AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 158:312–324 (2015)
Population-Specific Stature Estimation From Long Bones in the Early Medieval Pohansko (Czech Republic) dek,1* Jirı Macha cˇek,2 Christopher B. Ruff,3 Eliska Schuplerova ,1 Vladimır Sla ta Prichystalova ,2 and Martin Hora1 Rena 1
Department of Anthropology and Human Genetics, Faculty of Science, Charles University in Prague, Czech Republic 2 Department of Archaeology and Museology, Masaryk University, Czech Republic 3 The Center for Functional Anatomy and Evolution, Johns Hopkins University, Baltimore, USA KEY WORDS
body size; body shape; bioarchaeology; regression stature
ABSTRACT OBJECTIVES: We tested the effect of population-specific linear body proportions on stature estimation. MATERIALS AND METHODS: We used a skeletal sample of 31 males and 20 females from the Early Medieval site at Pohansko (Breclav, Central Europe) and a comparative Central European Early Medieval sample of 45 males and 28 females. We developed new populationspecific equations for the Pohansko sample using anatomical reconstructions of stature, then compared percentage prediction errors (%PEs) of anatomical stature from limb bone lengths using the derived Pohansko equations with those previously derived from more general European and other Early Medieval samples. RESULTS: Among general European equations, the lowest %PEs for the Pohansko sample were obtained using the equations of Formicola and Franceschi: Am J Phys Anthropol 100 (1996) 83–88 and Ruff et al.: Am J Phys Anthropol 148 (2012) 601–617. However, unexpectedly, the choice between tibial latitudinal variants proposed
by Ruff et al.: Am J Phys Anthropol 148 (2012) 601–617 appeared to be sex-specific, with northern and southern variants producing lower %PEs for males and females, respectively. Equations from Breitinger: Anthropol Anz 14 (1937) 249–274, Bach: Anthropol Anz 29 (1965) 12– 21, and Sjøvold: Hum Evol 5 (1990) 431–447 provided poor agreement with anatomical stature. When applied to the comparative Central European Early Medieval sample, our new formulae have generally lower %PE than previously derived formulae based on other European Early Medieval samples (Maijanen and Niskanen: Int J Osteoarchaeol 20 (2010) 472–480; Vercellotti et al.: Am J Phys Anthropol 140 (2009) 135–142. CONCLUSIONS: The best agreement with anatomical stature among our newly developed equations was obtained using femoral1tibial length, followed by femoral length. Upper limb bone lengths resulted in higher %PEs. Variation in the tibia is likely to contribute most to potential bias in stature estimation. Am J Phys Anthropol 158:312–324, 2015. VC 2015 Wiley Periodicals, Inc.
Because human stature is one of the key pieces of evidence used in bioarchaeological, forensic, and evolutionary research, any increase in the accuracy of living stature estimations can bring important improvements for further analyses of past human biology (see review in Ruff et al., 2012). Two alternative approaches exist for estimation of living stature from skeletons: anatomical and mathematical (Lundy, 1985). The anatomical approach was developed by Fully (1956), who summed heights and lengths of skeletal elements directly contributing to stature. It has been shown that anatomically derived stature estimates strongly correlate with living stature (r 5 0.98–0.99) and have high accuracy with average error < 1 cm (Maijanen, 2009). Anatomically reconstructed stature is not sensitive to individual and population-based differences in body proportions, and the anatomical approach also provides the best estimate of living stature for individuals from unknown populations and individuals with atypical body proportions (e.g., Olivier, 1969; Stewart and Kerley, 1979; Lundy, 1985; Ousley, 1995; Raxter et al., 2008; Maijanen, 2009). Fully’s (1956) anatomical approach has been modified by several authors (e.g., Fully and Pineau, 1960; Formicola, 1993; Niskanen and Junno, 2004; Raxter et al., 2006), and the modification by Raxter et al. (2006) provides the most accurate estimate with average error < 0.1% (Maijanen, 2009). Raxter et al. (2006) also reported
results for both sexes and provided a new definition of osteometric measurements (but see also Maijanen, 2009), continuous correction of soft tissue (see also Bidmos, 2006; Maijanen, 2009), and new analyses of stature decrease with age (see also review in Trotter and Gleser, 1951; Raxter et al., 2007; Raxter et al., 2008; Raxter and Ruff, 2010). Limits to the anatomical approach have been found mainly in skeletal preservation (see data and review in Auerbach, 2011) and effect of age on final stature estimate (see bibliography and review in Raxter et al., 2007). The mathematical approach is based on either regression of bone lengths against stature or the use of ratios (see review in Lundy, 1985; Feldesman and Fountain, 1996). The application of the regression approach to
Ó 2015 WILEY PERIODICALS, INC.
Grant sponsor: Czech Science Foundation; Grant number: GACR 14-22823S. *Correspondence to: V. Sl adek. E-mail: [email protected] Received 13 February 2015; revised 19 May 2015; accepted 26 May 2015 DOI: 10.1002/ajpa.22787 Published online 29 June 2015 in Wiley Online Library (wileyonlinelibrary.com).
STATURE ESTIMATION IN EARLY MEDIEVAL SKELETAL SAMPLE stature estimation is simple and is only partly limited by bone preservation. Several regression equations broadly applied also to European skeletal samples have been derived from specific population samples (e.g., Breitinger, 1937; Trotter and Gleser, 1952; Bach, 1965; Trotter, 1970; Formicola and Franceschi, 1996; Raxter et al., 2008; Vercellotti et al., 2009; Auerbach and Ruff, 2010) and from broader sampling (e.g., Sjøvold, 2000; Ruff et al., 2012). It frequently has been reported that the mathematical approach can produce substantial bias in several respects (e.g., Pearson, 1899; Stevenson, 1929; Dupertuis and Hadden, 1951; Trotter and Gleser, 1952; Lundy, 1985; Formicola, 1993; Ruff et al., 2012). First, error may be introduced through the statistical approach applied, and it has been shown that in many situations reduced major axis (RMA) regression should be favored over least squares regression (Sjøvold, 1990; Aiello, 1992; Formicola, 1993; Formicola and Franceschi, 1996; Konigsberg et al., 1998; Maijanen and Niskanen, 2010; Ruff et al., 2012). Second, the highest correlation and accuracy in stature estimate is provided by lengths of long bones directly involved in stature, such as femora and tibiae (e.g., Formicola and Franceschi, 1996; Ruff et al., 2012). The final source of error in stature estimation is variation in the proportion between bone lengths and stature with respect to eco-geographic variation and growth plasticity (e.g., Formicola, 1993; Molnar, 1998; Stinson et al., 2000; Bogin and Varela-Silva, 2010; Ruff et al., 2012) as well as a population structure (Roseman and Auerbach, 2015). It has been also shown that secular change can influence proportional differences between proximal and distal limb segments (Meadows and Jantz, 1995; Jantz and Jantz, 1999 see also references below). These observations have brought into question the use of single equations or ratios for stature estimation and imply that even lower limb bones can produce various biases in final stature estimates if they are applied to an population having different body proportions. Applying population-specific equations to individuals with similar proportions are therefore expected to provide greater accuracy in stature estimation than use of generic equations (Holliday and Ruff, 1997). The effect of variation in body proportions between samples on mathematically estimated stature can be reduced using a hybrid approach wherein living stature is estimated for the studied sample using either the anatomical technique or other direct methods (e.g., cadaver length) and then, in a second step, using estimated living stature to create population-specific equations for particular long bones (e.g., Formicola and Franceschi, 1996; Raxter et al., 2008; Vercellotti et al., 2009; Auerbach and Ruff, 2010; Maijanen and Niskanen, 2010; Ruff et al., 2012). It has been demonstrated that if anatomically derived stature is used, then the hybrid approach can produce very low mean percent prediction errors (%PEs) of stature (see for example results using equations of Formicola and Franceschi (1996) and Ruff et al. (2012) in Table 4 of Ruff et al., 2012). As indicated from comparative studies (e.g., Auerbach and Ruff, 2010; Ruff et al., 2012), however, the hybrid approach using anatomically estimated stature is not without potential problems. First, the majority of hybrid equations are derived from samples of limited size and limited archaeological periods (Formicola and Franceschi, 1996; Raxter et al., 2008; Vercellotti et al., 2009; Maijanen and Niskanen, 2010) and therefore their applicability for other bioarchaeological settings and even on other indi-
