomotor capacity (Scheuer 2002). ing these methods can offer some insight into the sex of the
When dealing with fossil remains of species that are extinct fossil individuals. In fact, they have been used with that pur-
today, it is necessary to clear up the uncertainty as to whether pose before (e.g., Boyle and DeSilva 2015). However, it is not
that dimorphism was already present in them or whether it is seen that they check the efficacy of the formulae used in those
something unique to our species. Previous works show that, specimens with other individuals that have an estimated sex
since the early hominins, sexual dimorphism has been present obtained by other methods.
to a greater or lesser extent (Arsuaga et al. 1997; Lee 2006; Through this research, we intend to approximate the sex
Lorenzo et al. 1998; Reno et al. 2003; Trinkaus 1980). based on the calcaneus and the talus, studying their variation
Therefore, it is possible to estimate sex in hominin fossil re- in a twentieth Century North American Black and White pop-
mains. It is also necessary to take into account the different ulation, from the Hamann-Todd Osteological Collection
body proportions that some fossil species present. Therefore, (HTOC), in order to build discriminant functions that will be
not all bone elements will be conclusive in estimating sex applied on fossil populations.
according to the same characteristics as in current populations. The calcaneus and talus are good options for applying these
There are several methods for evaluating the sexual dimor- metrical methods. The talus forms the primary connection
phism of human remains and determining to which sex they between the lower leg and the foot, and is vital for mobility.
belong. The first methods are based on physical characteristics The calcaneus directly supports the weight against the ground,
observable in certain bones, such as the pelvis and skull. Of constituting the first point of support for walking and absorb-
these two, the pelvis is considered the most accurate bone for ing ground reaction forces. Both are weight-bearing bones, so
sex determination. These non-metrical methods quickly ob- they are expected to exhibit sexual dimorphism since weight is
tain results that are more accurate, but they require experience a sexually dimorphic trait (Heymsfield et al. 2007;
on the part of the observer and it is necessary for the bones to Mahakkanukrauh et al. 2014).
be well preserved, which is not always the case (Bidmos and This is not the first study that attempts to develop discrim-
Dayal 2003; Dixit et al. 2007). On the other hand, there are inant functions for the bones of the foot. In 1976, Steele had
metrical methods based on anatomical measurements and sta- already carried out a similar study that used this type of anal-
tistical techniques. These require less experience, which ysis to generate discriminant functions using talus and calca-
makes it more likely that if another researcher repeats the neus measurements with the Terry Collection housed in the
analysis, they will obtain the same result (Bidmos and Dayal Smithsonian Institute (Washington D.C., USA). He obtained
2003). There are many studies that include this type of analy- an average accuracy in correct sex classification of 79 to 89%.
sis. They generate equations to determine the sex in different Other studies, such as those carried out by Murphy (2002a, b),
populations using different bones, such as the femur (King with prehistoric New Zealand Polynesian calcanei and tali,
et al. 1998; Trancho et al. 1997), the tibia (İşcan and Miller- achieved an accuracy ranging from 88.4 to 93.5% and 85.1
Shaivitz 1984), the patella (Introna et al. 1998), the humerus to 93.3%, respectively. For a Greek population, Peckmann
(İşcan et al. 1998), the radius (Machado Mendoza and Pablo et al. (2015a, b) attained an accuracy range from 70.0 to
Pozo 2008), the phalanges (Karakostis et al. 2014, 2015), the 90.0% for the calcaneus, and from 62.5 to 96.5% for the talus.
skull, and the mandible (Steyn and İşcan 1998), among others. Several authors worked with radiographs of the calcaneus,
In these cases, although it is always better for the bones to be instead of the bone itself (Riepert et al. 1996; Zakaria et al.
intact, it is possible to work with bone fragments. 2010). Basing their work solely on radiographic measure-
One of the major obstacles to studying human evolution ments, Riepert et al. (1996) correctly classified nearly 80%
using fossil remains is the fragmented state of conservation in of the sample using the length of the calcaneus. Zakaria
which the scarce remains are recovered, especially in compar- et al. (2010) obtained better results, reaching a 90.2% sex
ison with more modern archeological populations. In many allocation rate by using the length of the calcaneus. Using
cases, not enough skull or pelvis elements are recovered to multivariate analysis, the length and the minimum height of
be able to establish the sex. In these situations, metric methods the calcaneus provided a 92.6% accuracy rate, thus improving
could be the solution. However, one characteristic of these upon the results of the univariate analysis. Similarly, there are
methods is that they are population-specific, which causes studies in which calcaneus measurements are taken from CT
the discriminatory functions habitually used in forensic an- images (Ekizoglu et al. 2017), where sex is correctly classified
thropology to be considered invalid in their application to for 100% of individuals using the minimum breadth, as well
Archaeol Anthropol Sci (2019) 11:4927–4946 4929
as with several multivariate functions and logistic regression discriminant functions can be used on them, applying the
(see Ekizoglu et al. 2017). Studies have also been conducted equations first on individuals with a previous estimation of
on burned remains (Gonçalves 2011; Gonçalves et al. 2013). sex in order to check their percentages of correct allocation
They showed that, even after having burned for at least one with these populations.
hour at temperatures over 800 °C, the maximum length of Therefore, the third and ultimate purpose of this study is to
both calcaneus and talus bones still exhibits sexual seek out discriminatory functions that allow us to estimate the
dimorphism. Gonçalves et al. (2013) obtained an accuracy sex of fossil remains, combining calcaneus and talus measure-
of 95.7% using the maximum length of the calcaneus and an ments, and thus be able to assign a probable sex to some fossil
accuracy of 75.8% using the maximum length of the talus. individuals of unknown sex for now.
This type of analysis using calcanei and tali in different To do this, we have studied sexual dimorphism in modern
populations provides different results. This is indicative of populations by using their talus and calcaneus, testing their
the variability between populations. When determining indi- validity as sex estimators by means of discriminant functions
viduals’ sex through the use of discriminant functions, it is created by data from the HTOC. Then we applied both the
therefore important that those functions were generated based functions we created using the HTOC, as well as the equations
on data taken from the same population or one that is very published by other authors from other collections, on fossils
similar, due to the interpopulational variation that exists in with an estimated sex. The functions that provided satisfactory
human beings. This study aims to create its own equations results and assigned the correct sex to the estimated-sex fossils
for population studies, and to test their validity using the func- were used with the fossils of unknown sex in order to estimate
tions on excluded members of the same collection with which a probable sex.
the equations were calculated. It is also essential to use popu- Pending a better method to assign sex to fossil species, we
lations of known sex, i.e., when the sex corresponding to each hope that the probable-sex estimates carried out in this re-
individual is unequivocally known. Thus, we avoid the per- search will drive some progress in the study of human
centage of error typically observed in estimating the sex of evolution.
skeletal remains.
However, this begs the question: how population-
dependent are these equations? If we do not have equations
for the population we are working with, or if we do not know Material and methods
which population the remains we are studying belong to, is it
better to leave sex as an unknown or make an attempt with Anthropological samples used
another population’s equations? Sex can be estimated with
formulae not designed for that population, as long as we keep We studied a total of 164 calcanei from adult individuals, and
in mind that the percentages of reliability will be diminished. for 162 of them, the talus was also studied. They were part of
We want to check the validity of this type of formulae on the Hamann-Todd Osteological Collection, with an age-at-
different populations. Hence, to fulfill this second purpose, we death range between 14 and 50 years, according to the collec-
applied the equations published in other research to our data to tion database. This collection, located at the Cleveland
check the results. Perhaps, among all the variables used, Museum of Natural History in Ohio, includes more than
which are sexually quite dimorphic, there are a few that do 3000 human skeletons, in addition to more than 1000 non-
not exhibit great population variability, maintaining good per- human primate skeletons (www.cmnh.org). Human remains
centages of correct allocation outside their population of ori- comprise both Euro and African-Americans who died in the
gin. If so, could these discriminatory functions that use vari- first decades of the twentieth century. Since the discriminant
ables with little population variability be suitable for estimat- functions that we are going to generate will be applied outside
ing sex in fossil populations of already extinct species? the HTOC and we are going to use formulae that were gener-
Evidently, our osseous proportions and morphological ated with other populations from this collection, we think that
characteristics have changed considerably since the emer- it could be useful to not separate Afro-American individuals
gence of the first hominins on this planet, so attempting to from Euroamericans. Thus, the generated equations will be
use human discriminatory functions in other genera less specific to each separate group and more valid for mixed
(Australopithecus or Paranthropus) or even in the early populations and perhaps in turn for populations other than
Homo (Homo habilis) would not offer any reliable results. those used to generate such functions.
Nonetheless, we are trying to glean some insight into the sex This study includes a sample of those adult individuals
and the paleobiology of more similar species such as whose foot bones remained in good condition, leaving out
H. neanderthalensis or the hominins from the Sima de los those whose were pathological, as well as those whose record
Huesos (SH hominins). These are species close to ours whose of biological data was not available. Measurements were tak-
proportions are not extremely different, and we believe that en preferably on the elements from the right side, though in
the event that this was not available or was not in good con- difference/smallest value × 100, has yielded a value smaller
dition, the left one was measured. than 5% for all the variables except the 7 previously men-
The sample was divided into two groups, according to the tioned, which were discarded from the study. The other 14
researcher who took the measurements. Thus, group 1 was variables (5 of the calcaneus, 9 of the talus) were considered
composed of 114 individuals (57 males, 57 females) for the suitable. All the variables taken can be seen in Figs. 1 and 2.
calcaneus, and 112 for the talus (56 males, 56 females). This The description of the variables is taken from Pablos et al.
group was used to create the discriminant functions. Group 2, (2013b, 2014), which was based on the description of the
measured by a second researcher, was made up of 50 individ- measurements taken by Martin and Saller (1957), subsequent-
uals (27 males, 23 females) and used to test the previously ly compiled by Bräuer (1988). The abbreviation of the vari-
calculated functions, since they belong to the same population ables is a BCM^ followed by a number, according to the order
but are an independent sample not used in the construction of proposed by the authors for the variables of the calcaneus, and
the equations. It was decided to separate the groups according an BM^ followed by the number proposed by the authors for
to the researcher because, although it is known that this type of the variables taken in the talus.
study can be affected by observer error, the objective is to All measurements were taken with standard digital calipers
provide a set of equations to other researchers. Therefore, with an error of ± 0.01 mm.
when using discriminant functions, an error between ob- Variables studied in the calcaneus:
servers is expected. Verifying the reliability of these equations
with the same population measured by another researcher is – Maximum length of the calcaneus (CM1): maximum
indicative of the potential of these functions to be used by projected length from the most posterior point of the tu-
other researchers. bercle to the most anterior point of the cuboid facet
In order to check if the discriminant functions are applica- (Fig. 1b).
ble for fossil sex estimation, we select a sample of – Minimum breadth of the calcaneus (CM3): minimum
Neanderthals, SH hominins, and anatomically modern breadth of the calcaneal body (Fig. 1a).
H. sapiens. The Neanderthal sample consists of 27 tali and
18 calcanei of individuals with an estimation of sex, and 11
tali and 4 calcanei of individuals without any estimation of
sex. For the SH hominins, we have data from 14 tali and 10
calcanei of individuals with an estimated sex, and 7 tali and 5
calcanei without an estimated sex. Finally, for the H. sapiens,
we have data from 55 tali and 53 calcanei of individuals with
an estimation of sex, and 9 tali and 6 calcanei without any
estimation of sex. The sex of these fossil specimens was esti-
mated by applying morphological methods or, in some cases,
through the genetic profile of individuals, e.g., the individuals
from the El Sidrón (Estalrrich and Rosas 2013). These data
were obtained from several bibliographic sources, as well as
from our own measurements. The composition of the fossil
sample is detailed in Table S1.
Anatomical variables studied
The variables chosen for this study were those that reflect
general size and proportions and the size of the articular sur-
faces. Initially, 7 variables were measured in the calcaneus and
14 in the talus, but before proceeding with the analysis, we
calculated the interobserver error, i.e., the mean absolute error
produced between the measurements taken by each research-
er. This test was carried out with the intention of checking the
validity of the measurements taken, and we use a small sample Fig. 1 Variables taken in the calcaneus. a Dorsal view. CM2, medial
of 10 individuals measured by both researchers. The mean breadth of the calcaneus; CM3, minimum breadth of the calcaneus;
CM5, calcaneal body length; CM9, length of the talar posterior articular
absolute error was always below 2 mm, except for 2 of the surface of the calcaneus; CM10, breadth of the talar posterior articular
calcaneal measurements and 5 of the talar ones, that was surface of the calcaneus. b Medial view. CM1, maximum length of the
higher. The percentage of error, calculated as the absolute calcaneus; CM4, body height. Modified from Bräuer (1988)
Fig. 2 Variables taken in the talus. a Dorsal view. M1, talar length; M2, talus. d Anterior view. M7, lateral malleolar oblique height of the talus;
total breadth of the talus; M2b, articular breadth. b Dorsal view. M4, M9, length of the head of the talus; M10, breadth of the head of the talus.
trochlear length of the talus; M5, trochlear breadth of the talus. c e Medial view. M1a, total length of the talus; M3(1), medial height of the
Plantar view. M12, length of the calcaneal posterior articular surface of talus; M6, trochlear height of the talus. a–d Modified from Bräuer (1988),
the talus; M13, breadth of the calcaneal posterior articular surface of the e modified from Gebo (1992)
– Calcaneal body length (CM5): distance from the most – Total breadth of the talus (M2): Maximum projected dis-
anterior point of the posterior talocalcaneal joint surface tance from the lateral process of the talus to the medial
to the most posterior point of the tubercle (Fig. 1a). side, measured in the transversal plane. Both points of the
– Length of the talar posterior articular surface (CM9): caliper must be in contact with the surface where the bone
maximum length from the medio-posterior to the latero- rests (Fig. 2a).
anterior points of the posterior talocalcaneal articular sur- – Trochlear length of the talus (M4): Maximum length of
face. Measured parallel to the long axis of the surface the trochlea on the median sagittal talar plane (Fig. 2b).
(Fig. 1a). – Trochlear height of the talus (M6): Maximum distance
– Breadth of the talar posterior articular surface (CM10): from the highest point on the median sagittal talar plane
maximum breadth from the medio-anterior to latero- of the trochlea to the chord defined by the mid-line end
posterior points of the posterior talocalcaneal articular points of the sagittal axis (trochlear length) (Fig. 2e).
surface. Measured perpendicular to the long axis of the – Lateral malleolar oblique height (M7): Direct distance
surface (Fig. 1a). from the inferior edge of the lateral process to the superior
border of the trochlea. Measured in the transverse plane
Variables studied in talus: (Fig. 2d).
– Length of the head of the talus (M9): Maximum length of
– Talar length of the talus (M1): Maximum projected the navicular articular surface (Fig. 2d).
length from the groove for the tendon of the flexor – Length of the calcaneal posterior articular surface (M12):
hallucis longus muscle to the most anterior point of Maximum length of the calcaneal posterior articular sur-
the head. Both points of the caliper must be in face. Measured parallel to the long axis of the surface
contact with the surface where the bone rests (Fig. 2c).
(Fig. 2a). – Breadth of the calcaneal posterior articular surface (M13):
– Total length of the talus (M1a): Maximum length from Maximum breadth of the calcaneal posterior articular sur-
the posterior tubercle to the most anterior point of the face. Measured perpendicular to the long axis of the sur-
head (Fig. 2e). face (Fig. 2c).
Discriminant functions previously reported related, since it is indicative of its predictive value, providing
information on which variables will offer better results in the
We selected discriminant functions reported in previous stud- discriminant analysis.
ies to verify their validity both for our HTOC data and for After that, discriminant functions for group 1 were gener-
fossil populations. We chose equations calculated using pop- ated. Along with the discriminant analysis, the homogeneity
ulations of known sex for the same variables that we measured of within-group variance-covariance matrices was evaluated
in the HTOC. All the formulae taken from bibliographical using Box’s M test. In addition, the results of the classification
sources are shown in the supplementary information were cross-validated with the leave-one-out approach. Several
(Tables S2-S5). sets of equations were created: first, univariate discriminant
functions for each variable studied on the calcaneus and the
Statistical methodology and analysis talus; second, multivariate discriminant functions with differ-
ent combinations of the variables of each bone separately; and
The statistical analysis of the variables to build the discrimi- third, multivariate discriminant functions with different com-
nant functions was conducted with the statistical package binations of the variables of both of the studied bones. For the
SPSS Statistics v.21. multivariate analysis, we used the direct method to calculate
We started with a descriptive analysis of each variable, the equations using all the variables studied and different com-
where the mean, standard deviation (SD), minimum, and max- binations of the variables that yielded the best results with the
imum for each sex were calculated. Before the discriminant univariate analysis, in addition to the Bstepwise^ method.
analysis, it was necessary to analyze the distribution of the Next, all discriminant equations we created were tested on
variables, and check whether these have dimorphic capacity. the individuals in group 2, which belonged to the same pop-
For that, we carried out a non-parametric test (one-sample ulation but was not used to generate the equations so it is a
Kolmogorov-Smirnov test) and a t test (paired-samples t test) valid option for testing the reliability of the obtained
with the sex as a comparison group. Also, a correlation anal- functions.
ysis was performed to verify how the variables relate to sex— We apply formulae published by other authors to our pop-
if they are significantly related—and which are more highly ulation, and we calculate their percentages of correct
Table 1 Descriptive analysis of measured variables in group 1 (from HTOC) for each sex. Measurements in mm (♂: male; ♀: female; N: number of
individuals studied; SD: standard deviation)
Variable N Mean SD Minimum Maximum
Maximum length of the calcaneus ♂ 57 82.1 4.7 67.0 92.7

