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Body mass and stature estimation based on the first metatarsal in humans.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 144:625–632 (2011)
Body Mass and Stature Estimation Based on the
First Metatarsal in Humans
Isabelle De Groote1,2* and Louise T. Humphrey1
1
2
The Natural History Museum, Palaeontology Department, London, SW7 5BD, United Kingdom
University College London, Department of Anthropology, Gower Street, London, WC1E 6BT, United Kingdom
KEY WORDS
body mass; stature; metatarsal; human variation; regression
ABSTRACT
Archaeological assemblages often lack
the complete long bones needed to estimate stature and
body mass. The most accurate estimates of body mass
and stature are produced using femoral head diameter
and femur length. Foot bones including the first metatarsal preserve relatively well in a range of archaeological contexts. In this article we present regression
equations using the first metatarsal to estimate femoral
head diameter, femoral length, and body mass in a
diverse human sample. The skeletal sample comprised
87 individuals (Andamanese, Australasians, Africans,
Native Americans, and British). Results show that all
first metatarsal measurements correlate moderately to
highly (r 5 0.62–0.91) with femoral head diameter and
length. The proximal articular dorsoplantar diameter is
the best single measurement to predict both femoral
dimensions. Percent standard errors of the estimate
are below 5%. Equations using two metatarsal meas-
urements show a small increase in accuracy. Direct
estimations of body mass (calculated from measured
femoral head diameter using previously published
equations) have an error of just over 7%. No direct
stature estimation equations were derived due to the
varied linear body proportions represented in the
sample. The equations were tested on a sample of 35
individuals from Christ Church Spitalfields. Percentage
differences in estimated and measured femoral head
diameter and length were less than 1%. This study
demonstrates that it is feasible to use the first metatarsal in the estimation of body mass and stature. The
equations presented here are particularly useful for
assemblages where the long bones are either missing
or fragmented, and enable estimation of these fundamental population parameters in poorly preserved
assemblages. Am J Phys Anthropol 144:625–632,
2011. V 2011 Wiley-Liss, Inc.
The estimation of body mass and stature are fundamental steps in the evaluation of skeletal remains in
palaeoanthropology and osteoarchaeology and important
components of individual identification in forensic cases.
Body mass and stature are usually estimated mathematically using independent variables, such as long bone
lengths, in equations that reflect the linear relationship
between the skeletal variable and body mass or stature
(Feldesman and Lundy, 1988; Henry, 1992; Holliday and
Ruff, 1997; Ruff et al., 1997; Auerbach and Ruff, 2004;
Ruff et al., 2005; Sciulli and Blatt, 2008 and others). The
accuracy of the estimation is reflected in the strength of
the correlation between the independent and dependent
variables and the standard error of the estimate and
varies according to which part of the skeleton is represented and the completeness of the bones.
Intact long bones are not always available for measurement in forensic and archaeological contexts, where
bones are often found incomplete or in poor condition. In
particular, the articular surface of long-bones may be
damaged or incomplete such that long bone length or
articular dimensions cannot be determined. At some
archaeological sites, small compact bones such as those
of the hands and feet may be found in a more complete
condition than larger skeletal elements. At Çatalhöyük
(Konia, Turkey, 7000 BC), where most long bones were
severely fractured due to trampling of the sediment overlying the burials, the hand and foot remains were relatively well represented and complete (Bello, 2006). At
many sites, however, the hand and foot bones are underrepresented in skeletal assemblages due to taphonomic
processes, burial practice, and differential archaeological
recovery (Bello et al., 2003; Bello et al., 2006). Bell and
Cox (1999) show a recovery frequency of 40% of metatarsals in a Roman, early-medieval and modern forensic
assemblage. Reasons for low rate frequency of certain
skeletal elements need to be considered on a site-by-site
basis. Depositional disturbance such as carnivore activity, root damage, and erosion are more likely to cause a
physical relocation of the small bones, such as those in
the foot, than larger bones (Andrews, 1990; Waldron,
2008). In cases of secondary burial the smaller less
obvious bones are more likely to be left behind when the
more obvious skeletal elements are gathered up for reburial. Where a burial is disturbed or truncated due to
intercutting graves or other factors the foot bones may
be at greater risk of disturbance since they are often
located at the periphery of the grave (Mays, 1998;
Waldron, 2008). When they are present though, foot
bones are generally well preserved (Guthrie, 1967;
Defleur et al., 1993; Bello et al., 2002). Of the metatarsal
C 2011
V
WILEY-LISS, INC.