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viduals from the same population may be questionable. Second, regression formulae generated using the hybrid approach assume homogeneous variation in body proportion within a studied population, which probably does not occur if only due to the effects of population structure, migration, and growth plasticity (although this is an issue with all mathematical approaches). The hybrid approach has been improved by accounting for proportional differences due to eco-geographic variation between the studied individuals and reference samples. It has been shown that either specific northern and southern latitudinal equation variants (Ruff et al., 2012) or guidelines using the crural index for selecting the appropriate equation (Auerbach and Ruff, 2010) can help reduce the effect of ecogeographically introduced variation in body proportions on stature estimation. This is true, however, only in the case that body proportions are seen as the result of long-term adaptation and where migration plays a minor role. As emphasized above, the mathematical technique for stature estimation is sensitive to linear proportions such as limb length to trunk length and proximal/distal limb lengths. In general, stature and body proportions during human evolution have been determined by bipedal striding gait, long distance running, manipulation, and behavioral factors; however, among modern humans the most important factors are associated with ecogeographic variability in thermoregulation and with the effect of developmental plasticity in early postnatal life (Trinkaus, 1981; Tanner et al., 1982; Trinkaus, 1986; Eveleth and Tanner, 1990; Frisancho, 1993; Ruff, 1994; Holliday and Falsetti, 1995; Feldesman and Fountain, 1996; Holliday, 1997, 1999; Molnar, 1998; Stinson et al., 2000; Ruff, 2002; Bogin and Rios, 2003; Bogin and Varela-Silva, 2010; Hora and Sl adek, 2011). Ecogeographic variability of body proportions in relation to thermoregulation in humans generally follows Allen’s and Bergmann’s ecological rules (Bergmann, 1847; Allen, 1877; Roberts, 1953; Ruff, 1994; Katzmarzyk and Leonard, 1998). It has been shown that in colder climates humans exhibit a wider pelvis relative to stature (Ruff, 1994), shorter limbs relative to stature (Molnar, 1998), and low crural and brachial indices (e.g., Trinkaus, 1981; Holliday, 1999). Ecogeographic adjustment to climate has been shown to be a relatively long-term adaptation that is not on the scale of closely succeeding generations (Holliday, 1997, 1999). Thus, we can suggest that local adaptation to climate per se has a relatively low impact on differences in body proportions and stature among subgroups of individuals excavated from a single cemetery. However, ecogeographic factors may come into play with recent migrations of a group or subgroups of a population including gender-specific migrations for example in relation to patrilocal residence. In this case, the archaeological background can help to determine which eco-geographic equation provides the best estimates in a particular archaeological sample. It has also been shown that stature and body proportions are developmentally plastic and sensitive to factors influencing individual growth (Bogin, 1999). Stature can change significantly among successive generations and both negative and positive secular trends have been observed in several different geographic and socioeconomic contexts (e.g., Boas, 1930; Bogin and Rios, 2003; Cole, 2003). A secular trend has been observed especially in accelerating growth of lower limb length in comparison to trunk height during the first 2 years of postnatal American Journal of Physical Anthropology
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development (Tanner et al., 1982; Cole, 2000). For example, Bogin and Rios (2003) showed that in Maya children the increase in total stature during 20 years was about 10 cm, with an increase of lower limb length in the same period of about 7 cm. The acceleration of body segment growth follows a general craniocaudal growth pattern (Schultz, 1926; Scammon and Calkins, 1929) wherein prenatal acceleration is observed in cranial parts of the body (i.e., head size) whereas postnatal acceleration is observed in caudal and distal segments (such as the lower limb and in particular the tibia; Jantz and Jantz, 1999). Postnatal growth has been shown also to be more environmentally plastic than prenatal growth (Bogin, 2010; Ulijaszek, 2010), and therefore lower limb and distal limb segments in proportion to stature are more sensitive to variation in subsistence and living conditions than are trunk and proximal limb segments (Wadsworth et al., 2002; Li et al., 2007). Finally, it also has been observed that tibiae in proportion to stature show higher positive allometry than do femora (Meadows and Jantz, 1995). Thus, craniocaudal-induced secular changes have a stronger effect on tibiae than they do on femora. Probably because of these factors, tibiae are more variable in proportion to stature than femora (also see Holliday and Ruff, 1997); we can therefore expect that femora may provide better estimates of stature than do tibiae, when applying equations developed from one reference group to another target sample. Secular trends in stature variation have also been shown to be responsive to such general factors as socioeconomic status (SES) (Bogin, 1999; Stinson et al., 2000). It has been demonstrated, too, that SES has an impact on proportional differences mainly in the proportion between tibia and stature (Jankauskas and Kozlovskaya, 1999; Vercellotti et al., 2011). The effect of SES on secular trends and body proportions is important especially for Holocene applications inasmuch as during the Holocene human populations are undergoing substantial social and gender stratification (Johnson, 2000). Therefore, we can suggest that a single cemetery represents individuals from different local living conditions as well as from different local subsistence and nutritional histories and for whom it is difficult to apply a single common equation to estimate stature. Again, this raises the question to what extent factors operating at the scale of succeeding generations might affect accuracy in stature estimation using the mathematical approach. The goal of this study is to test differences in agreement between population-specific equations and available techniques for stature estimation frequently used in Central European bioarchaeological research (Breitinger, 1937; Bach, 1965; Sjøvold, 1990; Formicola and Franceschi, 1996) with special focus on the new and ostensibly broadly applicable technique provided by Ruff et al. (2012). The test sample is selected from the Early Medieval second church cemetery at Pohansko (Breclav, Czech Republic). Another goal of the study is to investigate the impact of body proportions on the accuracy of stature estimates, including consideration of possible ecogeographic and other environmental effects.
MATERIALS AND METHODS Skeletal sample The overall sample of 44 individuals (25 males, 19 females) with sufficiently preserved skeletal elements to calculate anatomical stature (Raxter et al., 2006; Ruff American Journal of Physical Anthropology
et al., 2012) was selected from the Early Medieval site at Pohansko (second church, NE suburb; Breclav, Czech Republic; Mach acˇek et al., 2014). The sample consists of 77% of all adult skeletons excavated in the Pohansko second church. The comparative sample used for more broadly testing Pohansko-derived stature estimation equations consists of 73 individuals (45 males, 28 females) from the NorthCentral European Early Medieval sites of Brucknendorf (Austria, AD 600–800), Dresden Briesnitz (Germany, AD 900–1200), Mikulcˇice (Czech Republic, AD 800–900), M€odling (Austria, AD 630–820), and Zwentendorf (Austria, AD 1000–1100). Complete skeletal height is preserved for 44 individuals (28 males, 16 females) and those individuals are also part of the European sample used in Ruff et al. (2012) stature estimation technique. Basion-bregma height is not preserved for 29 individuals (17 males, 12 females) and for these skeletal height was estimated from partial skeletal height, not including the cranium, using an equation derived from 537 individuals in the Ruff et al. (2012) European sample (r 5 0.996, SEE 5 0.707; Niskanen and Ruff, pers. comm.). Computation details about missing skeletal elements and the technique used for computation of living stature are provided in Ruff et al (2012).