♀ 57 75.4 4.5 67.3 86.4
Minimum breadth of the calcaneus ♂ 57 28.5 2.2 22.7 36.0
♀ 57 24.7 2.0 20.2 29.9
Calcaneal body length ♂ 57 59.5 3.6 49.0 69.5
♀ 57 54.2 4.0 42.8 63.8
Length of the talar posterior articular surface of the calcaneus ♂ 57 31.6 2.1 26.0 36.5
♀ 57 27.6 2.2 19.7 32.1
Breadth of the talar posterior articular surface of the calcaneus ♂ 57 22.6 1.6 17.1 27.1
♀ 57 20.4 1.3 17.5 23.6
Talar length ♂ 56 55.9 2.4 51.8 61.8
♀ 56 49.7 2.8 43.9 57.7
Total length of the talus ♂ 56 60.5 2.9 55.2 67.1
♀ 56 53.7 3.1 45.7 61.0
Total breadth of the talus ♂ 56 43.5 2.6 37.8 50.5
♀ 56 38.0 2.1 33.0 43.0
Trochlear length of the talus ♂ 56 35.0 1.9 30.4 39.0
♀ 56 31.1 1.9 25.8 34.4
Trochlear height of the talus ♂ 56 8.8 1.0 7.0 11.4
♀ 56 8.0 0.8 6.2 10.5
Lateral malleolar oblique height of the talus ♂ 56 24.6 2.8 17.2 30.0
♀ 56 22.9 2.0 16.7 27.7
Length of the head of the talus ♂ 56 33.6 5.1 0.0 39.3
♀ 56 30.7 2.4 23.7 39.2
Length of the calcaneal posterior articular surface of the talus ♂ 56 33.1 1.8 28.9 36.6
♀ 56 29.0 1.9 23.2 33.7
Breadth of the calcaneal posterior articular surface of the talus ♂ 56 22.8 1.6 19.6 26.0
♀ 56 19.8 1.3 16.5 22.8
Table 2 Discriminant functions