C
Grant sponsor: The Leverhulme Trust.
*Correspondence to: Isabelle De Groote, Department of Palaeontology, The Natural History Museum, London, SW7 5BD, United
Kingdom. E-mail: i.degroote@nhm.ac.uk
Received 30 September 2010; accepted 27 October 2010
DOI 10.1002/ajpa.21458
Published online 13 January 2011 in Wiley Online Library
(wileyonlinelibrary.com).
626
I. DE GROOTE AND L.T. HUMPHREY
bones, the first metatarsal tends to be the best preserved
(Bello and Andrews, 2006; Waldron, 2008).
Although the geometric mean of metatarsal measurements has been used as a proxy for body size (Griffin
et al., 2008), body mass estimation using first metatarsal
measurements has, as far as we know, not been reported
in the literature. Body mass is important from bioarchaeological and palaeoanthropological perspectives as it
facilitates overall size comparison of different populations and enables measures of post-cranial strength to
be standardized for body mass (Ruff et al., 1993; Pearson, 2000; Ruff and Trinkaus, 2000; Stock, 2002; Stock
and Pfeiffer, 2004; Stock and Shaw, 2007). Mechanical
methods of body mass estimation depend on the functional association between a weight bearing skeletal
element and body mass (Auerbach and Ruff, 2004). Adult
body mass is commonly estimated from femoral head
diameter, which is highly correlated with body mass
(McHenry, 1991; Ruff et al., 1991; Grine et al., 1995;
Auerbach and Ruff, 2004). Adult size of the femoral head
is established by the age at which the femoral head fuses
with the metaphysis of the proximal femur and is not
subject to remodeling (Ruff, 1988; Ruff et al., 1991). The
size of other load bearing articulations is also expected
to scale with body mass. Of the portions of the foot that
have contact with the ground, approximately 50% of the
load is borne by the heel and 50% is transmitted to the
metatarsal heads (Nordin and Frankel, 1989). The first
metatarsal carries twice as much load as the individual
load of the other metatarsals during normal stance. During the latter stance phase of the gait cycle, the load is
transferred from the heel to the second metatarsal and
then to the first metatarsal during toe-off (Nordin and
Frankel, 1989; Vereecke, 2003). Therefore it is predicted
that the articular joint size of the first metatarsal will
also reflect body size.
Stature estimation is important for both bioarchaeology and in forensic cases. There has been more interest
in the estimation of stature than body mass in forensic
application as body mass can vary substantially throughout adult life whereas stature shows only a small decline
with age (Ruff et al., 1991). The most accurate estimations of stature are derived from the length of intact
long bones, in particular femoral and tibial length, and
are available for a range of populations (Trotter and
Gleser, 1952, 1958; Steele, 1970; Trotter and Gleser,
1977; Sciulli et al., 1990; Radoinova et al., 2002; Duyar
and Pelin, 2003; Brown et al., 2004; Bidmos and Asala,
2005; Dayal et al., 2008; Raxter et al., 2008; Auerbach
and Ruff, 2010 among others). In recognition of the fact
that intact long bones are not always present or well
preserved, predictive equations have been developed
using partial long bones (Steele, 1970; Bidmos, 2008a;
Bidmos, 2008c) and other measurement of the skull and
the post-cranial skeleton (Byers et al., 1989; Meadows
and Jantz, 1992; Holland, 1995; Bidmos and Asala, 2005;
Bidmos, 2006; Ryan and Bidmos, 2007; Cordeiro et al.,
2009). Measurements of the postcranial skeleton generally yield more accurate estimates of stature than measurements of the skull (Ryan and Bidmos, 2007).