Archaeological background Pohansko (48.7289908N, 16.8966217E, Czech Republic) was one of the key Early Medieval centers in South Moravia during the time of the Great Moravian Empire and represented a strategic point between southern and northern territories for long-distance trading (Mach acˇek, 2007). Systematic archaeological research at Pohansko began in 1958 with discovery of the first church (9th century) and later continued with excavation of complex settlement features on 60 ha with a large central occupation area and two suburbs (SW and NE) (Mach acˇek, 2010, 2011). In 2006, a team headed by J. Mach acˇek discovered in Pohansko’s NE suburb a concentration of construction traces and a cemetery later identified by systematic archaeological excavation as the remains of a second Early Medieval church within the Pohansko settlement ap et al., 2011; Mach (C acˇek et al., 2014). The second church and surrounding cemetery are dated by archeological finds from graves (including specific artifacts such as an Old Hungarian battle axe, heavily gilded buttons with palmettes, silver earrings, temple rings, and lead pedants) and by analogy to other South Moravian Early Medieval sites to between the end of the 9th and beginning of the 10th century. This was likely in the late Great Moravian period. The excavated structure of the second church is relatively small compared with that of the first church and is characterized by less sophisticated building techniques. The cemetery related to the second church yielded 154 skeletons with a majority of nonadult individuals (38% adult and 62% nonadult). Compared with the first church cemetery, the new second church cemetery is smaller with relatively fewer archaeological remains characteristic of higher SES and nobility. This probably indicates that the second building and cemetery were used for a smaller and more closely related group belonging to the founder and owner of the second church (i.e., an Early Medieval familia) with a span of not more than three generations (Mach acˇek et al., 2014).
STATURE ESTIMATION IN EARLY MEDIEVAL SKELETAL SAMPLE
Paleodemographic data All individuals included in the analysis are adults with fused long bone epiphyses (20 years of age or older). To derive age estimates for applying the anatomical stature estimation formula with an age term [Eq. (1) in (Raxter et al., 2006)], we used pubic symphyseal morphology (Brooks and Suchey, 1990). For three individuals, age was estimated by senescence features on the auricular surface (Buckberry and Chamberlain, 2002). We observed high variation (even a decade and more) between different age techniques (Lovejoy, 1985; Schmitt, 2001, 2002; Boldsen et al., 2002). We chose the pubic symphysis technique, as these estimates provided the most reasonable demographic profile for the second church cemetery. As indicated by other studies, even broad age categories improve living stature estimates using the anatomical approach (Raxter et al., 2007). Sex assessment was based primarily on pelvic sexually dimorphic features (Bruzek, 2002) and two pelvic discriminant functions (Novotn y, 1975; Br˚uzek, 1984). There was agreement in sex allocation between morphology and discriminant function analysis for all studied individuals. Skeletal pathology was assessed on all skeletal elements included in anatomically reconstructed stature and individuals with gross pathology were excluded.
Osteometric data
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details about accuracy in Raxter et al., 2007; Maijanen, 2009). Completely preserved skeletal height was available for 27 individuals (61%), whereas some dimensions were reconstructed for 17 (39%) individuals. Following the recommendation of Auerbach (2011), we did not estimate basion–bregma height, femoral lengths, and tibial length from other dimensions. Nevertheless, for six individuals basion–bregma height was estimated from partially damaged crania with sufficient accuracy. Final presacral height was estimated for 10 individuals (23%) in cases where either an entire vertebral region or more than one individual vertebral height within a section was missing (six presacral heights were estimated using regression formulae based on the lumbar region, and four presacral heights were estimated using regression formulae based on the thoracic and lumbar regions). The technique for adjacent vertebra estimation used either averaging of adjacent vertebrae or relative height for adjacent vertebra as presented in Auerbach (2011) and the regional regression formulae used were from Auerbach (2011). Talocrural height (TC) was estimated for three individuals (7%) using sex-specific equations developed from the Pohansko sample (male SEE: 3.41 mm; female SEE: 1.42 mm). Pohansko-specific equations were generated using RMA regression with anatomical stature and long bone length. Pohansko RMA regression equations were computed for upper limbs using Hu1 and Ra1 and lower limbs using Fe1, Ti1a, and Fe11Ti1a (see details for abbreviations in Table 1). Both sex-specific and pooledsex equations were generated. Anatomical stature obtained for the Pohansko sample was compared with stature estimated by previously suggested equations. For stature estimation, we used general equations provided by Table 3 in Ruff et al. (2012; sex-specific and pooled-sex equations for Hu1, Ra1, Fe1, Ti1a, Fe1 1 Ti1a), Table 3 in Formicola and Franceschi (1996) (sex-specific equations for Hu1, Ra1, Fe1, Ti1, Fe2 1 Ti1), Table 1 in Sjøvold (1990) for “Caucasians” (pooled-sex equations for Hu1, Ra1, Fe1, Fe2, Ti1), page 17 of Bach (1965; equations available only for females using Hu1 and Fe1; we compared using the equation without the additive term), and page 266 of Breitinger (1937; equation available only for males using Fe1; we compared using the equation without the additive term).
Descriptive statistics for osteometric data in the Pohansko sample and measurement abbreviations are shown in Table 1, along with anatomically estimated statures. Lengths of long bones were measured using Martin’s technique (Br€ auer, 1988) by osteometric board to the nearest millimeter. For all lengths, both sides were taken and the average was used for stature regression estimate (see discussion about accuracy between right and left side for upper limb long bones in Ruff et al., 2012: p. 604). As bilateral asymmetry is somewhat larger for upper limb lengths, however, Table 1 also includes descriptive sample statistics for right and left upper limb long bones and only side-average descriptive statistics for lower limb bones. Biiliac breadth was measured using the maximum distance between right and left iliac crests on rearticulated coxae and sacrum. Most of the sample preserves intact coxae and sacrum, and it was therefore possible to measure biiliac breadths with high accuracy. Other osteometric dimensions used in anatomically reconstructing stature (i.e., basion–bregma height, vertebral body heights, and talocrural height) followed techniques revised by Raxter et al. (2006) (see details about definition of measurements in Raxter et al., 2006: Appendix, p. 382).
Body proportions were assessed by analysis of living biiliac breadth against stature, crural index, and Fe1, Ti1a, and Fe1 1 Ti1a lengths against stature. Living biiliac breadth was converted from skeletal biiliac breadth using Eq. (5) from Ruff et al. (1997) and crural index was computed using Fe2 and Ti1a.
Stature estimation
Statistical procedures
Anatomical stature was calculated from skeletal height using a modification of Fully’s technique for anatomical stature estimation by Raxter et al. (2006). Skeletal heights were obtained by the sum of basion–bregma height, C2 –S1 vertebral body heights, lengths of femur and tibia, and height of articulated talus/calcaneus. Conversion to living stature was obtained by Eq. 1 in Raxter et al. (2006) with soft tissue correction and age term included into the final living stature estimate (see
Reduced major axis regression analysis was employed to generate Pohansko-specific equations and to compare previous equations and Pohansko anatomical stature using RMA software v. 1.14 (Bohonak, 2002). Lengths were in millimeters and stature in centimeters. Estimation error for Pohansko equations is expressed as SEE, percentage standard error of estimate (%SEE), and percentage prediction error (%PE) using the formulae:
Body proportion estimates
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TABLE 1. Descriptive statistics for Pohansko sample Males
Females
Dimensionsa
n
Mean
SD
Range
n
Mean
SD
Range
Humeral max. length (Hu1) Humeral max. length right (Hu1) Humeral max. length left (Hu1) Radial max. length right (Ra1) Radial max. length right (Hu1) Radial max. length left (Hu1) Femoral max. length (Fe1) Femoral bicond. length (Fe2) Tibial lateral total length (Ti1) Tibial maximum length (Ti1a) Fe1 1 Ti1a length Fe2 1 Ti1 length Anatomical stature Living biiliac breadth
25 23 24 22 22 20 25 25 25 25 25 25 25 24
331.2 333.3 328.8 251.4 252.6 250.1 458.5 454.4 373.7 381.7 840.2 828.1 168.9 29.4
14.95 15.76 14.81 9.88 10.25 10.21 25.58 26.05 17.00 17.32 41.72 41.71 6.86 1.77
305.0–373.0 308.0–377.0 302.0–370.0 229.0–271.5 228.0–271.0 230.0–272.0 412.5–541.0 402.0–536.5 336.0–408.0 344.5–417.5 757.0–958.5 742.0–944.0 152.0–185.2 26.5–34.9
16 14 16 17 17 13 19 19 19 19 19 19 19 17
299.6 301.1 298.8 225.6 226.0 224.5 414.9 410.4 337.5 344.2 759.2 747.9 155.5 28.4
13.12 12.98 13.54 11.49 11.98 10.24 21.49 21.08 15.33 15.89 36.63 35.63 5.78 1.63
283.0–324.0 284.0–326.0 281.0–322.0 210.5–247.5 211.0–250.0 210.0–245.0 374.0–452.5 371.0–445.5 305.5–363.5 313.5–371.0 687.5–823.5 676.5–809.0 144.8–165.8 25.1–31.2
a
All dimensions are given in millimeters except biiliac breadths and statures, which are in centimeters. Living biiliac breadth is computed using skeletal biiliac breadth and Eq. (5) of Ruff et al. (1997). Further description is provided in the Materials and Methods.