score equations for group 1, using Variable Equationsa Accuracy (%) Sectioning point
variables measured in calcaneus
and talus from HTOC Maximum length of the calcaneus CM1 × 0.216 − 17.003 74.6 0.0
Minimum breadth of the calcaneus CM3 × 0.471 − 12.259 80.7 0.0
Calcaneal body length CM5 × 0.263 − 14.977 70.2 0.0
Length of the talar posterior articular CM9 × 0.465 − 13.755 86.0 0.0
surface of the calcaneus
Breadth of the talar posterior articular CM10 × 0.681 − 14.669 75.4 0.0
Talar length M1 × 0.390 − 20.567 90.2 0.0
Total length of the talus M1a × 0.33 − 18.845 84.8 0.0
Total breadth of the talus M2 × 0.430 − 17.491 88.4 0.0
Trochlear length of the talus M4 × 0.533 − 17.620 87.5 0.0
Trochlear height of the talus M6 × 1.103 − 9.276 68.8 0.0
Lateral malleolar oblique height of the talus M7 × 0.413 − 9.809 66.1 0.0
Length of the head of the talus M9 × 0.249 − 8.021 79.5 0.0
Length of the calcaneal posterior articular M12 × 0.540 − 16.753 85.7 0.0
surface of the talus
Breadth of the calcaneal posterior articular M13 × 0.687 − 14.629 83.9 0.0
a
CM1: maximum length of the calcaneus; CM3: minimum breadth of the calcaneus; CM5: calcaneal body length;
CM9: length of the talar posterior articular surface of the calcaneus; CM10: breadth of the talar posterior articular
surface of the calcaneus; M1: talar length; M1a: total length of the talus; M2: total breadth of the talus; M4:
trochlear length of the talus; M6: trochlear height of the talus; M7: lateral malleolar oblique height of the talus; M9:
length of the head of the talus; M12: length of the calcaneal posterior articular surface of the talus; M13: breadth of
the calcaneal posterior articular surface of the talus
allocation in the HTOC. We selected several published papers estimated sex with measurements for the same variables of
where they worked with the same variables as us in the same calcaneus and talus, and the discriminatory functions that
bones, generating both univariate and multivariate functions. obtained good results were used to estimate the probable sex
Finally, both the formulae we calculated from the HTOC in fossils of unknown sex. A result was considered Bgood^
bone, as well as those calculated by other authors, were ap- when the correct allocation was greater than 80% and bal-
plied to data from the fossil record for individuals that have an anced between both sexes. For this purpose, different
Table 3 Validity of univariate

discriminant functions on group Variable N Accuracy N Accuracy N Accuracy
2, using variables measured in (%) ♂ (%) ♀ (%)
calcaneus and talus from HTOC
(♂: male; ♀: female; N: number Maximum length of the calcaneus 50 78.0 23 78.3 27 77.8
of individuals studied) Minimum breadth of the calcaneus 50 72.0 23 78.3 27 66.7
Calcaneal body length 50 80.0 23 87.0 27 74.1
Length of the talar posterior articular 50 84.0 23 69.6 27 96.3
Breadth of the talar posterior articular 50 82.0 23 82.6 27 81.5
Talar length 50 92.0 27 88.9 23 95.7
Total length of the talus 50 92.0 27 88.9 23 95.7
Total breadth of the talus 50 76.0 27 88.9 23 60.9
Trochlear length of the talus 50 86.0 27 81.5 23 91.3
Trochlear height of the talus 50 66.0 27 63.0 23 69.6
Lateral malleolar oblique height of the talus 50 66.0 27 59.3 23 73.9
Length of the head of the talus 50 74.0 27 77.8 23 69.6
Length of the calcaneal posterior articular 50 86.0 27 92.6 23 78.3
Breadth of the calcaneal posterior articular 50 82.0 27 85.2 23 78.3
malleolar oblique height of the talus; M9: length of the head of the talus; M12: length of the calcaneal posterior articular surface of the talus; M13: breadth of the calcaneal posterior articular surface of the
Sectioning point
talar posterior articular surface of the calcaneus; M1: talar length; M1a: total length of the talus; M2: total breadth of the talus; M4: trochlear length of the talus; M6: trochlear height of the talus; M7: lateral
CM1: maximum length of the calcaneus; CM3: minimum breadth of the calcaneus; CM5: calcaneal body length; CM9: length of the talar posterior articular surface of the calcaneus; CM10: breadth of the
populations within the fossils were taken into account, thus
obtaining the most precise formulae possible within each of
these subpopulations. First, the formulae were applied to the
remains recovered from the Sima de los Huesos; second, to
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
the remains of H. sapiens from different sites; and third, to the
remains of H. neanderthalensis from different sites. The sex
estimation was considered valid when at least 75% of the
applied formulae resulted in the same sex, and a minimum
Accuracy (%)
of three different equations could be applied.
86.0
86.8
87.7
87.7
83.3
86.8
96.4
92.0
92.9
89.3
92.0
86.6
88.4
93.8
Results
The first test performed was a descriptive analysis of group 1,

where we obtained the mean, standard deviation (SD), mini-
CM1 × 0.020 + CM3 × 0.210 + CM5 × 0.032 + CM9 × 0.199 + CM10 × 0.265 − 20.568
mum, and maximum for all variables studied in each sex, as
M1 × 0.146 + M1a × 0.027 + M4 × 0.091 + M12 × 0.201 + M13 × 0.189 − 22.505

shown in Table 1. The one-sample Kolmogorov-Smirnov test
Multivariate discriminant functions score equations for group 1, using variables measured in calcaneus and talus from HTOC
M1 × 0.064 + M1a × 0.046 + M2 × 0.148 + M4 × 0.098 + M6 × 0.268 + M7 ×

carried out showed a significance (p value) greater than 0.05
for all variables, which means that they are normally distrib-
CM1 × 0.040 + CM3 × 0.207 + CM9 × 0.209 + CM10 × 0.267 − 20.528

uted and are suitable for this study. The T test provided a p
(− 0.093) + M9 × 0.007 + M12 × 0.153 + M13 × 0.129 − 23.046
M1 × 0.177 + M6 × 0.279 + M12 × 0.226 + M13 × 0.210 − 23.155

value of 0.00 for all variables, meaning that they are all
dimorphically significant and therefore valid for generating
CM5 × 0.057 + CM9 × 0.302 + CM10 × 0.327 − 19.206

CM3 × 0.219 + CM9 × 0.238 + CM10 × 0.297 − 19.260
discriminant functions. The correlation analysis indicates that
CM1 × 0.065 + CM3 × 0.235 + CM9 × 0.242 − 18.511
M1 × 0.205 + M12 × 0.226 + M13 × 0.201 − 22.138

M4 × 0.212 + M12 × 0.246 + M13 × 0.279 − 20.569
all variables are significantly related to sex (p value of 0.00),
with a correlation range between 0.771 and 0.327, the talar
length being the variable most related to sex, and the lateral
CM9 × 0.348 + CM10 × 0.358 − 18.014

malleolar oblique height the least.
M1 × 0.245 + M12 × 0.289 − 21.939

M6 × 0.476 + M13 × 0.623 − 17.265
M6 × 0.418 + M12 × 0.497 − 18.934
Next, a discriminant analysis was performed to calculate
the univariate discriminant functions with each of the vari-
ables studied on the calcaneus and talus, which are provided
in Table 2. For the calcaneus, the worst accuracies of correct
allocation were the maximum length and the body length of
the calcaneus, at 74.6% and 70.2%, respectively, while the
Equationsa
highest cross-validated accuracies were the length of the talar

posterior articular surface at 86.0%, and the minimum breadth
with an 80.7% rate of correct allocation. For the talus, the
worst accuracy was obtained using the lateral malleolar
oblique height, providing a 66.1% correct allocation rate.
The highest cross-validated success rates were obtained from
M1 + M1a + M2 + M4 + M6 + M7 + M9 + M12 + M13
the talar length and the total breadth of the talus, at 90.2% and
88.4%, respectively. The predictive validity of the equation
was assessed with group 2 from the same population. The
accuracies obtained are shown in Table 3. For the calcaneus,
the length of the talar posterior articular surface still provided
CM1 + CM3 + CM5 + CM9 + CM10
M1 + M6 + M12 + M13 (stepwise)
the best accuracy (84.0%). For the talus, the variables that
CM3 + CM9 + CM10 (stepwise)
M1 + M1a + M4 + M12 + M13
offer the greatest allocation accuracies were the talar and the
CM1 + CM3 + CM9 + CM10
total length, both coming in at 92.0%. Of all the univariate

functions, the highest and lowest correct allocations coincide
CM5 + CM9 + CM10
CM1 + CM3 + CM9
with the correlation analysis.