Several studies have derived predictive equations for
the estimation of stature from metatarsal measurements
based on samples of documented stature. Byers (1989)
found significant correlations between metatarsal
lengths and stature for European and African Americans
from the Terry Collection and Maxwell Museum of
Anthropology and showed that metatarsal length can be
American Journal of Physical Anthropology
used to predict stature using linear regression. The associated errors of estimates were higher than those for
regressions using complete long bones (Byers et al.,
1989) but similar to or lower than those for regressions
using fragmentary long bones (Byers et al., 1989; Wilbur,
1998). More recently, predictive equations have been
developed for South Africans using skeletons from the
Raymond A. Dart Collection (Bidmos, 2008). In this
study the standard error of estimate for the metatarsal
equations was lower than that obtained for equations
using measures of the skull or long bone fragments for
stature estimation but higher than for equations using
intact long bones. Regression equations for estimating
stature from the lengths of the first and second metatarsals have also been determined for a Portuguese population using bones from documented cadavers of known
stature (Cordeiro et al., 2009).
In this article we explore the use of the first metatarsal for body mass and stature estimation based on a
sample of individuals with diverse body shape and population origins. To do this, we evaluate the use of metatarsal dimensions as a proxy for the femoral dimensions
that are typically used for body mass and stature estimation since body mass and stature are unavailable for
this broader series of populations. Specifically, we
explore whether metatarsal dimensions can be used to
estimate femoral head diameter, which accurately predicts body mass (Ruff et al., 1991; Auerbach and Ruff,
2004) and femoral length, which is the most accurate
long bone measurement for stature estimation (Steele,
1970). Estimated femoral length can then be used in
population-specific regression formulae for stature estimation. This indirect method for stature estimation is
necessary since population vary substantially in body
shape and proportions (Ruff, 1994) whereas the equation
for femoral head diameter could be converted to enable
the direct estimation of body mass.
MATERIALS AND METHODS
Metric data were collected on the femur and first
metatarsal of 87 skeletons representing a wide range of
body sizes. The sample consists of 33 individuals from
Abingdon (UK), 12 individuals from Newark Bay (UK),
9 individuals of African origin, 21 Andamanese, 7
Australasians, and 5 Native Americans from Santa Cruz
(USA). An additional 35 individuals from Christ Church
Spitalfields (London, UK) were measured and used to
test the regression equations. All skeletons are held at
the Natural History Museum, London, UK.
Femoral length was measured as maximum length of
the femur (Martin n81). Femoral head diameter refers to
the superoinferior diameter of the femoral head. The
first metatarsal was oriented with the dorsal diaphyseal
surface horizontal for all measurements (see Fig. 1). All
measurements were taken with sliding calipers. Maximum length (MTL) was measured from the proximal
articular surface of the head, to the tip of the styloid process. The size of the proximal articular facet was measured to obtain the greatest dorsoplantar diameter (DPP)
with the arms of the calipers oriented parallel to the
diaphysis. The mediolateral diameter (MLP) of the proximal articular facet was measured from the most medial
point on the medial side to the most medial point on the
concavity of the lateral side of the articular facet. The
size of the first metatarsal head (distal articular facet)
was measured as the dorsoplantar height (DPD) and the
FIRST METATARSAL, BODY SIZE, AND STATURE
Fig. 1. Measurements taken on the first metatarsal. MTL,
metatarsal length; DPP, dorsoplantar diameter of the proximal
articulation; MLP, mediolateral diameter of the proximal articulation; DPD, dorsoplantar diameter of the distal articulation;
MLd, mediolateral diameter of the distal articulation.
mediolateral width (MLD), measured on the plantar side
of the head. All first metatarsals are right bones. For the
femur, the best preserved bone was measured. Analyses
were carried out on a combined sex sample.
Intraobserver error was evaluated by re-measuring
three individuals over a period of two weeks and calculating the percentage difference between trials for each
measurement (White and Folkens, 1999). The mean percentage error between repeats of the same measurement
was 0.96%. Interobserver error was evaluated using
measurements of three individuals taken by another
observer. The mean percentage difference between
observers was 2.69%.