P 1. SEE ¼ ðð ð½true-predictedÙ 2ÞÞ=nÞÙ 0:5 2. %SEE ¼ ðSEE=y Þ 3 100 3. %PE ¼ ½ðtrue – predictedÞ=predicted 3 100, where y is mean y, “true” is anatomical stature, and “predicted” is stature estimated by the given regression equation. Standard error of estimate and %SEE are measures for random errors, whereas %PE is for directional bias. Measures of differences between regression techniques and anatomical stature are expressed as %PEs. All indices were tested using the nonparametric Mann–Whitney U-test. Statistical analysis was carried out using STATISTICA 12 for Windows (StatSoft, 2013) and Excel 2010 (Microsoft).
RESULTS Stature estimation for Pohansko sample Table 2 presents stature estimation equations for the Pohansko sample. As expected, upper limb bone equations show greater SEEs than do lower limb bone equations. Upper limb bone stature equations show also greater dispersion (SD) of individual %PEs than do lower limb bone equations (also see Figs. 1 and 2). Humeral equations provide somewhat smaller SEEs and dispersion of %PEs than do radial equations. Femoral 1 tibial stature estimation equations produce the smallest SEEs in this study sample and slightly smaller dispersion of individual %PEs of stature. Tibial equations provide higher SEEs than do other lower limb bone equations but remain below the range of SEEs derived from the upper limb bones. Sex-specific equations for the Pohansko sample do not substantially reduce SEEs and dispersion of %PEs, with the single exception of a slight increase in SEEs in humeral and femoral sex-specific equations for females.
General stature equations Boxplots of %PEs of stature predicted from upper limb bones using equations from the present study and from four previous “generic” European studies are shown in Figure 1. Only sex-average results (i.e., obtained as the average of male and female values) are shown. On average, the most accurate estimates provided by generic American Journal of Physical Anthropology
equations are given by Ruff’s et al. (2012) humeral equations, with average %PEs (0.2%) almost equal to errors estimated from the present study equations. The upper limb bone equations of Formicola and Franceschi (1996) and Sjøvold (1990) overestimate or underestimate anatomically derived stature on average in the range of 21.8–0.8%. The least accurate estimate on average is provided by the equation from Bach (1965; 23.85%; only the humeral equation for females is available for this technique). The 62SD range of %PEs is consistent among all compared generic methods. The 62SD range is slightly smaller in humeral %PEs of stature than it is in radial. Figure 2 provides boxplots of %PEs of stature predicted from femoral lengths using equations from the present study and five previous studies. Sex-average results and results by sex are shown. The most accurate stature estimates are given by methods using anatomically derived stature: for males by the method of Formicola and Franceschi (1996) (average %PE 20.03%) and for females by the method of Ruff et al. (2012; 0.02– 0.19%). In sex-averaged results, all other compared femoral equations have mean %PEs within a range of 60.5% except for the femoral bicondylar length equation of Sjøvold (1990; 21.6%) and Bach’s (1965) equation (3.7%). In the case of sex-specific results, %PEs of stature are higher for males than they are for females with the exception of Sjøvold’s (1990) maximum femoral length equation (22.3%) and Bach’s (1965) equation (23.7%; Bach’s equation is available only for females). Figure 3 presents boxplots of %PEs of stature predicted from tibial lengths using equations from the present and previous studies. On average, tibial equations produce greater %PEs than did femoral and femoral 1 tibial equations, with a range between 20.9 and 0.9% for sex-average results. In analyses broken down by sex, the most accurate estimates for males are given by the northern European tibial equations of Ruff et al. (2012) (average %PEs between 20.63 and 20.39). However, surprisingly, the best estimates for females are obtained not from the northern latitude equations of this study (21.5 to 21.3%), as would be expected for the northern latitude Pohansko site, but rather from the southern latitude equations (0.08–0.5%). In fact, the northern equations give worse predictions than those derived other
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Fig. 1. Box plots of %PE of stature estimated from (a) maximum humeral length and (b) maximum radial length. Mean 6 SE and 62SD; only sex-average results are shown. Pohansko: this study; Ruff: Ruff et al. (2012); F 1 F: Formicola and Franceschi (1996); Sjovold: Sjøvold (1990); Bach: Bach (1965), M 1 F: average of sex-specific equations, Pooled: pooled-sex equations.
Fig. 2. Box plots of %PE of stature estimated from femoral lengths: (a) sex-average, (b) males, and (c) females. Mean 6 SE and 62SD. Sjov (Fe1): Fe1 Sjøvold (1990); Sjov (Fe2): Fe2 Sjøvold (1990); Breitinger: Breitinger (1937; see Fig. 1 legend for other samples).
available generic equations with the exception of Sjøvold’s equation. Sjøvold’s (1990) method estimates anatomically derived stature with the highest error among all tibial comparisons, with a %PE range of 21.67 to 23.37%. Boxplots of %PEs of stature predicted from femoral 1 tibial lengths using equations from the present study and from two comparative studies are shown in Figure 4. In general, %PEs of stature predicted from femoral 1 tibial length are between 20.2 and 0.8% for sex-average results. In the sex-average sample, the most accurate estimate is given by the equation of Ruff et al. (2012) that is derived from the northern latitude equation. Femoral 1 tibial equations show better performance for males than they do for females. Moreover, the northern equations of Ruff et al. (2012) estimate stature with
smaller %PEs for males (0.1%) than they do for females (20.6 to 20.7%), whereas the best performance for females is again provided by the southern equation (0.1– 0.5%).