M1 + M12 + M13
M4 + M12 + M13
CM9 + CM10
After the univariate discriminant analysis, a multivariate

M1 + M12
M6 + M13
M6 + M12
Variablesa
discriminant analysis was carried out in an attempt to obtain

Table 4
more effective equations for determining the sex of our pop-

talus
ulation. The results are shown in Table 4. In this case, all the
a
functions obtained had cross-validated accuracies higher than from the same individuals. All the equations obtained had cross-
80.0%, with a maximum of 87.7% for the calcaneus with the validated success rates that were higher than 90.0%, with a range
equation combining the maximum length, the minimum from 90.2 to 95.5% (Table 6). The best function included the
breadth, and the length of the talar posterior articular surface talar length and the trochlear length of the talus and the maxi-
(CM1 + CM3 + CM9), and a maximum of 96.4% for the talus, mum length and the minimum breadth of the calcaneus (M1 +
with the equation combining all the variables measured. In M4 + CM1 + CM3).
both cases, the second-best accuracy was that obtained by Once again, we tested these multivariate functions on
applying the Bstepwise^ method, which yielded 86.8% for group 2. An accuracy range between 86.0 and 94.0% was
the calcaneus and combines the minimum breadth, the length, obtained, and the best equation included the talar length, the
and the breadth of the talar posterior articular surface (CM3 + trochlear length, the length and breadth of the calcaneal pos-
CM9 + CM10). For the talus, the Bstepwise^ equation provid- terior articular surface of the talus, and the maximum length
ed a 93.8% correct allocation rate and it used four variables: and the length and breadth of the talar posterior articular sur-
the talar length, the trochlear height, the length, and the face of the calcaneus (M1 + M4 + M12 + M13 + CM1 +
breadth of the calcaneal posterior articular surface (M1 + CM9 + CM10), with 94.0% accuracy (Table 7).
M6 + M12 + M13). As was done with the univariate discrim- Several discriminant functions previously reported in other
inant functions, the multivariate equations were also tested on populations were used to estimate the sex of the HTOC pop-
group 2 (Table 5). For the calcaneus, the correct classification ulation to check if any variable maintained good percentages
is higher than 80.0%, with an accuracy ranging from 82.0 to of correct allocation. We selected those formulae that
88.0%, and the best equation is that which includes the length maintained correct allocation percentages higher than 80%,
and the breadth of the talar posterior articular surface (CM9 + and were balanced between both sexes. Those results are
CM10). For the talus, the correct classification offers accuracy shown in Table 8. The complete results with all the formulae
ranging from 78.0 to 100%, and the best equations are those applied are available in Table S2.
that include the talar and total length, the trochlear length and In the same way, the formulae published in other stud-
the length and breadth of the calcaneal posterior articular sur- ies and those generated using the HTOC in this paper
face (M1 + M1a + M4 + M12 + M13), and the trochlear length were applied to the talus and calcaneus data of fossil
and the length and breadth of the calcaneal posterior articular remains with sex estimates already available, to the three
surface (M4 + M12 + M13), both with 100% accuracy. subpopulations established. Those formulae that
We also carried out a multivariate analysis combining the maintained allocation percentages greater than 80%, and
variables measured in the calcaneus with the talus measurements were balanced between the sexes, were again selected.
Table 5 Validity of multivariate discriminant functions on group 2, using variables measured in calcaneus and talus from HTOC (♂: male; ♀: female;
N: number of individuals studied)
Variablesa N Accuracy (%) N♀ Accuracy (%) N♂ Accuracy (%)
CM1 + CM3 + CM5 + CM9 + CM10 50 82.0 23 78.3 27 85.2

CM1 + CM3 + CM9 + CM10 50 82.0 23 78.3 27 85.2
CM1 + CM3 + CM9 50 86.0 23 82.6 27 88.9
CM5 + CM9 + CM10 50 86.0 23 82.6 27 88.9
CM9 + CM10 50 88.0 23 82.6 27 82.6
CM3 + CM9 + CM10 (stepwise) 50 82.0 23 78.3 27 85.2
M1 + M1a + M2 + M4 + M6 + M7 + M9+ M12 + M13 50 78.0 27 96.3 23 56.5
M1 + M1a + M4 + M12 + M13 50 100.0 27 100.0 23 100.0
M1 + M12 + M13 50 92.0 27 92.6 23 91.3
M4 + M12 + M13 50 100.0 27 100.0 23 100.0
M1 + M12 50 94.0 27 92.6 23 95.7
M6 + M13 50 84.0 27 85.2 23 82.6
M6 + M12 50 92.0 27 96.3 23 87.0
M1 + M6 + M12 + M13 (stepwise) 50 92.0 27 92.6 23 91.3
a
CM1: maximum length of the calcaneus; CM3: minimum breadth of the calcaneus; CM5: calcaneal body length; CM9: length of the talar posterior
articular surface of the calcaneus; CM10: breadth of the talar posterior articular surface of the calcaneus; M1: talar length; M1a: total length of the talus;
M2: total breadth of the talus; M4: trochlear length of the talus; M6: trochlear height of the talus; M7: lateral malleolar oblique height of the talus; M9:
length of the head of the talus; M12: length of the calcaneal posterior articular surface of the talus; M13: breadth of the calcaneal posterior articular surface
of the talus
CM3: minimum breadth of the calcaneus; CM5: calcaneal body length; CM9: length of the talar posterior articular surface of the calcaneus; CM10: breadth of the talar posterior articular surface of the
of the head of the talus; M12: length of the calcaneal posterior articular surface of the talus; M13: breadth of the calcaneal posterior articular surface of the talus; CM1: maximum length of the calcaneus;
M1: talar length; M1a: total length of the talus; M2: total breadth of the talus; M4: trochlear length of the talus; M6: trochlear height of the talus; M7: lateral malleolar oblique height of the talus; M9: length
The results are shown in Tables 9, 10, and 11. The com-
Sectioning
plete results with all the formulae applied are available in
point
Tables S3-S5.
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
For formulae that maintained high correct allocation per-
centages for each group (Tables 9, 10, and 11), sex was esti-
Accuracy
mated in fossils that had not previously been estimated.

92.9
94.6
92.0
92.0
90.2
93.8
95.5
93.8
95.5
93.8
(%)
Formulae with correct allocation percentages greater than

80% for the same subgroup were applied to each fossil spec-
CM1 × (− 0.113) + CM3 × 0.118 + CM5 × 0.084 + CM9 × (− 0.108) + CM10 × (− 0.021) − 22.668
imen belonging to one of the established subpopulations. The

results of the estimates are depicted in Table 12, along with the
number of formulae that could be applied in each case. The
M12 × 0.320 + M13 × 0.195 + CM3 × 0.165 + CM9 × (− 0.040) + CM10 × 0.144 − 20.412
M1 × 0.205 + M12 × 0.280 + M13 × 0.182 + CM9 × (− 0.059) + CM10 × 0.036 − 22.424
estimation of the sex was considered valid when at least 75%

M1 × 0.191 + M4 × 0.086 + M12 × 0.259 + M13 × 0.200 + CM1 × (− 0.028) + CM9 ×
+ CM1 × (− 0.038) + CM3 × 0.134 + CM9 × (− 0.075) + CM10 × 0.005 − 23.142
of the applied formulae resulted in the same sex. The complete

M1 × 0.155 + M6 × 0.277 + M12 × 0.181 + M13 × 0.193 + CM3 × 0.123 − 23.480 results with all the formulae applied are available in Table S6.
M1 × 0.070 + M1a × 0.091 + M2 × 0.139 + M4 × 0.094 + M6 × 0.300 + M7 ×
M1 × 0.157 + M4 × 0.070 + M6 × 0.274 + M12 × 0.232 + M13 × 0.215
M1 × 0.193 + M4 × 0.157 + CM9 × 0.141 + CM10 × 0.137 − 22.491

M1 × 0.202 + M4 × 0.192 + CM1 × 0.002 + CM3 × 0.196 − 22.426
Discussion
Multivariate discriminant functions score equations for group 1, using variables measured in talus and calcaneus from HTOC
(− 0.075) + M9 × (− 0.012) + M12 × 0.181 + M13 × 0.172 +
A study of sexual dimorphism and sex estimation was carried

out on the calcaneus and talus, using a twentieth century North
M1 × 0.217 + M12 × 0.234 + CM3 × 0.134 − 22.278
American population. As in similar previous studies (Bidmos

and Asala 2003; Bidmos and Dayal 2004; Kim et al. 2013;
Murphy 2002a, b; among others), all the variables studied
(− 0.053) + CM10 × 0.031 − 22.134
show a significant sexual dimorphism. Therefore, they are

M1 × 0.303 + CM3 × 0.200 − 21.347
considered appropriate for determining sex. For a variable to

be dimorphic, and therefore a good discriminator of sex, not
only should the average value for each sex be different, but
also the distribution of measurements should overlap as little
as possible. Calcaneus and talus sexual dimorphism is attrib-
uted to the body weight support function of these bones, as
Equationsa
well as to the amount of physical activity, which is also affect-

ed by weight (Heymsfield et al. 2007; Mahakkanukrauh et al.
2014; Rivero de la Calle et al. 1995).
This type of study is considered population-dependent
(Bidmos and Asala 2003; Bidmos and Dayal 2004; Gualdi-
Russo 2007), which is why there are so many of them.
Population differences in foot bones have been known for
decades. They were studied by Wells (1931) who found dif-
ferences in the shape of the talus and calcaneus between three
distinct populations. These have also been noted by other
authors, such as the study by Gualdi-Russo (2017) or
M1 + M1a + M2 + M4 + M6 + M7 + M9 + M12+
M13 + CM1 + CM3 + CM5 + CM9 + CM10
Bidmos (2006). It is logical to deduce that the equations

established to determine sex in one population will not pro-
M1 + M6 + M12 + M13 + CM3 (stepwise)
M1 + M4 + M6 + M12 + M13 + CM1+
vide satisfactory results in another. In spite of that, in isolated

M12 + M13 + CM3 + CM9 + CM10
cases when some remains of unknown origin are found, as in