All statistical analyses were carried out using SPSS
v.15. Pearson’s Product Moment Correlations were determined between all metatarsal and femoral variables.
The first metatarsal measurement with the highest
correlation with femoral head diameter was used to create a predictive equation for femoral head diameter.
Additional equations with lower correlations are also
included in the results. A second equation to infer body
mass directly from the metatarsal measurements was
derived using estimates of body mass determined from
femoral head diameter. Body mass was calculated as the
average of estimates based on three separate pooled-sex
regressions (Ruff et al., 1991; McHenry, 1992; Grine
et al., 1995) since the sample consisted of individuals of
both large and small body size. An additional regression
formula was calculated to predict femur length from the
first metatarsal measurements, which can then be used
to estimate stature. Because there are marked differences in the relationship between femur length and stature
between populations (Trotter and Gleser, 1952; Sciulli
et al., 1990; Radoinova et al., 2002; Duyar and Pelin,
2003; Ruff et al., 2005; Dayal et al., 2008) we did not develop a further equation to estimate stature directly
from metatarsal measurements.
Estimation equations were generated using ordinary
least squares regression. This is the most appropriate
627
technique in this instance as the x-variable is used to
predict values of y such that the relationship between
the variables is asymmetric (Smith, 2009). It is unlikely
that predicted values for a target sample of modern
humans will fall outside the range of variation of the reference sample since this sample encompasses both large
and small-bodied individuals (Ruff, 2007).
The standard error of estimate (SEE) is the usual
measure of the expected accuracy of a regression equation in the estimation of a particular variable for an individual from the same population group from which the
equation was originally derived. The percent standard
error of estimate (%SEE) is the standard error of estimate (SEE) divided by the mean of the dependent variable. The advantage of the %SEE over the SEE is that it
can be compared over different dimensional units, as are
used here, and it allows for comparison across studies
(Ruff, 2007).
The Spitalfields sample was used to test the regression
equations. The distributions of estimated femoral head
diameter and estimated femoral length derived from the
regression equations were compared to the actual distributions of femoral head diameter and femoral length
respectively. A Student’s t-test was used to determine
any significant differences.
RESULTS
Table 1 represents the descriptive statistics of the
femur and first metatarsal by population. As might be
expected, the data show the variability of our samples
reflecting differences in stature and overall size in these
populations. The Africans have the longest femora but
are more gracile in all other dimensions than Abingdon,
the second tallest population. The Abingdon sample
shows the highest average femoral head diameter. The
Andamanese group has the smallest measurements out
of the entire sample.
Correlations between the variables are presented in
Table 2 and indicate a significant correlation between all
femoral and first metatarsal measurements. Proximal
dorsoplantar diameter is most highly correlated with
femoral head diameter (r 5 0.911) (see Fig. 2) followed
by the measures of metatarsal head size (DPP (r 5
0.832) and MLD (r 5 0.831). Dorsoplanar diameter of
the proximal articulation is also highly correlated with
femoral length (r 5 0.786) with a correlation that is
slightly higher than that between femur length and first
metatarsal length (r 5 0.770) (see Fig. 3).
Linear regression formulae in the form of y 5 c1mc 6
standard error of estimate, for the estimation of femoral
head diameter, body size and femoral length are presented in Table 3. The most accurate regression equation
is indicated by the lowest % standard error of estimate.
The equations for both the femoral head and femoral
length using metatarsal dorsoplantar diameter have a
%SEE below 5%. Additional equations based on single
metatarsal articular dimensions have a %SEE between
6% and 7%. The equations for estimating body mass
directly from metatarsal measurements have a higher
%SEE of 7.01% using two measurements and 7.19%
using just one. The equation for estimation of femoral
length from metatarsal length only had a %SEE of
5.05%. The population-specific equation for femoral
length derived from the UK sample has a %SEE lower
than 4%.
American Journal of Physical Anthropology
628
I. DE GROOTE AND L.T. HUMPHREY
TABLE 1. Descriptive statistics for the study sample
Population
Abingdon
Mean
S.D.
African
Mean
S.D.
Andamanese
Australasian
Mean
Mean
S.D.
