Methods for estimating missing human skeletal element osteometric dimensions employed in the revised fully technique for estimating stature

One of the greatest limitations to the application of the revised Fully anatomical stature estimation method is the inability to measure some of the skeletal elements required in its calculation. These element dimensions cannot be obtained due to taphonomic factors, incomplete excavation, or disease processes, and result in missing data. This study examines methods of imputing these missing dimensions using observable Fully measurements from the skeleton and the accuracy of incorporating these missing element estimations into anatomical stature reconstruction. These are further assessed against stature estimations obtained from mathematical regression formulae for the lower limb bones (femur and tibia). Two thousand seven hundred and seventeen North and South American indigenous skeletons were measured, and subsets of these with observable Fully dimensions were used to simulate missing elements and create estimation methods and equations. Comparisons were made directly between anatomically reconstructed statures and mathematically derived statures, as well as with anatomically derived statures with imputed missing dimensions. These analyses demonstrate that, while mathematical stature estimations are more accurate, anatomical statures incorporating missing dimensions are not appreciably less accurate and are more precise. The anatomical stature estimation method using imputed missing dimensions is supported. Missing element estimation, however, is limited to the vertebral column (only when lumbar vertebrae are present) and to talocalcaneal height (only when femora and tibiae are present). Crania, entire vertebral columns, and femoral or tibial lengths cannot be reliably estimated. Further discussion of the applicability of these methods is discussed.     

Estimation of australopithecine stature from long bones: A.L.288-1 as a test case

Regression equations for the estimation of stature from long bones, although derived from modern human populations, are frequently applied to early hominids. In fact, some of these equations have even been recommended or especially created to be applied to Australopithecus remains. In this study, 45 sets of regression and correlation formulae, recurrent in anthropological and medico-legal literature, are applied to long bones of the Pliocene hominid A.L.288-1 ('Lucy'), in order to assess which, if any, could be considered suitable for stature reconstruction in 'gracile' australopithecines. Virtually every method based on regression equations overestimates stature as compared with the estimate based on reconstruction of all the preserved skeletal parts. In addition, most methods failed to give consistent results with data from different limb segments. None of the sets of regression formulae tested here can be recommended as a reliable means of stature estimation in 'gracile' australopithecines.     

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

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 = 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 measurements 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.     

中国汉族女性长骨碎片的身高推断

本文作者通过对69副有生前确切资料的中国汉族女性四肢长骨的研究,在女性四肢长骨推断身高的基础上,参考国内外学者的研究方法,选择左右侧肱骨,尺骨,桡骨,股骨,胫骨,腓骨的局部测量项目,其中肱骨8项,尺骨3项,桡骨3项,股骨14项,胫骨8项,腓骨3项,用SPSS软件包对测量项目进行统计分析,建立了中国汉族女性破碎长骨推断身高的回归方程。本文所建方程可以用于中国汉族女性破碎长骨的身高推断,其中肱骨,股骨,胫骨碎片推断身高的效果较好。     

Estimating stature in fossil hominids: which regression model and reference sample to use?

coResearchers have long appreciated the significant relationship between body size and an animal's overall adaptive strategy and life history. However, much more emphasis has been placed on interpreting body size than on the actual calculation of it. One measure of size that is especially important for human evolutionary studies is stature. Despite a long history of investigation, stature estimation remains plagued by two methodological problems: (1) the choice of the statistical estimator, and (2) the choice of the reference population from which to derive the parameters.This work addresses both of these problems in estimating stature for fossil hominids, with special reference to A.L. 288-1 (Australopithecus afarensis) and WT 15000 (Homo erectus). Three reference samples of known stature with maximum humerus and femur lengths are used in this study: a large (n=2209) human sample from North America, a smaller sample of modern human pygmies (n=19) from Africa, and a sample of wild-collected African great apes (n=85). Five regression techniques are used to estimate stature in the fossil hominids using both univariate and multivariate parameters derived from the reference samples: classical calibration, inverse calibration, major axis, reduced major axis and the zero-intercept ratio model. We also explore a new diagnostic to test extrapolation and allometric differences with multivariate data, and we calculate 95% confidence intervals to examine the range of variation in estimates for A.L. 288-1, WT 15000 and the new Bouri hominid (contemporary with [corrected] Australopithecus garhi). Results frequently vary depending on whether the data are univariate or multivariate. Unique limb proportions and fragmented remains complicate the choice of estimator. We are usually left in the end with the classical calibrator as the best choice. It is the maximum likelihood estimator that performs best overall, especially in scenarios where extrapolation occurs away from the mean of the reference sample. The new diagnostic appears to be a quick and efficient way to determine at the outset whether extrapolation exists in size and/or shape of the long bones between the reference sample and the target specimen.     