M1 + M12 + M13 + CM9 + CM10
M1 + M4 + M12 + M13 + CM1+
forensic cases, these functions can be a rough calculation and

offer an estimated sex that can help with identification.
M1 + M4 + CM9 + CM10
M1 + M4 + CM1 + CM3
Nevertheless, they should be used with caution as they can

CM3 + CM9 + CM10
be deceptive.
M1 + M12 + CM3
In this study, taking this into consideration, in addition to

CM9 + CM10
M1 + CM3
Variablesa
constructing equations from HTOC data, we have applied

calcaneus
Table 6
previously published functions on these data, and all sets of

formulae on fossil remains of estimated sex. The formulae
a
Table 7 Validity of multivariate discriminant functions, using variables measured in talus and calcaneus, on group 2 from HTOC (♂: male; ♀: female;
N: number of individuals studied)
Variablesa N Accuracy (%) N♂ Accuracy (%) N♀ Accuracy (%)
M1 + M1a + M2 + M4 + M6 + M7 + M9 + M12 + M13 + CM1 50 86.0 27 85.2 23 87.0

+ CM3 + CM5 + CM9 + CM10
M1 + M4 + M6 + M12+ M13 + CM1 + CM3 + CM9 + CM10 50 90.0 27 92.6 23 87.0
M1 + M4 + M12 + M13+ CM1 + CM9 + CM10 50 94.0 27 92.6 23 95.7
M1 + M12 + M13 + CM9 + CM10 50 90.0 27 92.6 23 87.0
M12 + M13 + CM3 + CM9 + CM10 50 86.0 27 88.9 23 82.6
M1 + M4 + CM9 + CM10 50 90.0 27 88.9 23 91.3
M1 + M4 + CM1 + CM3 50 86.0 27 81.5 23 91.3
M1 + M12 + CM3 50 90.0 27 92.6 23 87.0
M1 + CM3 50 90.0 27 85.2 23 95.7
M1 + M12 + CM3 (stepwise) 50 90.0 27 92.6 23 87.0
a
M1: talar length; M1a: total length of the talus; M2: total breadth of the talus; M4: trochlear length of the talus; M6: trochlear height of the talus; M7:
lateral malleolar oblique height of the talus; M9: length of the head of the talus; M12: length of the calcaneal posterior articular surface of the talus; M13:
breadth of the calcaneal posterior articular surface of the talus; CM1: maximum length of the calcaneus; CM3: minimum breadth of the calcaneus; CM5:
calcaneal body length; CM9: length of the talar posterior articular surface of the calcaneus; CM10: breadth of the talar posterior articular surface of the
calcaneus
generated from each bone separately offer good results. and are not good options for estimating the sex of an
However, the combination of variables from both bones im- American population. Therefore, in the absence of adequate
proved the correct allocation percentages. Therefore, if it is equations for the population with which we work, formulae
possible to have both bones to determine sex, combining them from another population can be used, but a population with
would be the best option. similar proportions must be selected, in addition to being care-
When applying the functions obtained in other published ful not to pass the results off as infallible.
research to the HTOC data, and although a considerable When applying the different sets of discriminant functions
amount of formulae provided allocation percentages that were to the fossil remains data, depending on the subgroup used,
lower than 80% or too unbalanced between the sexes to be different functions were the most appropriate, although some
considered acceptable, a significant amount yielded good re- had good results in all the subgroups, such as the equation
sults (see Table 8), even slightly improving the correct alloca- using the maximum length of the calcaneus or the one using
tion percentages in most cases, such as the equation using talar the talar length generated by this research.
length and total length of the talus from Steele (1976), who In the three subgroups established for fossil remains, sev-
obtained 83%. When this was applied to the HTOC data, eral equations determined sex with 100% accuracy (see
91.4% was obtained. Similarly, one of Silva’s equations Table 9). In the case of the specimens from the Sima de los
(Silva 1995) improves its correct allocation when used on a Huesos, however, for some of them, it should be taken into
modern Japanese population (Sakaue 2011). It may be that account that 100% of the individuals belonged to the same sex
each population differs from others in regard to the propor- as there were no individuals for both sexes on which to apply
tions of some variables, but not in others, causing them to those equations in particular. Although we do not want to rule
maintain good percentages in any population applied. It is them out completely, future tests with fossils that have an
possible that the HTOC has a high degree of dimorphism, estimation of sex are required to confirm their validity.
though it is more likely that the origin and proportions of the Interestingly enough, the set of formulae where a greater
sample are not so different from other populations used and, number of equations is acceptable is the one generated by our
therefore, retains good percentages of allocation. For example, research using the HTOC data. One possible explanation is
the collection used by Steele (1976) also comprises Black and that it constitutes a more mixed population, since Euro-
White American individuals. Even the South African popula- Americans have not been separated from African-
tion used by Bidmos (Bidmos and Asala 2003; Bidmos and Americans, which makes the formulae less specific to a more
Asala 2004; Bidmos and Dayal 2003; Bidmos and Dayal homogeneous sample.
2004) may be similar to the individuals of African origin from It is also notable that the worst fossil group these types of
the HTOC. However, more remote populations such as the formulae can be applied to is the anatomically modern
Korean sample used by Kim et al. (2013), or the Egyptian H. sapiens, where only 15 functions are valid, as opposed to
one used by Abd-Elhakim et al. (2012), did not pass the test the 41 that each of the other two groups have. This leads us to
4938
Table 8 Percentages of correct allocation obtained in the HTOC for the formulae published by other authors in previous studies. Only the formulae that yielded results greater than 80% are presented. The
complete results are provided in the supplementary information (Supplementary Table 2)
Discriminant functiona Paper Population Sample size Original accuracy Accuracy for HTOC
(%) (%)
Total Male Female Total
M1 × 0.42002 + M2 × 0.41096 − 38.75 Steele (1976) s. XX. American Blacks and 120 (60 males, 60 83.0 90.0 92.0 91.4
Whites. Terry Collection females)
M1 × 0.359 − 19.135 Bidmos y Dayal (2003) s. XX. South African Whites. 120 (60 males, 60 81.7 85.5 96.2 90.7
M13 × 0.516 − 11.185 Raymond A. Dart Collection females) 80.0 77.1 88.6 82.7
M2 × 0.412 − 16.740 76.7 86.7 83.5 85.2
M4 × 0.389 − 13.193 71.7 73.5 98.7 85.8
M1 × 0.230 + M13 × 0.149 + M2 × 0.088 − 19.066 83.3 86.7 97.5 92.0
M1 × 0.131 + M4 × 0.141 + M12 × 0.294 − 20.341 Bidmos y Dayal (2004) s. XX. South African Blacks. 120 (60 males, 60 85.0 95.2 79.7 87.7
M12 × 0.390 + M13 × 0.312 − 19.513 Raymond A. Dart Collection females) 84.2 73.5 94.9 84.0
M13 SP 20.95 80.0 84.3 82.3 83.3
M1 × (− 0.2642) + M2 × (− 0.1699) + 21.000 − 0.353 Gualdi-Russo (2007) s. XX. Northern Italians. 118 (62 male, 56 90.7 92.8 92.4 92.6
Frassetto Collection female)
M1 × 0.5959 − 31.627 Mahakkanukrauh et al. s. XX. Thai. Chiang Mai University Skeletal 252 (126 male, 126 85.2 89.2 93.7 91.4
M1 × 0.6390 − 33.937 (2014) Collection female) 85.8 88.0 93.7 90.7
M2 × 0.239 + M1a × 0.155 − 18.442 Peckman et al. (2015b) s. XX. Greek. University of Athens 182 (96 males, 86 84.7 88.0 88.6 88.3
M1a SP 57.43 Human Skeletal Reference Collection females) 85.0 83.1 91.1 87.0
M4 SP 32.78 79.1 86.7 87.3 87.0
M12 SP 31.84 79.1 79.5 91.1 85.2
M2 SP 39.94 82.6 90.4 74.7 82.7
M13 SP 21.63 72.4 77.1 88.6 82.7
CM9 × 0.448 − 13.080 - 0.052 Bidmos y Asala (2003) s. XX. South African Whites. 113 (53 male, 60 81.4 89.2 75.9 82.7
CM1 × 0.163 + CM9 × 0.180 − 18.343 - 0.010 Raymond A. Dart Collection female) 88.7 78.3 89.9 84.0
M1 × (− 0.1933) + M2 × (− 0.1704) + CM1 × Gualdi-Russo (2007) s. XX. Northern Italians. 118 (62 male, 56 92.2 95.2 83.5 89.5
(− 0.0581) + 21.839 − 0.494 Frassetto Collection female)
a
calcaneus. SP: sectioning point
Archaeol Anthropol Sci (2019) 11:4927–4946
Table 9 Percentages of correct allocation obtained in the Sima de los Huesos specimens for the formulae generated in this paper and the ones published by other authors in previous studies. Only the
formulae that yielded results greater than 80% are presented. The complete results are provided in the supplementary information (Supplementary Table 3)
Discriminant functiona Paper Population Sample size Original Accuracy for

accuracy (%) Sima (%)
CM1 × 0.216 − 17.003 Present study s. XX. American Blacks and Whites. 114 (57 males, 74.6 85.7 100.0 90.0
CM5 × 0.263 − 14.977 Hamann-Todd Osteological Collection 57 females) 70.2 100.0 100.0 100.0
CM9 × 0.465 − 13.755 86.0 100.0 100.0 100.0
M1 × 0.390 − 20.567 112 (56 males, 90.2 100.0 100.0 100.0
M1a × 0.33 − 18.845 56 females) 84.8 83.3 100.0 92.3
M4 × 0.533 − 17.620 87.5 100.0 100.0 100.0
M1 × 0.064 + M1a × 0.046 + M2 × 0.148 + 97.3 100.0 85.7 91.7
M4 × 0.098 + M6 × 0.268 + M7 × (− 0.093)