Early medieval stature equations Figure 5 presents boxplots for %PEs of Pohansko statures predicted from long bones using equations derived from Early Medieval populations by Vercellotti et al. (2009) and by Maijanen and Niskanen (2010). Pohansko statures are estimated with greater agreement with anatomical stature using the method of Maijanen and Niskanen (2010) when stature is calculated from radii (average %PE 20.5 to 0.2%), femora (0.4 to 0.1%), and femora 1 tibiae (20.5 to 20.3%), whereas the method of American Journal of Physical Anthropology
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TABLE 2. Population-specific stature equations for Pohansko sample. %PEa Boneb Humerus (Hu1) Radius (Ra1) Femur (Fe1) Tibia (Ti1a) Fe1 1 Ti1a
a b
Sex
n
Slope
Intercept
r
SEE
%SEE
Mean
SD
Males Females Pooled Males Females Pooled Males Females Pooled Males Females Pooled Males Females Pooled
25 16 41 22 17 39 25 19 44 25 19 44 25 19 44
0.4591 0.4771 0.4399 0.6235 0.5273 0.5581 0.2683 0.2687 0.2881 0.3963 0.3634 0.3706 0.1645 0.1577 0.1643
16.91 12.81 23.54 13.05 36.75 29.61 45.93 43.95 36.43 17.66 30.34 27.64 30.74 35.75 30.79
0.779 0.923 0.916 0.673 0.787 0.886 0.904 0.887 0.946 0.896 0.874 0.948 0.926 0.899 0.960
4.66 2.53 3.83 5.11 4.09 4.48 3.07 2.83 3.08 3.20 2.98 3.01 2.70 2.67 2.65
2.76 1.63 2.34 3.01 2.63 2.74 1.82 1.82 1.89 1.90 1.92 1.85 1.60 1.71 1.62
0.029 0.006 0.017 0.035 0.030 0.041 0.008 0.019 0.021 0.023 0.027 0.024 0.002
Population-Specific Stature Estimation From Long Bones in the Early Medieval Pohansko (Czech Republic) dek,1* Jirı Macha cˇek,2 Christopher B. Ruff,3 Eliska Schuplerova ,1 Vladimır Sla ta Prichystalova ,2 and Martin Hora1 Rena 1
Department of Anthropology and Human Genetics, Faculty of Science, Charles University in Prague, Czech Republic 2 Department of Archaeology and Museology, Masaryk University, Czech Republic 3 The Center for Functional Anatomy and Evolution, Johns Hopkins University, Baltimore, USA KEY WORDS
body size; body shape; bioarchaeology; regression stature
ABSTRACT OBJECTIVES: We tested the effect of population-specific linear body proportions on stature estimation. MATERIALS AND METHODS: We used a skeletal sample of 31 males and 20 females from the Early Medieval site at Pohansko (Breclav, Central Europe) and a comparative Central European Early Medieval sample of 45 males and 28 females. We developed new populationspecific equations for the Pohansko sample using anatomical reconstructions of stature, then compared percentage prediction errors (%PEs) of anatomical stature from limb bone lengths using the derived Pohansko equations with those previously derived from more general European and other Early Medieval samples. RESULTS: Among general European equations, the lowest %PEs for the Pohansko sample were obtained using the equations of Formicola and Franceschi: Am J Phys Anthropol 100 (1996) 83–88 and Ruff et al.: Am J Phys Anthropol 148 (2012) 601–617. However, unexpectedly, the choice between tibial latitudinal variants proposed
by Ruff et al.: Am J Phys Anthropol 148 (2012) 601–617 appeared to be sex-specific, with northern and southern variants producing lower %PEs for males and females, respectively. Equations from Breitinger: Anthropol Anz 14 (1937) 249–274, Bach: Anthropol Anz 29 (1965) 12– 21, and Sjøvold: Hum Evol 5 (1990) 431–447 provided poor agreement with anatomical stature. When applied to the comparative Central European Early Medieval sample, our new formulae have generally lower %PE than previously derived formulae based on other European Early Medieval samples (Maijanen and Niskanen: Int J Osteoarchaeol 20 (2010) 472–480; Vercellotti et al.: Am J Phys Anthropol 140 (2009) 135–142. CONCLUSIONS: The best agreement with anatomical stature among our newly developed equations was obtained using femoral1tibial length, followed by femoral length. Upper limb bone lengths resulted in higher %PEs. Variation in the tibia is likely to contribute most to potential bias in stature estimation. Am J Phys Anthropol 158:312–324, 2015. VC 2015 Wiley Periodicals, Inc.
Because human stature is one of the key pieces of evidence used in bioarchaeological, forensic, and evolutionary research, any increase in the accuracy of living stature estimations can bring important improvements for further analyses of past human biology (see review in Ruff et al., 2012). Two alternative approaches exist for estimation of living stature from skeletons: anatomical and mathematical (Lundy, 1985). The anatomical approach was developed by Fully (1956), who summed heights and lengths of skeletal elements directly contributing to stature. It has been shown that anatomically derived stature estimates strongly correlate with living stature (r 5 0.98–0.99) and have high accuracy with average error < 1 cm (Maijanen, 2009). Anatomically reconstructed stature is not sensitive to individual and population-based differences in body proportions, and the anatomical approach also provides the best estimate of living stature for individuals from unknown populations and individuals with atypical body proportions (e.g., Olivier, 1969; Stewart and Kerley, 1979; Lundy, 1985; Ousley, 1995; Raxter et al., 2008; Maijanen, 2009). Fully’s (1956) anatomical approach has been modified by several authors (e.g., Fully and Pineau, 1960; Formicola, 1993; Niskanen and Junno, 2004; Raxter et al., 2006), and the modification by Raxter et al. (2006) provides the most accurate estimate with average error < 0.1% (Maijanen, 2009). Raxter et al. (2006) also reported
results for both sexes and provided a new definition of osteometric measurements (but see also Maijanen, 2009), continuous correction of soft tissue (see also Bidmos, 2006; Maijanen, 2009), and new analyses of stature decrease with age (see also review in Trotter and Gleser, 1951; Raxter et al., 2007; Raxter et al., 2008; Raxter and Ruff, 2010). Limits to the anatomical approach have been found mainly in skeletal preservation (see data and review in Auerbach, 2011) and effect of age on final stature estimate (see bibliography and review in Raxter et al., 2007). The mathematical approach is based on either regression of bone lengths against stature or the use of ratios (see review in Lundy, 1985; Feldesman and Fountain, 1996). The application of the regression approach to
Ó 2015 WILEY PERIODICALS, INC.
Grant sponsor: Czech Science Foundation; Grant number: GACR 14-22823S. *Correspondence to: V. Sl adek. E-mail: [email protected] Received 13 February 2015; revised 19 May 2015; accepted 26 May 2015 DOI: 10.1002/ajpa.22787 Published online 29 June 2015 in Wiley Online Library (wileyonlinelibrary.com).
STATURE ESTIMATION IN EARLY MEDIEVAL SKELETAL SAMPLE stature estimation is simple and is only partly limited by bone preservation. Several regression equations broadly applied also to European skeletal samples have been derived from specific population samples (e.g., Breitinger, 1937; Trotter and Gleser, 1952; Bach, 1965; Trotter, 1970; Formicola and Franceschi, 1996; Raxter et al., 2008; Vercellotti et al., 2009; Auerbach and Ruff, 2010) and from broader sampling (e.g., Sjøvold, 2000; Ruff et al., 2012). It frequently has been reported that the mathematical approach can produce substantial bias in several respects (e.g., Pearson, 1899; Stevenson, 1929; Dupertuis and Hadden, 1951; Trotter and Gleser, 1952; Lundy, 1985; Formicola, 1993; Ruff et al., 2012). First, error may be introduced through the statistical approach applied, and it has been shown that in many situations reduced major axis (RMA) regression should be favored over least squares regression (Sjøvold, 1990; Aiello, 1992; Formicola, 1993; Formicola and Franceschi, 1996; Konigsberg et al., 1998; Maijanen and Niskanen, 2010; Ruff et al., 2012). Second, the highest correlation and accuracy in stature estimate is provided by lengths of long bones directly involved in stature, such as femora and tibiae (e.g., Formicola and Franceschi, 1996; Ruff et al., 2012). The final source of error in stature estimation is variation in the proportion between bone lengths and stature with respect to eco-geographic variation and growth plasticity (e.g., Formicola, 1993; Molnar, 1998; Stinson et al., 2000; Bogin and Varela-Silva, 2010; Ruff et al., 2012) as well as a population structure (Roseman and Auerbach, 2015). It has been also shown that secular change can influence proportional differences between proximal and distal limb segments (Meadows and Jantz, 1995; Jantz and Jantz, 1999 see also references below). These observations have brought into question the use of single equations or ratios for stature estimation and imply that even lower limb bones can produce various biases in final stature estimates if they are applied to an population having different body proportions. Applying population-specific equations to individuals with similar proportions are therefore expected to provide greater accuracy in stature estimation than use of generic equations (Holliday and Ruff, 1997). The effect of variation in body proportions between samples on mathematically estimated stature can be reduced using a hybrid approach wherein living stature is estimated for the studied sample using either the anatomical technique or other direct methods (e.g., cadaver length) and then, in a second step, using estimated living stature to create population-specific equations for particular long bones (e.g., Formicola and Franceschi, 1996; Raxter et al., 2008; Vercellotti et al., 2009; Auerbach and Ruff, 2010; Maijanen and Niskanen, 2010; Ruff et al., 2012). It has been demonstrated that if anatomically derived stature is used, then the hybrid approach can produce very low mean percent prediction errors (%PEs) of stature (see for example results using equations of Formicola and Franceschi (1996) and Ruff et al. (2012) in Table 4 of Ruff et al., 2012). As indicated from comparative studies (e.g., Auerbach and Ruff, 2010; Ruff et al., 2012), however, the hybrid approach using anatomically estimated stature is not without potential problems. First, the majority of hybrid equations are derived from samples of limited size and limited archaeological periods (Formicola and Franceschi, 1996; Raxter et al., 2008; Vercellotti et al., 2009; Maijanen and Niskanen, 2010) and therefore their applicability for other bioarchaeological settings and even on other indi-