Using scapular measurements in regression formulae for the estimation of stature

There are very few papers in forensic literature in which scapular dimensions have been used for estimation of living stature. Allowing the forensic duty to estimate the living stature of skeletal remains, using intact or fragmented scapulae, the Authors have performed multiple regression analysis between the measurements taken from 80 scapula (40 male and 40 female) belonging to a skeletal collection with anthropometric known data. Seven parameters (max length, max breadth, max acrocoracoid distance, length of acromion, max length of coracoid, length of glenoid cavity, width of glenoid cavity) have been recorded. By statistical analysis multiple and linear regressions have been obtained. The results show that living stature may be determined by using regression formulae of single or associated parameters taken from whole or fragmented scapulae. In absence of intact or fragmented long limb bones, scapula sample can be reliably employed for the estimation of stature in forensic practice.     

Skeletal growth of children from the Iron Age site at K2 (South Africa)

Cross-sectional growth data were obtained from the skeletal remains of children from the Iron Age site of K2 near the Limpopo River. Standard measurements of the diaphyseal lengths of the long bones from both limbs were recorded and compared to published skeletal data. For this purpose, data on Eskimo and Aleut skeletons, Libben skeletons, and skeletons from Indian Knoll and Altenerding were used. An attempt to study growth allometrically was made. K2 children were growing as well as children from these other groups. Comparison of data for K2 children with those on living South African “Cape Coloured” rural children, studied during the late 1980s, shows the similarity of growth of both groups. © 1996 Wiley-Liss, Inc.     

Estimation stature from X-rays of metacarpals in the Turkish population

Determination of stature is as important as the determination of sex and age when analyzing and identifying the remains of skeletons. Stature, in an approximate and widespread manner, is determined by the femur and tibia, i.e. those long bones that affect stature directly. However, when long bones are not available or when they are found in a very badly preserved condition that does not permit any estimation on stature, then other bones of the body can also be used for this purpose. The aim of this study is to determine stature with the help of metacarpals in the Turkish population. In this study, by using the X-ray films of metacarpal bones of 100 females and 100 males, regression equations have been set up for 5 metacarpal bones. The coefficients of correlation existing between the metacarpal bones and stature, together with the standard errors of these equations, have been intensively examined in this study. The results of studies conducted by other researchers such as Musgrave & Harneja (1978) and Meadows & Jantz (1992) have been compared with the results of our study. As a result of this comparison, the difference existing between them has been found to be significant according to the results of the t-test (p < 0.05, p < 0.01 and p < 0.001). The significance of such results proves that the general body characteristics and body proportions of populations are differing from each other and therefore specific regression equations for the different populations have to be set up.     