S.D.
Santa Cruz
Mean
S.D.
Newark Bay
Mean
S.D.
Spitalfields
Mean
S.D.
MT length
60.70 3.86 60.93 3.57 54.84 3.48 60.08 1.87 55.43 4.94 59.87 3.96 58.58 4.67
MT ML 50%
13.05 1.34 12.57 1.18
11.14 1.08 12.21 1.14
11.75 2.06 13.27 1.26
11.72 1.63
MT DP 50%
13.49 1.66 12.54 1.13 10.70 0.97 12.54 1.09
11.97 1.37 13.60 1.19 12.41 1.17
MT Prox ML diam
20.14 1.96 18.21 1.95 16.45 1.82 17.71 0.71 17.06 2.10 19.78 1.60 19.04 2.25
MT Prox DP diam
28.57 2.14 27.06 2.39 24.19 1.34 26.84 0.95 26.07 2.88 28.17 2.00 27.80 2.38
MT Dist ML diam
21.78 1.79 20.21 2.07 19.05 1.81 20.42 1.40 19.55 3.02 22.12 1.97 20.94 2.43
MT Dist DP diam
20.66 1.99 18.03 2.04 16.49 1.82 19.62 1.65 19.51 2.58 20.48 1.63 19.56 1.93
Femur length
433
24
439
23
381
20
428
37
421
32
427
29
425
35
BodyMassRuff91
67.34 6.83 58.79 5.13 49.92 5.19 60.22 5.06 59.31 8.79 64.72 6.95 62.39 7.46
BodyMassMcHenry92 63.37 7.86 53.51 5.90 43.31 5.98 55.16 5.83 54.12 10.12 60.35 8.00 57.66 8.60
BodyMassGrine95
68.11
7.97 58.12 5.98 47.79 6.06 59.80 5.90 58.74 10.25 65.05 8.11
62.32 8.71
Body Mass Average
66.27 7.55 56.81 5.67 47.01 5.75 58.39 5.60 57.39 9.72 63.37 7.69 60.79 8.26
All measurements are in mm. MT 5 1st metatarsal.
TABLE 2. Correlations for first metatarsal and femoral measurements
N 5 87
MT length (MTL)
MT ML 50%
MT DP 50%
MT Prox ML diam (MLP)
MT Prox DP diam (DPP)
MT Dist ML diam (MLD)
MT Dist DP diam (DPD)
Pearson correlation
Sig. (2-tailed)
Pearson correlation
Sig. (2-tailed)
Pearson correlation
Sig. (2-tailed)
Pearson correlation
Sig. (2-tailed)
Pearson correlation
Sig. (2-tailed)
Pearson correlation
Sig. (2-tailed)
Pearson correlation
Sig. (2-tailed)
Femur length
Femur Head diameter
0.770(**)
0.000
0.702(**)
0.000
0.708(**)
0.000
0.624(**)
0.000
0.786(**)
0.000
0.666(**)
0.000
0.688(**)
0.000
0.743(**)
0.000
0.743(**)
0.000
0.764(**)
0.000
0.801(**)
0.000
0.911(**)
0.000
0.831(**)
0.000
0.832(**)
0.000
** Correlation is significant at the 0.01 level (2-tailed).
Equations were tested on an unsexed sample of 35
individuals from Christ Church, Spitalfields (Table 4).
The Spitalfields sample is of average size (mean femoral
length 5 425 mm) but has relatively high variability
(S.D. 5 35 mm) and falls well within the size range of
the sample used to develop the regression formulae
(Table 1). Femoral head diameter was estimated using
the proximal dorsoplantar diameter, a combination of
the proximal dorsoplantar diameter and the distal
mediolateral diameter. Additional regressions for single
measurements are also reported (Table 3). The difference
between the estimated mean femoral head diameter for
the Spitalfields sample and the actual sample mean was
0.37 mm using proximal dorsoplantar diameter (equation
a) and 0.23 mm using the combination of proximal
dorsoplantar diameter and distal mediolateral diameter
(equation b) resulting in an improvement in percentage
difference from 0.84% to 0.53% (Table 4).