+ M9 × 0.007 + M12 × 0.153 + M13 × 0.129 − 23.046
M1 × 0.146 + M1a × 0.027 + M4 × 0.091 + M12 × 92.9 100.0 100.0 100.0
0.201 + M13 × 0.189 − 22.505
M1 × 0.205 + M12 × 0.226 + M13 × 0.201 − 22.138 92.9 100.0 100.0 100.0
M1 × 0.245 + M12 × 0.289 − 21.939 92.9 100.0 100.0 100.0
M1 × 0.155 + M6 × 0.277 + M12 × 0.181 + M13 × 0.193 94.6 100.0 – 100.0
+ CM3 × 0.123 − 23.480 (stepwise)
M1 × 0.157 + M4 × 0.070 + M6 × 0.274 + M12 × 0.232 + M13 × 0.215 + 95.5 100.0 – 100.0
CM1 × (− 0.038) + CM3 × 0.134 + CM9 × (− 0.075) + CM10 × 0.005 − 23.142
M1 × 0.205 + M12 × 0.280 + M13 × 0.182 + CM9 × (− 0.059) + CM10 × 0.036 − 22.424 92.0 100.0 100.0 100.0
M12 × 0.320 + M13 × 0.195 + CM3 × 0.165 + CM9 × (− 0.040) + CM10 × 0.144 − 20.412 91.1 100.0 – 100.0
M1 × 0.193 + M4 × 0.157 + CM9 × 0.141 + CM10 × 0.137 − 22.491 93.8 100.0 100.0 100.0
M1 × 0.202 + M4 × 0.192 + CM1 × 0.002 + CM3 × 0.196 − 22.426 96.4 100.0 100.0 100.0
M1 × 0.217 + M12 × 0.234 + CM3 × 0.134 − 22.278 95.5 100.0 – 100.0
M1 × 0.303 + CM3 × 0.200 − 21.347 95.5 100.0 100.0 100.0
M1 × 0.191 + M4 × 0.086 + M12 × 0.259 + M13 × 0.200 92.9 100.0 100.0 100.0
+ CM1 × (− 0.028) + CM9 × (− 0.053) + CM10 × 0.031 − 22.134
M1 × 0.42002 + M2 × 0.41096 − 38.75 Steele (1976) s. XX. American Blacks 120 (60 males, 83.0 100.0 100.0 100.0
and Whites. Terry Collection 60 females)
M1 × 0.359 − 19.135 Bidmos y Dayal s. XX. South African Whites. Raymond A. 120 (60 males, 81.7 83.3 100.0 92.9
M13 × 0.516 − 11.185 (2003) Dart Collection 60 females) 80.0 100.0 87.5 92.9
M12 × 0.451 − 14.927 75.8 80.0 100.0 91.7
M4 × 0.389 − 13.193 71.7 83.3 100.0 92.9
M1 × 0.230 + M13 × 0.149 + M2 × 0.088 − 19.066 83.3 100.0 100.0 100.0
M12 × 0.281 + M13 × 0.268 − 15.130 81.7 100.0 100.0 100.0
M1 × 0.131 + M4 × 0.141 + M12 × 0.294 − 20.341 Bidmos y Dayal s. XX. South African Blacks. Raymond A. 120 (60 males, 84.2 100.0 100.0 100.0
M12 SP 32.35 (2004) Dart Collection 60 females) 82.5 80.0 100.0 91.7
M1 × (− 0.2642) + M2 × (− 0.1699) + 21.000 − 0.353 Gualdi-Russo s. XX. Northern Italians. Frassetto 118 (62 male, 90.7 100.0 100.0 100.0
(2007) Collection 56 female)
M1 × 0.5959 − 31.627 Mahakkanukrauh s. XX. Thai. Chiang Mai University 252 (126 male, 85.2 100.0 100.0 100.0
M1 × 0.6390 − 33.937 et al. (2014) Skeletal Collection 126 female) 85.8 83.3 100.0 92.9
M2 × 0.239 + M1a × 0.155 − 18.442 Peckman et al. s. XX. Greek. University of Athens Human 182 (96 males, 84.7 100.0 100.0 100.0
M4 SP 32.78 (2015b) Skeletal Reference Collection 86 females) 79.1 100.0 87.5 92.9
M13 SP 21.63 72.4 100.0 87.5 92.9
CM1 × 0.1 × 3.14 − 23.80 Introna et al. s. XX. Southern Italian 80 (40 male, 83.8 100.0 100.0 100.0
CM1 × 0.1 × 2.54 + CM10 × 0.1 × 3.85 − 28.75 (1997) 40 female) 85.0 100.0 100.0 100.0
CM10 × 0.552 − 12.152 − 0.065 Bidmos y Asala s. XX. South African Whites. Raymond A. 113 (53 male, 84.9 85.7 100.0 90.0
CM1 × 0.163 + CM9 × 0.180 − 18.343 − 0.010 (2003) Dart Collection 60 female) 88.7 100.0 100.0 100.0
CM1 × 0.118 + CM9 × 0.315 − 18.115 Bidmos y Asala s. XX. South African Blacks. Raymond A. 116 (58 male, 80.2 100.0 100.0 100.0
CM1 SP 76.8 (2004) Dart Collection 58 female) 75.8 100.0 100.0 100.0
CM1 × 0.244 − 18.790 − 0.06 Kim et al. (2013) s. XX. Korean 104 (50 male, 81.7 100.0 100.0 100.0
54 female)
CM1 SP 79.27 83.5 85.7 100.0 90.0
4939
100.0
100.0
Male Female Total
believe that, for measurements taken in the calcaneus and
Accuracy for talus, the current populations are more like
100.0 100.0
Sima (%) H. neanderthalensis or the SH hominins than the first
H. sapiens, despite the known differences between the groups
100.0 –
(Pablos et al. 2019; Pablos et al. 2013b; Pablos et al. 2014;
Pablos et al. 2017; Rhoads and Trinkaus 1977; Rosas et al.
2017). This is indicative of the variability of sexual dimor-
accuracy (%)
phism throughout time, which may hinder the estimation of

Original
sex. It also highlights the value of this type of studies to im-

Total
118 (62 male, 92.2

165 (80 males, 84.2
prove the estimation of sex from fossil remains.

By applying the formulae that yielded good results to the
85 females)
56 female)
Sample size
males, 95
females)
unknown sex fossils of the different subpopulations, a series

s. XX. Greek. University of Athens Human 198 (103
of sex estimates were obtained. In some cases, as can be seen

in Table S6, non-definitive results are obtained. Other cases
were ruled out because a minimum number of equations could
not be applied. However, another number of fossils now has
s. XX. Portuguese. Identified Skeleton
an estimate of the sex that we consider acceptable. In some

s. XX. Northern Italians. Frassetto
Skeletal Reference Collection
cases, a high number of formulae were applied, such as several

Collection of the Museum of
from the Sima de los Huesos (AT-575, AT-1700, and AT-

3133) or H. neanderthalensis (Kra238.2 + Kra238.7). In other
cases, although fewer formulae can be applied, the results
Anthropology
coincide 100%, which is why we consider them valid, such

Collection
as in AT-859 of Sima de los Huesos.

Population
It is notable that the percentages obtained in Tables 9, 10,

and 11 must be taken with caution since the known sex of
fossils are mostly estimates based on morphological traits,
and above all, because we are leaving the zone of confidence
Peckman et al.
Gualdi-Russo
Silva (1995)
provided by modern populations, applying formulae that are

(2015a)
(2007)
not specifically designed for this type of population. However,

Paper
in the study of fossil remains, there are never records of sex

and age at the time of death. We are always forced to work on
the basis of estimates, so we do not have the opportunity to
corroborate our results. It is for this reason that we believe that
the sex estimates calculated in this work can be considered
valid and that they provide information relevant to the study of
M1 × (− 0.1933) + M2 × (− 0.1704) + CM1 × (− 0.0581) + 21.839 − 0.494
the paleobiology of fossil individuals.

In fact, it is common to find papers where data from
modern populations are used to estimate biological char-
acteristics of fossil populations. Functions created from
modern populations are frequently used to calculate body
mass. For example, Boyle and DeSilva (2015) used the
M1 × 0.3261971 + CM1 × 0.04486827 − 19.91041
formulae from McHenry (1992) generated for fossils from

modern apes and humans, to estimate the body mass of a
specimen of Homo erectus, to which male sex has been
assigned according to its large size, although McHenry
(1992) has been recently criticized (e.g., Grabowski

et al. 2018; Grabowski et al. 2015; Lacoste Jeanson
Discriminant functiona
et al. 2017). Furthermore, with respect to Homo naledi,