An assessment of sex using the skull of black South Africans by discriminant function analysis

The derivation of discriminant function equations for skeletal elements of South African populations continues to be an area of interest to both forensic anthropologists and skeletal biologists alike. The skull of black South Africans has previously been subjected to discriminant function analysis, using four measurements and two indices; however, no equations were derived to address the issue of sex determination. Recently Franklin, Freedman and Milne [2005. Sexual dimorphism and discriminant function sexing in indigenous South African crania. HOMO J. Comp. Hum. Biol. 55, 213-228] used the crania of black South Africans, in a three-dimensional approach, with eight linear measurements to investigate sex determination. This study, although valuable, requires the use of highly technical and expensive morphometric equipment that renders it less feasible in South Africa. In response to this, our study uses traditional anthropometric measurements and equipment to address the question of sex determination from the crania and mandible of blacks. One hundred and twenty non-pathological skulls were randomly selected from the Raymond Dart Collection of Human Skeletons, equally distributed by sex and belonging to individuals whose age at death ranges between 25 and 70 years. Fourteen cranial and six mandibular measurements were subjected to discriminant function analyses and discriminant function equations were derived for sex determination. Average accuracies ranged between 80% and 85% and were on par with that obtained in previous studies. Our study shows that traditional methods provide average accuracies that are comparable to those obtained using more complex techniques.     

The reliability of osteometric techniques for the sex determination of burned human skeletal remains

The influence of heat-induced shrinkage on the osteometric sexual dimorphism of human skeletons is still poorly known. In order to investigate this issue, a sample composed of 84 Portuguese individuals cremated at a modern crematorium was examined using standard measurements from the femur, the talus and the calcaneus. In addition, sex determination of the sample was attempted by using osteometric standards developed from the Coimbra collection of identified skeletons. This was carried out to assess the extent of the effect of heat-induced shrinkage on the correct classification of known-sex skeletons while using standards developed on unburned skeletons.Results demonstrated that sexual dimorphism was still observable in the sample of calcined bones despite shrinkage. However, the application of conventional osteometric standards was unsuccessful. As expected, shrinkage caused most females to be correctly classified according to sex, but the sex allocation of males was very poor for all standard measurements.The results were obtained on a small sample but suggest that univariate metric techniques specifically developed for calcined bones may be valuable for sex determination. This would bring new methodological possibilities for biological anthropology and would enlarge the set of techniques regarding sex determination of burned skeletal remains.     

Stature estimation in prehistoric Native Americans of Ohio

In the present report we investigate stature estimation techniques in a sample of 64 (35 male, 29 female) prehistoric Native Americans from Ohio. Because living stature is unknown for these 64 individuals, we use Fully's (1956) anatomical method to provide the best estimates of living stature. In this method all osseous components of skeletal height are measured and soft tissue correction is added. Comparisons of regression equations commonly used for stature estimation in prehistoric Eastern Woodland Native American populations, but developed for East Asian and East Asian-derived populations (using lower extremity components), show that these commonly used equations consistently yield stature estimates 2 to 8 cm in excess of the best estimates from Fully's method. Based on the skeletal height measures of the 64 individuals in the present sample, we develop regression equations for the estimation of stature. These equations yield stature estimates virtually identical to estimates from Fully's method and may prove useful for stature reconstruction in other prehistoric Eastern Woodland Native American populations.     

Technical note: a re-evaluation of stature estimation from skeletal length in the grave

Several methods for stature estimation have been proposed over the years. Among these methods is anatomical reconstruction, regression based on long bone lengths, and measuring skeletal vertex - talus length in the grave for individuals buried in a supine position. Recent studies have dealt with the applicability of skeletal length in the grave (Petersen: Int J Osteoarchaeol 15 (2005) 106-114) and anatomical reconstruction (Raxter et al.: Am J Phys Anthropol 130 (2006) 374-384). The results from the latter study calls into question the results of the former study. Therefore an investigation of the potential bias of using skeletal length in the grave as an estimate of living stature has been performed. Twenty Medieval Danish skeletons were measured both in situ and in the laboratory, and the anatomically reconstructed stature (Raxter et al.: Am J Phys Anthropol 130 (2006) 374-384) was compared with the skeletal length in the grave. The results show that 2.5 cm should be added to skeletal length in the grave in order to obtain an unbiased estimate ofliving stature.     