Body mass estimates showed a higher percentage
error than estimates of femoral head diameter (Table 4).
The difference between body mass estimations based on
metatarsal dimensions and those calculated from the
femoral head measurements was less than 1 kg for both
regressions. The mean % difference was 1.33% for proximal dorsoplantar diameter only, and 0.75% for proximal
dorsoplantar diameter and distal mediolateral diameter.
Femur length was estimated using the equations
based on all individuals in the sample and using the
equations based on the British samples from Newark
American Journal of Physical Anthropology
Bay and Abingdon only. The difference between the
estimated mean femoral length for the Spitalfields
sample and the actual sample mean was 1.4 mm using
the equation derived from all individuals and 2.37 mm
using the equation derived from other British samples
(Table 4). Neither estimate was improved by the addition
of the metatarsal length to the proximal dorsoplantar
diameter measurement. Estimation error was less than
0.6% for all estimates and there were no significant
differences between estimated sample and actual sample
means (paired t-test: all comparisons P [ 0.369).
DISCUSSION
Overall, the results for the use of the first metatarsal as
an estimate of body mass are particularly encouraging.
The high correlation between the diameters of the femoral
head and measurements of the proximal articulation of
the first metatarsal reflects the weight bearing properties
of these skeletal elements and is consistent with the expectation that weight bearing articular surfaces should
have a functional association with body mass (Jungers,
1988; Ruff et al., 1991; Lieberman et al., 2001; Auerbach
and Ruff, 2004). Epiphyseal union of the proximal articulations of the femur and first metatarsal takes place at a
similar stage of development suggesting similar developmental constraints relating to the attainment of adult size
and function in these skeletal elements (Scheuer and
Black, 2004). Equations for the estimation of femoral head
FIRST METATARSAL, BODY SIZE, AND STATURE
Fig. 2. Correlation between femoral head diameter and the
dorsoplantar diameter of the first metatarsal.
Fig. 3. Correlation between femur length and first metatarsal length.
diameter based on the proximal dorsoplantar diameter or
a combination of the proximal dorsoplantar diameter and
the distal mediolateral diameter had a low percentage
error of estimate. This result indicates that measurements
of the proximal end of the first metatarsal can be used either independently as a measure of body mass, or to estimate femoral head diameter when the femoral head is
absent or poorly preserved. Other single measurements on
the epiphyses of the first metatarsal were able to estimate
femoral head diameter with some accuracy and could be
used to estimate femoral head diameter and hence body
mass from partially preserved first metatarsals.
629
The predictive value of the regression equation for
proximal dorsoplantar diameter was tested on a population from Spitalfields that had not been included in the
series used to develop the predictive equation. The percentage difference between the actual and predicted
mean value for femoral head diameter was very low
indicating that the regression equation is well suited to
individuals of varied but average size. There was no
obvious bias in the patterning of residuals indicating
that the equation predicts femoral head diameter equally
well for small and large individuals within the size
range of the Spitalfields series. A further regression
equation to predict body mass directly from the proximal
dorsoplantar diameter of the first metatarsal was
derived based on mean estimated body mass estimates
from three published equations using femoral head
diameter (McHenry, 1991; Ruff et al., 1991; Grine et al.,
1995). The regression formula for body mass should be
used with a degree of caution as it has a relatively high
estimation error due to the cumulative error results
from the multiple steps needed to predict body mass.
The exact body mass estimation errors are not calculated
here because the equation is the average of the three
published equations that are based on different samples
and methods (Ruff, 2010). It is therefore recommended
that, when the actual body mass of the individual is not
a priority, dorsoplantar diameter of the proximal articulation is used as a proxy for body mass in analyses of
the relationship between body mass and other factors.
As part of this study the use of the first metatarsal in
the estimation of stature was also assessed. Previous
work on stature estimation using intact long bones or
other complete or partial skeletal elements has shown
that the relationship between skeletal measurements
and stature varies between populations and between
males and females (Trotter and Gleser, 1952; Sciulli
et al., 1990; Ruff, 1991; Holliday and Ruff, 1997; Radoinova et al., 2002; Ruff et al., 2005; Dayal et al., 2008;
Raxter et al., 2008; Auerbach and Ruff, 2010). Where
available, an appropriate population and sex-specific
formula for the estimation of stature from a skeletal
dimension should always be used. For this reason, we
only present regression formulae for the estimation of
femoral length.
