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: email@example.com 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. LITERATURE CITED Andrews P. 1990. 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