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viduals from the same population may be questionable. Second, regression formulae generated using the hybrid approach assume homogeneous variation in body proportion within a studied population, which probably does not occur if only due to the effects of population structure, migration, and growth plasticity (although this is an issue with all mathematical approaches). The hybrid approach has been improved by accounting for proportional differences due to eco-geographic variation between the studied individuals and reference samples. It has been shown that either specific northern and southern latitudinal equation variants (Ruff et al., 2012) or guidelines using the crural index for selecting the appropriate equation (Auerbach and Ruff, 2010) can help reduce the effect of ecogeographically introduced variation in body proportions on stature estimation. This is true, however, only in the case that body proportions are seen as the result of long-term adaptation and where migration plays a minor role. As emphasized above, the mathematical technique for stature estimation is sensitive to linear proportions such as limb length to trunk length and proximal/distal limb lengths. In general, stature and body proportions during human evolution have been determined by bipedal striding gait, long distance running, manipulation, and behavioral factors; however, among modern humans the most important factors are associated with ecogeographic variability in thermoregulation and with the effect of developmental plasticity in early postnatal life (Trinkaus, 1981; Tanner et al., 1982; Trinkaus, 1986; Eveleth and Tanner, 1990; Frisancho, 1993; Ruff, 1994; Holliday and Falsetti, 1995; Feldesman and Fountain, 1996; Holliday, 1997, 1999; Molnar, 1998; Stinson et al., 2000; Ruff, 2002; Bogin and Rios, 2003; Bogin and Varela-Silva, 2010; Hora and Sl adek, 2011). Ecogeographic variability of body proportions in relation to thermoregulation in humans generally follows Allen’s and Bergmann’s ecological rules (Bergmann, 1847; Allen, 1877; Roberts, 1953; Ruff, 1994; Katzmarzyk and Leonard, 1998). It has been shown that in colder climates humans exhibit a wider pelvis relative to stature (Ruff, 1994), shorter limbs relative to stature (Molnar, 1998), and low crural and brachial indices (e.g., Trinkaus, 1981; Holliday, 1999). Ecogeographic adjustment to climate has been shown to be a relatively long-term adaptation that is not on the scale of closely succeeding generations (Holliday, 1997, 1999). Thus, we can suggest that local adaptation to climate per se has a relatively low impact on differences in body proportions and stature among subgroups of individuals excavated from a single cemetery. However, ecogeographic factors may come into play with recent migrations of a group or subgroups of a population including gender-specific migrations for example in relation to patrilocal residence. In this case, the archaeological background can help to determine which eco-geographic equation provides the best estimates in a particular archaeological sample. It has also been shown that stature and body proportions are developmentally plastic and sensitive to factors influencing individual growth (Bogin, 1999). Stature can change significantly among successive generations and both negative and positive secular trends have been observed in several different geographic and socioeconomic contexts (e.g., Boas, 1930; Bogin and Rios, 2003; Cole, 2003). A secular trend has been observed especially in accelerating growth of lower limb length in comparison to trunk height during the first 2 years of postnatal American Journal of Physical Anthropology
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development (Tanner et al., 1982; Cole, 2000). For example, Bogin and Rios (2003) showed that in Maya children the increase in total stature during 20 years was about 10 cm, with an increase of lower limb length in the same period of about 7 cm. The acceleration of body segment growth follows a general craniocaudal growth pattern (Schultz, 1926; Scammon and Calkins, 1929) wherein prenatal acceleration is observed in cranial parts of the body (i.e., head size) whereas postnatal acceleration is observed in caudal and distal segments (such as the lower limb and in particular the tibia; Jantz and Jantz, 1999). Postnatal growth has been shown also to be more environmentally plastic than prenatal growth (Bogin, 2010; Ulijaszek, 2010), and therefore lower limb and distal limb segments in proportion to stature are more sensitive to variation in subsistence and living conditions than are trunk and proximal limb segments (Wadsworth et al., 2002; Li et al., 2007). Finally, it also has been observed that tibiae in proportion to stature show higher positive allometry than do femora (Meadows and Jantz, 1995). Thus, craniocaudal-induced secular changes have a stronger effect on tibiae than they do on femora. Probably because of these factors, tibiae are more variable in proportion to stature than femora (also see Holliday and Ruff, 1997); we can therefore expect that femora may provide better estimates of stature than do tibiae, when applying equations developed from one reference group to another target sample. Secular trends in stature variation have also been shown to be responsive to such general factors as socioeconomic status (SES) (Bogin, 1999; Stinson et al., 2000). It has been demonstrated, too, that SES has an impact on proportional differences mainly in the proportion between tibia and stature (Jankauskas and Kozlovskaya, 1999; Vercellotti et al., 2011). The effect of SES on secular trends and body proportions is important especially for Holocene applications inasmuch as during the Holocene human populations are undergoing substantial social and gender stratification (Johnson, 2000). Therefore, we can suggest that a single cemetery represents individuals from different local living conditions as well as from different local subsistence and nutritional histories and for whom it is difficult to apply a single common equation to estimate stature. Again, this raises the question to what extent factors operating at the scale of succeeding generations might affect accuracy in stature estimation using the mathematical approach. The goal of this study is to test differences in agreement between population-specific equations and available techniques for stature estimation frequently used in Central European bioarchaeological research (Breitinger, 1937; Bach, 1965; Sjøvold, 1990; Formicola and Franceschi, 1996) with special focus on the new and ostensibly broadly applicable technique provided by Ruff et al. (2012). The test sample is selected from the Early Medieval second church cemetery at Pohansko (Breclav, Czech Republic). Another goal of the study is to investigate the impact of body proportions on the accuracy of stature estimates, including consideration of possible ecogeographic and other environmental effects.
MATERIALS AND METHODS Skeletal sample The overall sample of 44 individuals (25 males, 19 females) with sufficiently preserved skeletal elements to calculate anatomical stature (Raxter et al., 2006; Ruff American Journal of Physical Anthropology
et al., 2012) was selected from the Early Medieval site at Pohansko (second church, NE suburb; Breclav, Czech Republic; Mach acˇek et al., 2014). The sample consists of 77% of all adult skeletons excavated in the Pohansko second church. The comparative sample used for more broadly testing Pohansko-derived stature estimation equations consists of 73 individuals (45 males, 28 females) from the NorthCentral European Early Medieval sites of Brucknendorf (Austria, AD 600–800), Dresden Briesnitz (Germany, AD 900–1200), Mikulcˇice (Czech Republic, AD 800–900), M€odling (Austria, AD 630–820), and Zwentendorf (Austria, AD 1000–1100). Complete skeletal height is preserved for 44 individuals (28 males, 16 females) and those individuals are also part of the European sample used in Ruff et al. (2012) stature estimation technique. Basion-bregma height is not preserved for 29 individuals (17 males, 12 females) and for these skeletal height was estimated from partial skeletal height, not including the cranium, using an equation derived from 537 individuals in the Ruff et al. (2012) European sample (r 5 0.996, SEE 5 0.707; Niskanen and Ruff, pers. comm.). Computation details about missing skeletal elements and the technique used for computation of living stature are provided in Ruff et al (2012).