Table 9 (continued)
Berger et al. (2015) estimated its body mass with equa-

tions made from a sample of modern European individ-
uals. The same goes for stature; Berger et al. (2015) used
formulae generated from two African populations, one of
them composed of individuals from medieval Nubia,
a
Table 10 Percentages of correct allocation obtained in the H. sapiens specimens from different sites for the formulae generated in this paper and the ones published by other authors in previous studies.
Only the formulae that yielded results greater than 80% are presented. The complete results are provided in the supplementary information (Supplementary Table 4)
Discriminant functiona Paper Population Sample size Original accuracy (%) Accuracy for H. sapiens
(%)
CM1 × 0.216 − 17.003 Present study s. XX. American Blacks and Whites. 114 (57 males, 57 females) 83.9 87.0 80.0 84.8
CM1 × 0.040 + CM3 × 0.207 + CM9 × Hamann-Todd Osteological Collection 87.7 83.3 100.0 87.0
0.209 + CM10 × 0.267 − 20.528
CM1 × 0.065 + CM3 × 0.235 + CM9 92.9 85.7 80.0 84.2
× 0.242 − 18.511
M1 × 0.390 − 20.567 112 (56 males, 56 females) 94.6 83.3 100.0 87.5
M1a × 0.33 − 18.845 95.5 85.7 100.0 88.9
M2 × 0.430 − 17.491 92.0 90.9 80.0 87.5
M4 × 0.533 − 17.620 91.1 88.9 100.0 90.9
M1 × 0.205 + M12 × 0.226 + M13 × 0.201 − 22.138 92.9 89.5 80.0 86.2
M4 × 0.212 + M12 × 0.246 + M13 × 0.279 − 20.569 90.2 81.0 80.0 80.6
M1 × 0.245 + M12 × 0.289 − 21.939 92.9 89.5 90.0 89.7
M1 × 0.191 + M4 × 0.086 + M12 × 0.259 + M13 × 92.9 90.9 80.0 87.5
0.200 + CM1 × (− 0.028) + CM9 × (− 0.053) +
CM10 × 0.031 − 22.134
M1 × 0.359 − 19.135 Bidmos y Dayal (2003) s. XX. South African Whites. 120 (60 males, 60 females) 80.0 82.6 80.0 81.8
Raymond A. Dart Collection
M1 × 0.131 + M4 × 0.141 + M12 × 0.294 − 20.341 Bidmos y Dayal (2004) s. XX. South African Blacks. 120 (60 males, 60 females) 85.0 94.7 80.0 89.7
M12 SP 32.35 Raymond A. Dart Collection 82.5 81.0 90.0 83.9
M13 SP 20.95 80.0 87.0 80.0 84.8
M2 × 0.239 + M1a × 0.155 − 18.442 Peckman et al. (2015b) s. XX. Greek. University of \Athens 182 (96 males, 86 females) 79.1 85.7 90.0 87.1
M13 SP 21.63 Human Skeletal Reference Collection 72.4 82.6 80.0 81.8
CM1 × 0.118 + CM9 × 0.315 − 18.115 Bidmos y Asala (2004) s. XX. South African Blacks. 116 (58 male, 58 female) 80.2 83.3 80.0 82.4
CM1 SP 76.8 Raymond A. Dart Collection 75.8 81.8 93.8 85.7
a
4941
Table 11 Percentages of correct allocation obtained in the H. neanderthalensis specimens from different sites for the formulae generated in this paper and the ones published by other authors in previous
4942
studies. Only the formulae that yielded results greater than 80% are presented. The complete results are provided in the supplementary information (Supplementary Table 5)

accuracy H. neanderthalensis
(%) (%)
CM1 × 0.216 − 17.003 Present study s. XX. American Blacks and Whites. Hamann-Todd 114 (57 males, 70.2 84.6 100.0 87.5
CM3 × 0.471 − 12.259 Osteological Collection 57 females) 86.0 84.6 100.0 87.5
CM1 × 0.065 + CM3 × 90.4 100.0 100.0 100.0
0.235 + CM9 × 0.242 − 18.511
CM5 × 0.057 + CM9 × 0.302 87.7 100.0 100.0 100.0
+ CM10 × 0.327 − 19.206
M1 × 0.390 − 20.567 112 (56 males, 87.5 87.5 100.0 91.3
M12 × 0.540 − 16.753 56 females) 85.7 93.8 100.0 95.5
M13 × 0.687 − 14.629 83.9 100.0 100.0 100.0
M1 × 0.177 + M6 × 0.279 + M12 × 0.226 + M13 × 0.210 − 23.155 (stepwise) 94.6 91.7 100.0 94.1
M1 × 0.064 + M1a × 0.046 + M2 × 0.148 + M4 × 0.098 97.3 100.0 100.0 100.0
+ M6 × 0.268 + M7 × (− 0.093) + M9 × 0.007
+ M12 × 0.153 + M13 × 0.129 − 23.046
M1 × 0.146 + M1a × 0.027 + M4 × 0.091 + M12 × 0.201 + M13 × 0.189 − 22.505 92.9 91.7 100.0 94.1
M1 × 0.205 + M12 × 0.226 + M13 × 0.201 − 22.138 92.9 91.7 100.0 94.4
M4 × 0.212 + M12 × 0.246 + M13 × 0.279 − 20.569 90.2 91.7 100.0 94.4
M1 × 0.245 + M12 × 0.289 − 21.939 92.9 87.5 100.0 90.9
M6 × 0.476 + M13 × 0.623 − 17.265 87.5 91.7 100.0 94.1
M6 × 0.418 + M12 × 0.497 − 18.934 88.4 92.3 100.0 94.4
M1 × 0.155 + M6 × 0.277 + M12 × 0.181 + M13 94.6 100.0 100.0 100.0
× 0.193 + CM3 × 0.123 − 23.480 (stepwise)
M1 × 0.157 + M4 × 0.070 + M6 × 0.274 + M12 × 0.232 95.5 83.3 100.0 87.5
+ M13 × 0.215 + CM1 × (− 0.038) + CM3 × 0.134
+ CM9 × (− 0.075) + CM10 × 0.005 − 23.142
M1 × 0.205 + M12 × 0.280 + M13 × 0.182 + CM9 × 92.0 88.9 100.0 90.9
(− 0.059) + CM10 × 0.036 − 22.424
M12 × 0.320 + M13 × 0.195 + CM3 × 0.165 + CM9 × 91.1 100.0 100.0 100.0
(− 0.040) + CM10 × 0.144 − 20.412
M1 × 0.193 + M4 × 0.157 + CM9 × 0.141 + CM10 × 0.137 − 22.491 93.8 80.0 100.0 83.8
M1 × 0.202 + M4 × 0.192 + CM1 × 0.002 + CM3 × 0.196 − 22.426 96.4 85.7 100.0 90.0
M1 × 0.217 + M12 × 0.234 + CM3 × 0.134 − 22.278 95.5 85.7 100.0 88.9
M1 × 0.42002 + M2 × 0.41096 − 38.75 Steele (1976) s. XX. American Blacks and Whites. Terry Collection 120 (60 males, 83.0 100.0 100.0 100.0
60 females)
M1 × 0.2573032 + M2 × 0.1910786 − 20.53448 Silva (1995) s. XX. Portuguese. Identified Skeleton Collection of 165 (80 males, 86.1 100.0 85.7 95.7
the Museum of Anthropology 85 females)
M1 × 0.359 − 19.135 Bidmos y Dayal s. XX. South African Whites. Raymond A. Dart 120 (60 males, 80.0 100.0 100.0 100.0
M13 × 0.516 − 11.185 (2003) Collection 60 females) 75.8 87.5 100.0 90.9
M12 × 0.451 − 14.927 71.7 87.5 100.0 91.3
M4 × 0.389 − 13.193 83.3 83.3 100.0 88.9
M1 × 0.230 + M13 × 0.149 + M2 × 0.088 − 19.066 81.7 91.7 100.0 94.4
M1 × 0.131 + M4 × 0.141 + M12 × 0.294 − 20.341 Bidmos y Dayal s. XX. South African Blacks. Raymond A. Dart 120 (60 males, 85.0 93.8 100.0 95.5
M12 × 0.390 + M13 × 0.312 − 19.513 (2004) Collection 60 females) 84.2 91.7 100.0 94.4
Table 11 (continued)

accuracy H. neanderthalensis
(%) (%)
M12 SP 32.35 82.5 87.5 100.0 90.9

M13 SP 20.95 80.0 100.0 100.0 100.0
M1 × (− 0.2642) + M2 × (− 0.1699) + 21.000 − 0.353 Gualdi-Russo s. XX. Northern Italians. Frassetto Collection 118 (62 male, 90.7 100.0 100.0 100.0
(2007) 56 female)
M1 × 0.5959 − 31.627 Mahakkanukrauh s. XX. Thai. Chiang Mai University Skeletal 252 (126 male, 86.5 93.8 100.0 95.7
M1 × 0.6390 − 33.937 et al. (2014) Collection 126 female) 89.8 93.8 100.0 95.7
M4 × 1.1280 − 36.190 85.5 100.0 83.3 95.5

M4 × 1.3760 − 44.070 83.5 100.0 83.3 95.5
M2 × 0.239 + M1a × 0.155 − 18.442 Peckman et al. s. XX. Greek. University of Athens Human Skeletal 182 (96 males, 84.7 92.3 100.0 94.7
M4 SP 32.78 (2015b) Reference Collection 86 females) 79.1 93.8 100.0 95.7
M12 SP 31.84 79.1 93.8 100.0 95.5
M13 SP 21.63 72.4 100.0 100.0 100.0
CM1 × 0.1 × 3.14 − 23.80 Introna et al. s. XX. Southern Italian 80 (40 male, 40 85.0 81.8 100.0 84.6
(1997) female)
CM10 × 0.552 − 12.152 − 0.065 Bidmos y Asala s. XX. South African Whites. Raymond A. Dart 113 (53 male, 85.8 90.9 100.0 92.3
CM1 × 0.118 + CM9 × 0.315 − 18.115 Bidmos y Asala s. XX. South African Blacks. Raymond A. Dart 116 (58 male, 80.2 100.0 100.0 100.0
M1 × 0.3261971 + CM1 × 0.04486827 − 19.91041 Silva (1995) s. XX. Portuguese. Identified Skeleton Collection of 165 (80 males, 84.2 91.7 100.0 93.8
the Museum of Anthropology 85 females)
M1 × (− 0.1933) + M2 × (− 0.1704) + CM1 × (− 0.0581) + 21.839 − 0.494 Gualdi-Russo s. XX. Northern Italians. Frassetto Collection 118 (62 male, 92.2 100.0 100.0 100.0
(2007) 56 female)
a
4943
Table 12 Estimation of the sex of fossils of unknown sex from the when at least 75% of the applied formulae resulted in the same sex. The
equations that maintain good percentages of correct allocation in the complete results are provided in the supplementary information
different subpopulations of fossil remains. Only results are presented (Supplementary Table 6)
Specimen Site Species/group Sidea % of female % of male N of equations Estimated

results results applied sexb
Talus AT-575 Sima de los Huesos SH hominins R 87.5 12.5 16 F