Previous research has reported a high correlation
between metatarsal length and stature within specific
population groups (Byers et al., 1989; Meadows and
Jantz, 1992; Bidmos, 2008; Cordeiro et al., 2009).
Contrary to expectations femur length was more highly
correlated with the proximal dorsoplantar diameter of
the first metatarsal (r2 5 0.617) than with metatarsal
length (r2 5 0.592). The combination of these two measurements gives the most accurate regression formula
(r2 5 0.669). The %SEE is less than 5.05% for all regressions. All three regressions equations were demonstrated
to yield very low estimation error for mean femoral
length in our test population (less than 1.8%). The accuracy of the estimations was improved (estimation error
less than 0.5%) using regressions based on a UK sample
only, suggesting that population-specific regressions are
most suitable for the estimation of femur length from
metatarsal dimensions.
The distribution of residuals revealed that femur
length was overestimated for shorter individuals and
underestimated for taller individuals from Spitalfields
regardless of which predictive equations was used. This
effect has been previously reported in other stature estiAmerican Journal of Physical Anthropology
630
I. DE GROOTE AND L.T. HUMPHREY
TABLE 3. Regressions for femoral head diameter, body size, and femur length
Femoral head diameter
a) 1.652 3 Prox DP diameter 2 1.981
b) (1.349 3 Prox DP diameter) 1 (0.424 3 Dist ML Diameter) 2 2.578
c) 1.589 3 Prox ML diameter 1 13.117
d) 1.559 3 Dist DP diameter 1 12.812
e) 1.795 3 Dist ML diameter 1 5.411
Body mass
a) 3.553 3 Prox DP diameter 2 37.167
b) (2.900 3 Prox DP dameter) 1 (0.911 3 Dist ML Diameter) 2 38.450
Femoral Length all individuals
a) 9.870 3 Prox DP diameter 1 151.759
b) (5.926 3 Prox DP diameter) 1 (2.861 3 Length) 1 90.024
c) 5.683 3 MT length 1 84.298
Femoral Length UK only
a) 8.642 3 Prox DP diameter 1 184.486
b) (6.089 3 Prox DP diameter) 1 (1.956 3 Length) 1 139.046
c) 4.356 3 MT length 1 167.807
SEE
r
r2
P
%SEE*
1.955
1.912
2.867
2.660
2.667
0.917
0.922
0.801
0.832
0.831
0.841
0.850
0.637
0.692
0.686
0.000
0.000
0.000
0.000
0.000
4.60%
4.50%
6.70%
6.22%
6.23%
4.251
4.144
0.911
0.917
0.830
0.840
0.000
0.000
7.19%
7.01%
20.520
19.201
21.176
0.786
0.818
0.770
0.617
0.669
0.592
0.000
0.000
0.000
4.90%
4.58%
5.05%
17.012
16.304
18.621
0.745
0.775
0.683
0.555
0.601
0.467
0.000
0.000
0.000
3.94%
3.78%
4.32%
* SEE/mean
TABLE 4. Estimations for the test sample from Spitalfields
Directional
difference*
Actual mean Estimated mean Raw (mm)
Femoral head diameter
Reg. a)
43.57
43.94
Reg. b)
43.57
43.80
Reg. c)
43.57
43.37
Reg. d)
43.57
43.31
Reg. e)
43.57
43.01
Body mass (kg)
Reg. a)
60.79
61.60
Reg. b)
60.79
61.24
Femoral Length all individuals
Reg. a)
424.72
426.12
Reg. b)
424.72
422.35
Reg. c)
424.72
417.21
Femoral Length Europeans only
Reg. a)
424.72
424.71
Reg. b)
424.72
422.89
Reg. c)
424.72
422.98
%
0.37
0.23
20.20
20.26
20.56
0.84%
0.53%
20.46%
20.60%
21.29%
0.81
0.45
1.33%
0.75%
1.40
22.37
27.51
0.33%
20.56%
21.77%
20.01
21.83
21.74
0.00%
20.43%
20.41%
* None are significant (t-test).