Archaeological background Pohansko (48.7289908N, 16.8966217E, Czech Republic) was one of the key Early Medieval centers in South Moravia during the time of the Great Moravian Empire and represented a strategic point between southern and northern territories for long-distance trading (Mach acˇek, 2007). Systematic archaeological research at Pohansko began in 1958 with discovery of the first church (9th century) and later continued with excavation of complex settlement features on 60 ha with a large central occupation area and two suburbs (SW and NE) (Mach acˇek, 2010, 2011). In 2006, a team headed by J. Mach acˇek discovered in Pohansko’s NE suburb a concentration of construction traces and a cemetery later identified by systematic archaeological excavation as the remains of a second Early Medieval church within the Pohansko settlement ap et al., 2011; Mach (C acˇek et al., 2014). The second church and surrounding cemetery are dated by archeological finds from graves (including specific artifacts such as an Old Hungarian battle axe, heavily gilded buttons with palmettes, silver earrings, temple rings, and lead pedants) and by analogy to other South Moravian Early Medieval sites to between the end of the 9th and beginning of the 10th century. This was likely in the late Great Moravian period. The excavated structure of the second church is relatively small compared with that of the first church and is characterized by less sophisticated building techniques. The cemetery related to the second church yielded 154 skeletons with a majority of nonadult individuals (38% adult and 62% nonadult). Compared with the first church cemetery, the new second church cemetery is smaller with relatively fewer archaeological remains characteristic of higher SES and nobility. This probably indicates that the second building and cemetery were used for a smaller and more closely related group belonging to the founder and owner of the second church (i.e., an Early Medieval familia) with a span of not more than three generations (Mach acˇek et al., 2014).
STATURE ESTIMATION IN EARLY MEDIEVAL SKELETAL SAMPLE
Paleodemographic data All individuals included in the analysis are adults with fused long bone epiphyses (20 years of age or older). To derive age estimates for applying the anatomical stature estimation formula with an age term [Eq. (1) in (Raxter et al., 2006)], we used pubic symphyseal morphology (Brooks and Suchey, 1990). For three individuals, age was estimated by senescence features on the auricular surface (Buckberry and Chamberlain, 2002). We observed high variation (even a decade and more) between different age techniques (Lovejoy, 1985; Schmitt, 2001, 2002; Boldsen et al., 2002). We chose the pubic symphysis technique, as these estimates provided the most reasonable demographic profile for the second church cemetery. As indicated by other studies, even broad age categories improve living stature estimates using the anatomical approach (Raxter et al., 2007). Sex assessment was based primarily on pelvic sexually dimorphic features (Bruzek, 2002) and two pelvic discriminant functions (Novotn y, 1975; Br˚uzek, 1984). There was agreement in sex allocation between morphology and discriminant function analysis for all studied individuals. Skeletal pathology was assessed on all skeletal elements included in anatomically reconstructed stature and individuals with gross pathology were excluded.
Osteometric data
315
details about accuracy in Raxter et al., 2007; Maijanen, 2009). Completely preserved skeletal height was available for 27 individuals (61%), whereas some dimensions were reconstructed for 17 (39%) individuals. Following the recommendation of Auerbach (2011), we did not estimate basion–bregma height, femoral lengths, and tibial length from other dimensions. Nevertheless, for six individuals basion–bregma height was estimated from partially damaged crania with sufficient accuracy. Final presacral height was estimated for 10 individuals (23%) in cases where either an entire vertebral region or more than one individual vertebral height within a section was missing (six presacral heights were estimated using regression formulae based on the lumbar region, and four presacral heights were estimated using regression formulae based on the thoracic and lumbar regions). The technique for adjacent vertebra estimation used either averaging of adjacent vertebrae or relative height for adjacent vertebra as presented in Auerbach (2011) and the regional regression formulae used were from Auerbach (2011). Talocrural height (TC) was estimated for three individuals (7%) using sex-specific equations developed from the Pohansko sample (male SEE: 3.41 mm; female SEE: 1.42 mm). Pohansko-specific equations were generated using RMA regression with anatomical stature and long bone length. Pohansko RMA regression equations were computed for upper limbs using Hu1 and Ra1 and lower limbs using Fe1, Ti1a, and Fe11Ti1a (see details for abbreviations in Table 1). Both sex-specific and pooledsex equations were generated. Anatomical stature obtained for the Pohansko sample was compared with stature estimated by previously suggested equations. For stature estimation, we used general equations provided by Table 3 in Ruff et al. (2012; sex-specific and pooled-sex equations for Hu1, Ra1, Fe1, Ti1a, Fe1 1 Ti1a), Table 3 in Formicola and Franceschi (1996) (sex-specific equations for Hu1, Ra1, Fe1, Ti1, Fe2 1 Ti1), Table 1 in Sjøvold (1990) for “Caucasians” (pooled-sex equations for Hu1, Ra1, Fe1, Fe2, Ti1), page 17 of Bach (1965; equations available only for females using Hu1 and Fe1; we compared using the equation without the additive term), and page 266 of Breitinger (1937; equation available only for males using Fe1; we compared using the equation without the additive term).
Descriptive statistics for osteometric data in the Pohansko sample and measurement abbreviations are shown in Table 1, along with anatomically estimated statures. Lengths of long bones were measured using Martin’s technique (Br€ auer, 1988) by osteometric board to the nearest millimeter. For all lengths, both sides were taken and the average was used for stature regression estimate (see discussion about accuracy between right and left side for upper limb long bones in Ruff et al., 2012: p. 604). As bilateral asymmetry is somewhat larger for upper limb lengths, however, Table 1 also includes descriptive sample statistics for right and left upper limb long bones and only side-average descriptive statistics for lower limb bones. Biiliac breadth was measured using the maximum distance between right and left iliac crests on rearticulated coxae and sacrum. Most of the sample preserves intact coxae and sacrum, and it was therefore possible to measure biiliac breadths with high accuracy. Other osteometric dimensions used in anatomically reconstructing stature (i.e., basion–bregma height, vertebral body heights, and talocrural height) followed techniques revised by Raxter et al. (2006) (see details about definition of measurements in Raxter et al., 2006: Appendix, p. 382).
Body proportions were assessed by analysis of living biiliac breadth against stature, crural index, and Fe1, Ti1a, and Fe1 1 Ti1a lengths against stature. Living biiliac breadth was converted from skeletal biiliac breadth using Eq. (5) from Ruff et al. (1997) and crural index was computed using Fe2 and Ti1a.
Stature estimation
Statistical procedures
Anatomical stature was calculated from skeletal height using a modification of Fully’s technique for anatomical stature estimation by Raxter et al. (2006). Skeletal heights were obtained by the sum of basion–bregma height, C2 –S1 vertebral body heights, lengths of femur and tibia, and height of articulated talus/calcaneus. Conversion to living stature was obtained by Eq. 1 in Raxter et al. (2006) with soft tissue correction and age term included into the final living stature estimate (see
Reduced major axis regression analysis was employed to generate Pohansko-specific equations and to compare previous equations and Pohansko anatomical stature using RMA software v. 1.14 (Bohonak, 2002). Lengths were in millimeters and stature in centimeters. Estimation error for Pohansko equations is expressed as SEE, percentage standard error of estimate (%SEE), and percentage prediction error (%PE) using the formulae:
Body proportion estimates
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TABLE 1. Descriptive statistics for Pohansko sample Males
Females
Dimensionsa
n
Mean
SD
Range
n
Mean
SD
Range
Humeral max. length (Hu1) Humeral max. length right (Hu1) Humeral max. length left (Hu1) Radial max. length right (Ra1) Radial max. length right (Hu1) Radial max. length left (Hu1) Femoral max. length (Fe1) Femoral bicond. length (Fe2) Tibial lateral total length (Ti1) Tibial maximum length (Ti1a) Fe1 1 Ti1a length Fe2 1 Ti1 length Anatomical stature Living biiliac breadth
25 23 24 22 22 20 25 25 25 25 25 25 25 24
331.2 333.3 328.8 251.4 252.6 250.1 458.5 454.4 373.7 381.7 840.2 828.1 168.9 29.4
14.95 15.76 14.81 9.88 10.25 10.21 25.58 26.05 17.00 17.32 41.72 41.71 6.86 1.77
305.0–373.0 308.0–377.0 302.0–370.0 229.0–271.5 228.0–271.0 230.0–272.0 412.5–541.0 402.0–536.5 336.0–408.0 344.5–417.5 757.0–958.5 742.0–944.0 152.0–185.2 26.5–34.9
16 14 16 17 17 13 19 19 19 19 19 19 19 17
299.6 301.1 298.8 225.6 226.0 224.5 414.9 410.4 337.5 344.2 759.2 747.9 155.5 28.4
13.12 12.98 13.54 11.49 11.98 10.24 21.49 21.08 15.33 15.89 36.63 35.63 5.78 1.63
283.0–324.0 284.0–326.0 281.0–322.0 210.5–247.5 211.0–250.0 210.0–245.0 374.0–452.5 371.0–445.5 305.5–363.5 313.5–371.0 687.5–823.5 676.5–809.0 144.8–165.8 25.1–31.2
a
All dimensions are given in millimeters except biiliac breadths and statures, which are in centimeters. Living biiliac breadth is computed using skeletal biiliac breadth and Eq. (5) of Ruff et al. (1997). Further description is provided in the Materials and Methods.