AT-859 Sima de los Huesos SH hominins L 0.0 100.0 3 M
AT-1480 Sima de los Huesos SH hominins L 0.0 100.0 9 M
AT-1700 Sima de los Huesos SH hominins R 13.6 86.4 22 M
AT-1832 Sima de los Huesos SH hominins R 100.0 0.0 5 F
AT-3133 Sima de los Huesos SH hominins L 100.0 0.0 21 F
AT-4445 Sima de los Huesos SH hominins R 25.0 75.0 8 M
Grotte des Enfants 1? Grotte des Enfants H. sapiens ? 0.0 100.0 3 M
Mladeč 30 Mladeč H. sapiens L 0.0 100.0 12 M
Pavlov 37a Pavlov H. sapiens R 0.0 100.0 13 M
Pavlov 37b Pavlov H. sapiens L 0.0 100.0 6 M
Pavlov 38a Pavlov H. sapiens R 75.0 25.0 12 F
Tianyuan 1 Tianyuan H. sapiens L 0.0 100.0 12 M
Kra238.1 Krapina H. neanderthalensis L 100.0 0.0 9 F
Kra238.2 + Kra238.7 Krapina H. neanderthalensis L 100.0 0.0 25 F
Moula Guercy (M-D2-566) Moula Guercy H. neanderthalensis R 0.0 100.0 4 M
Calcaneus AT-3130 Sima de los Huesos SH hominins R 81.8 18.2 11 F
Pavlov 37c Pavlov H. sapiens R 0.0 100.0 4 M
Pavlov 38c Pavlov H. sapiens R 100.0 0.0 4 F
a
R: right; L: left; ?: unknown
b
F: female; M: male
whose statures had been estimated. In the work of Conclusions

Carretero et al. (2015), the functions used by Pablos
et al. (2013a) are applied to estimate the stature, and those After conducting the statistical analysis on the measurements
used by Auerbach and Ruff (2004)—also criticized—for taken on the calcaneus and talus, the sex discriminant capacity
the body mass for the El Mirón human remains dated to of all the variables used was noted. Thus, these bones become
15,460 ± 40 BP. In Pomeroy et al. (2017), they estimated a useful tool for determining sex and working on the recon-
the stature of newly remains belonging to Shanidar 5, struction of the biological profile. We generated several dis-
applying the equations from Pablos et al. (2013a) and criminant functions that achieved 96.4% cross-validated accu-
Will and Stock (2015). Sex is no exception; when it can- racy with a multivariate equation. This study also confirms
not be estimated by other methods, some authors establish that it is better to use multivariate functions rather than uni-
it based on discriminatory functions, such as Kuzmin variate ones when possible for this population.
et al. (2009), who, for a talus of doubtful taxonomy (prob- Because the necessity to determine the sex of a few bones
ably H. sapiens) recovered in Siberia and with an age of of unknown origin sometimes arises, we applied the previous-
43,000–40,000 BP, used the equations published by Steele ly published discriminant functions on our HTOC data,
(1976). Moreover, Carretero et al. (2015) used the func- obtaining a series of formulae that maintain good results. It
tions of Marino (1995) for C1 (atlas), among others. would be necessary to repeat the same tests using data from
Hence, when to use these formulae must be decided care- other populations of known sex, to verify if they maintain
fully; it does not work on just any hominin fossil. Our size and good results in any population.
proportions have varied too much throughout evolutionary Finally, all sets of formulae were applied on different fossil
history. Therefore, it is necessary to restrict their use to species populations with the aim of estimating the sex of fossil samples
that are similar to ours, i.e., individuals whose proportions do of these bones when there are no other more suitable osseous
not differ too much from ours, as it seems to be the case of elements to do so. Several equations were valid for each fossil
Neanderthals and SH hominins, since both maintain good population, which provided the sex estimation of 16 individuals.
allocation percentages. It is also not recommended in isolated Although we are aware of the limitations involved in the
remains of doubtful taxonomy, because it may lead to improp- application of this type of equations on fossil populations, the
er classification as it is not an appropriate specimen for the sex estimated here may be a first approximation, pending any
formulae used. technological advances and better methods that would allow
us to establish it reliably, safely, and non-destructively.
Acknowledgments We would like to acknowledge Carlos Lorenzo, who Gonçalves D (2011) The reliability of osteometric techniques for the sex
provided some data. We appreciate the constructive and fruitful discus- determination of burned human skeletal remains Homo. J Comp
sion provided by Ignacio Martínez. Lauren Ames kindly reviewed a pre- Human Biol 62:351–358
vious English version. We are indebted to the people who have allowed us Gonçalves D, Thompson T, Cunha E (2013) Osteometric sex determina-
access to the important skeletal collection in their care and kindly provid- tion of burned human skeletal remains. J Forensic Legal Med 20:
ed assistance at the Cleveland Museum of Natural History (CMNH) for 906–911
access to the Hamann-Todd Osteological Collection. Grabowski M, Hatala KG, Jungers WL, Richmond BG (2015) Body
mass estimates of hominin fossils and the evolution of human body
Funding information This research has received support in part from the size. J Hum Evol 85:75–93. https://doi.org/10.1016/j.jhevol.2015.
‘Ministerio de Ciencia, Innovación y Universidades (MICINN)’ of Spain 05.005
(Project PGC2018-093925-B-C33). Grabowski M, Hatala KG, Jungers WL (2018) Body mass estimates of
the earliest possible hominins and implications for the last common
ancestor. J Hum Evol 122:84–92. https://doi.org/10.1016/j.jhevol.
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Archaeological and Anthropological Sciences (2019) 11:4927–4946

Sex estimation from the calcaneus and talus using discriminant

Introduction fundamental step in the process, along with other biolog-

Anatomical variables studied

Variable N Mean SD Minimum Maximum

Maximum length of the calcaneus ♂ 57 82.1 4.7 67.0 92.7

Table 2 Discriminant functions

Table 3 Validity of univariate

The first test performed was a descriptive analysis of group 1,

M1 × 0.146 + M1a × 0.027 + M4 × 0.091 + M12 × 0.201 + M13 × 0.189 − 22.505

M1 × 0.064 + M1a × 0.046 + M2 × 0.148 + M4 × 0.098 + M6 × 0.268 + M7 ×

CM1 × 0.040 + CM3 × 0.207 + CM9 × 0.209 + CM10 × 0.267 − 20.528

(− 0.093) + M9 × 0.007 + M12 × 0.153 + M13 × 0.129 − 23.046

M1 × 0.177 + M6 × 0.279 + M12 × 0.226 + M13 × 0.210 − 23.155

CM5 × 0.057 + CM9 × 0.302 + CM10 × 0.327 − 19.206

CM1 × 0.065 + CM3 × 0.235 + CM9 × 0.242 − 18.511

M1 × 0.205 + M12 × 0.226 + M13 × 0.201 − 22.138

CM9 × 0.348 + CM10 × 0.358 − 18.014

M1 × 0.245 + M12 × 0.289 − 21.939

highest cross-validated accuracies were the length of the talar

M1 + M6 + M12 + M13 (stepwise)

M1 + M1a + M4 + M12 + M13

total length, both coming in at 92.0%. Of all the univariate

with the correlation analysis.

After the univariate discriminant analysis, a multivariate

discriminant analysis was carried out in an attempt to obtain

more effective equations for determining the sex of our pop-

Variablesa N Accuracy (%) N♀ Accuracy (%) N♂ Accuracy (%)

CM1 + CM3 + CM5 + CM9 + CM10 50 82.0 23 78.3 27 85.2

mated in fossils that had not previously been estimated.

Formulae with correct allocation percentages greater than

imen belonging to one of the established subpopulations. The

estimation of the sex was considered valid when at least 75%

of the applied formulae resulted in the same sex. The complete

M1 × 0.157 + M4 × 0.070 + M6 × 0.274 + M12 × 0.232 + M13 × 0.215

M1 × 0.193 + M4 × 0.157 + CM9 × 0.141 + CM10 × 0.137 − 22.491

(− 0.075) + M9 × (− 0.012) + M12 × 0.181 + M13 × 0.172 +

A study of sexual dimorphism and sex estimation was carried

American population. As in similar previous studies (Bidmos

show a significant sexual dimorphism. Therefore, they are

considered appropriate for determining sex. For a variable to

well as to the amount of physical activity, which is also affect-

Bidmos (2006). It is logical to deduce that the equations

vide satisfactory results in another. In spite of that, in isolated

cases when some remains of unknown origin are found, as in

forensic cases, these functions can be a rough calculation and

Nevertheless, they should be used with caution as they can

In this study, taking this into consideration, in addition to

constructing equations from HTOC data, we have applied

previously published functions on these data, and all sets of

Variablesa N Accuracy (%) N♂ Accuracy (%) N♀ Accuracy (%)

M1 + M1a + M2 + M4 + M6 + M7 + M9 + M12 + M13 + CM1 50 86.0 27 85.2 23 87.0

Total Male Female Total

Discriminant functiona Paper Population Sample size Original Accuracy for

Total Male Female Total

M4 × 0.098 + M6 × 0.268 + M7 × (− 0.093)

phism throughout time, which may hinder the estimation of

sex. It also highlights the value of this type of studies to im-