mation studies and interpreted as an artifact of the
regression analysis (Trotter and Gleser, 1952; Sjøvold,
1990; Formicola and Franceschi, 1996; Duyar and Pelin,
2003). Applying a Reduced Major Axis regression instead
did not alter the bias in the estimation, indicating that it
is not an artifact of the regression equation. The bias
reflects a difference in the relationship between metatarsal dimensions and femur length between the Spitalfields sample and both the original series and other UK
populations. A regression line fitted to the Spitalfields
series has a shallower slope and lower intercept at y 5 0
than regression lines for either reference sample (see
Fig. 4). Since the regression line for Spitalfields intersects regression lines for the original and UK series
differences in estimated femur length for individuals in
the middle range are small, whereas those at the
extremes of the range are under- or overestimated.
Further research is required to understand the nature of
variation in the relationship between femoral length and
metatarsal dimensions among geographically diverse
populations and between urban and rural populations
from a restricted geographical region.
American Journal of Physical Anthropology
Fig. 4. Correlation between femur length and the dorsoplantar diameter of the first metatarsal. Crosses and the solid line
represent the regression sample (b 5 9.870; intercept 5
151.759; r2 5 0.617); circles and the dashed line are the Spitalfields test sample (b 5 10.039; intercept 5 145.659; r2 5 0.453).
CONCLUSION
This study is a preliminary evaluation of the use of
the first metatarsal as a proxy for body mass and stature
in fragmentary and poorly preserved archaeological
assemblages. The results presented demonstrate that
epiphyseal dimensions of the first metatarsal are highly
correlated with femoral head diameter and hence body
mass. The correlations vary across the different measurements but all single articular dimensions can be used
in the estimation of femoral head diameter. This is
consistent with the expectation that weight bearing
articular surfaces should have a functional association
with body mass. First, the first metatarsal dimensions
can be used independently as a measure of body mass in
studies where it is necessary to correct for body mass or
where the remains are comingled and the researcher
wants to assess the range of body sizes represented in
the sample. Second, the first metatarsal dimensions can
be used to estimate femoral head diameter to allow comparisons across a range of samples where the femoral
FIRST METATARSAL, BODY SIZE, AND STATURE
head is missing for some individuals but where associated partial or complete metatarsals are present. Third,
the regression equations for femoral head diameter presented here allow body mass (weight) to be estimated in
a two stage process by estimating femoral head diameter
from measurements of the first metatarsal and using
published equations for the estimation of body mass
from femoral head diameter. In this situation it is important to keep in mind the cumulative error of this
estimate when making comparisons across populations.
Correlations between metatarsal size and femur
length were lower than their equivalents for femoral
head diameter for all metatarsal measurements apart
from length. Previous studies have demonstrated the
usefulness of metatarsal length for stature estimation
but the results of this study indicate that proximal
dorsoplantar diameter may ultimately be a better predictor of femoral length, and potentially living stature.
Although this study has not tested the regression on
actual living stature, the femoral length estimates produced by the equations presented in this paper can be
used in published population-specific regressions to
estimate living stature, but again, bearing in mind the
accumulative error in the use of multiple estimations
and the need for population-specific regressions.
The regression equations presented here are particularly suited for archaeological and fossil assemblages
where the long bones are either missing or too fragmentary to use for the estimation of body mass or stature.
They enable femoral length and body mass to be estimated from both complete and incomplete first metatarsals. The encouraging results of the analyses presented
above warrant further investigation and the refinement
of these regression equations on a sample of known body
mass and stature. Such a study would circumvent the
problem of cumulative error and allow for a comparison
of estimation error with other skeletal elements.
ACKNOWLEDGMENTS
The authors thank Robert Kruszynski at the Natural
History Museum London for collections advice and
Laura Buck for help with collecting data and carrying
out the interobserver error tests.
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