P 1. SEE ¼ ðð ð½true-predictedÙ 2ÞÞ=nÞÙ 0:5 2. %SEE ¼ ðSEE=y Þ 3 100 3. %PE ¼ ½ðtrue – predictedÞ=predicted 3 100, where y is mean y, “true” is anatomical stature, and “predicted” is stature estimated by the given regression equation. Standard error of estimate and %SEE are measures for random errors, whereas %PE is for directional bias. Measures of differences between regression techniques and anatomical stature are expressed as %PEs. All indices were tested using the nonparametric Mann–Whitney U-test. Statistical analysis was carried out using STATISTICA 12 for Windows (StatSoft, 2013) and Excel 2010 (Microsoft).
RESULTS Stature estimation for Pohansko sample Table 2 presents stature estimation equations for the Pohansko sample. As expected, upper limb bone equations show greater SEEs than do lower limb bone equations. Upper limb bone stature equations show also greater dispersion (SD) of individual %PEs than do lower limb bone equations (also see Figs. 1 and 2). Humeral equations provide somewhat smaller SEEs and dispersion of %PEs than do radial equations. Femoral 1 tibial stature estimation equations produce the smallest SEEs in this study sample and slightly smaller dispersion of individual %PEs of stature. Tibial equations provide higher SEEs than do other lower limb bone equations but remain below the range of SEEs derived from the upper limb bones. Sex-specific equations for the Pohansko sample do not substantially reduce SEEs and dispersion of %PEs, with the single exception of a slight increase in SEEs in humeral and femoral sex-specific equations for females.
General stature equations Boxplots of %PEs of stature predicted from upper limb bones using equations from the present study and from four previous “generic” European studies are shown in Figure 1. Only sex-average results (i.e., obtained as the average of male and female values) are shown. On average, the most accurate estimates provided by generic American Journal of Physical Anthropology
equations are given by Ruff’s et al. (2012) humeral equations, with average %PEs (0.2%) almost equal to errors estimated from the present study equations. The upper limb bone equations of Formicola and Franceschi (1996) and Sjøvold (1990) overestimate or underestimate anatomically derived stature on average in the range of 21.8–0.8%. The least accurate estimate on average is provided by the equation from Bach (1965; 23.85%; only the humeral equation for females is available for this technique). The 62SD range of %PEs is consistent among all compared generic methods. The 62SD range is slightly smaller in humeral %PEs of stature than it is in radial. Figure 2 provides boxplots of %PEs of stature predicted from femoral lengths using equations from the present study and five previous studies. Sex-average results and results by sex are shown. The most accurate stature estimates are given by methods using anatomically derived stature: for males by the method of Formicola and Franceschi (1996) (average %PE 20.03%) and for females by the method of Ruff et al. (2012; 0.02– 0.19%). In sex-averaged results, all other compared femoral equations have mean %PEs within a range of 60.5% except for the femoral bicondylar length equation of Sjøvold (1990; 21.6%) and Bach’s (1965) equation (3.7%). In the case of sex-specific results, %PEs of stature are higher for males than they are for females with the exception of Sjøvold’s (1990) maximum femoral length equation (22.3%) and Bach’s (1965) equation (23.7%; Bach’s equation is available only for females). Figure 3 presents boxplots of %PEs of stature predicted from tibial lengths using equations from the present and previous studies. On average, tibial equations produce greater %PEs than did femoral and femoral 1 tibial equations, with a range between 20.9 and 0.9% for sex-average results. In analyses broken down by sex, the most accurate estimates for males are given by the northern European tibial equations of Ruff et al. (2012) (average %PEs between 20.63 and 20.39). However, surprisingly, the best estimates for females are obtained not from the northern latitude equations of this study (21.5 to 21.3%), as would be expected for the northern latitude Pohansko site, but rather from the southern latitude equations (0.08–0.5%). In fact, the northern equations give worse predictions than those derived other
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Fig. 1. Box plots of %PE of stature estimated from (a) maximum humeral length and (b) maximum radial length. Mean 6 SE and 62SD; only sex-average results are shown. Pohansko: this study; Ruff: Ruff et al. (2012); F 1 F: Formicola and Franceschi (1996); Sjovold: Sjøvold (1990); Bach: Bach (1965), M 1 F: average of sex-specific equations, Pooled: pooled-sex equations.
Fig. 2. Box plots of %PE of stature estimated from femoral lengths: (a) sex-average, (b) males, and (c) females. Mean 6 SE and 62SD. Sjov (Fe1): Fe1 Sjøvold (1990); Sjov (Fe2): Fe2 Sjøvold (1990); Breitinger: Breitinger (1937; see Fig. 1 legend for other samples).
available generic equations with the exception of Sjøvold’s equation. Sjøvold’s (1990) method estimates anatomically derived stature with the highest error among all tibial comparisons, with a %PE range of 21.67 to 23.37%. Boxplots of %PEs of stature predicted from femoral 1 tibial lengths using equations from the present study and from two comparative studies are shown in Figure 4. In general, %PEs of stature predicted from femoral 1 tibial length are between 20.2 and 0.8% for sex-average results. In the sex-average sample, the most accurate estimate is given by the equation of Ruff et al. (2012) that is derived from the northern latitude equation. Femoral 1 tibial equations show better performance for males than they do for females. Moreover, the northern equations of Ruff et al. (2012) estimate stature with
smaller %PEs for males (0.1%) than they do for females (20.6 to 20.7%), whereas the best performance for females is again provided by the southern equation (0.1– 0.5%).
Early medieval stature equations Figure 5 presents boxplots for %PEs of Pohansko statures predicted from long bones using equations derived from Early Medieval populations by Vercellotti et al. (2009) and by Maijanen and Niskanen (2010). Pohansko statures are estimated with greater agreement with anatomical stature using the method of Maijanen and Niskanen (2010) when stature is calculated from radii (average %PE 20.5 to 0.2%), femora (0.4 to 0.1%), and femora 1 tibiae (20.5 to 20.3%), whereas the method of American Journal of Physical Anthropology
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TABLE 2. Population-specific stature equations for Pohansko sample. %PEa Boneb Humerus (Hu1) Radius (Ra1) Femur (Fe1) Tibia (Ti1a) Fe1 1 Ti1a
a b
Sex
n
Slope
Intercept
r
SEE
%SEE
Mean
SD
Males Females Pooled Males Females Pooled Males Females Pooled Males Females Pooled Males Females Pooled
25 16 41 22 17 39 25 19 44 25 19 44 25 19 44
0.4591 0.4771 0.4399 0.6235 0.5273 0.5581 0.2683 0.2687 0.2881 0.3963 0.3634 0.3706 0.1645 0.1577 0.1643
16.91 12.81 23.54 13.05 36.75 29.61 45.93 43.95 36.43 17.66 30.34 27.64 30.74 35.75 30.79
0.779 0.923 0.916 0.673 0.787 0.886 0.904 0.887 0.946 0.896 0.874 0.948 0.926 0.899 0.960
4.66 2.53 3.83 5.11 4.09 4.48 3.07 2.83 3.08 3.20 2.98 3.01 2.70 2.67 2.65
2.76 1.63 2.34 3.01 2.63 2.74 1.82 1.82 1.89 1.90 1.92 1.85 1.60 1.71 1.62
0.029 0.006 0.017 0.035 0.030 0.041 0.008 0.019 0.021 0.023 0.027 0.024 0.002