Estimation of stature and body mass from the skeleton among coastal and mid-altitude Andean populations

Adult stature and body mass represent fundamental biological characteristics of individuals and populations, as they are relevant to a range of problems from assessing nutrition and health to longer term evolutionary processes. Stature and body mass estimation from skeletal dimensions are therefore key to addressing biological and social questions about past populations. Anatomical reconstruction provides the most direct proxy for living stature but is only suitable for well-preserved remains. Regression equations for estimating stature from bone lengths are therefore extremely useful, though it is well recognized that differences in body proportions limit the cross-application of equations between samples. Here, we assess the accuracy of published stature estimation equations from worldwide and New World groups applied to archaeological samples from the central Andean coast and highlands of South America. As no existing equations are clearly appropriate, new sample-specific regression equations are presented. Anatomical stature reconstruction is further complicated by artificial cranial modification (ACM) influencing cranial height in Andean samples, so this problem is investigated in the current sample. Although ACM has minimal impact here, the possibility should be explored in other samples before anatomical stature estimation is attempted. Recommendations are also made for estimating body mass from femoral head diameter. The mean of three previously published equations is shown to offer minimal bias and the most reliable estimate of body mass in the study samples.     

Weight of the skeleton during postnatal development

The weight of all bones and the length of humeri, radii, femora and tibiae have been determined in a series of 150 dry, fat-free skeletons from American Whites and Negroes of both sexes, ranging in age from 23 days to 22 years. Six skeletons were eliminated from the series because of evidence of previous illness. A comparison of the lengths of femur plus tibia of this series with the mean statures of a large series of living children at given ages indicates similarity in the growth patterns. Statistical analyses of the data show that the skeletal weight cannot be estimated reliably from age by cither an exponential growth equation or by a logistic function. The weight of the skeleton, however, is related to the lengths of the measured limb bones by allometric equations, and such equations involving each of the four bones are presented for estimation of skeletal weight in the living. Although the standard errors of estimate of the equations based on lengths of each of these four bones differ very little, the radius is recommended over the other three because it is more readily accessible in the living for a roentgenogram and its shadow on the film shows least distortion.     

华南地区男性成年人由长骨长度推算身长的回归方程

从近年来收集的华南地区汉族成年男性50具已知生前身长的骨骼材料,算出从各长骨推算身长的常数(a)及回归系数(b),并算出长骨长度与身高的相关系数(r)数值在0.516—0.913之间,表明相关度较为密切,在此基础上算出10个由各长骨的估计身长的回归方程。并采用校正值:0.6毫米×(年龄—30),校正因年龄所造成的身长误差。从肱骨、腓骨及肱骨加桡骨、股骨加胫骨的长度推算身长最为理想。本文所得的回归方程,适用于华南人。     

Life expectancy of the 20th century Venda: A compilation of skeletal and cemetery data

Little information is available on the 20th century mortality rates of rural black South African groups, such as the Venda. The purpose of this study was to apply abridged life tables in order to estimate life expectancy from both skeletal remains and death registry information of modern South African communities. Comparisons were also made with prehistoric and contemporary groups as a means to better evaluate life expectancy for this time period. The sample consisted of 160 skeletons of known Venda origin and burial registry information for 1364 black South Africans from the Rebecca Street and Mamelodi Cemeteries in Pretoria, South Africa. Standard anthropological techniques were applied to determine sex and estimate age from the skeletal remains. The stationary and non-stationary life table models were used to analyse the data. A high rate of child mortality, low juvenile and adult mortality with a steady increase in mortality after the age of 30 years was observed for both the Venda and the cemetery samples. Throughout the 20th century, life expectancy was shown to increase for black South Africans. However, due to the widespread HIV infection/AIDS of the 21st century, infant and young adult mortality rates continue to rise at such a speed that the decline in mortality seen for South Africans in the last 50 years will most likely to be lost in the next decade due to this disease.     

How large were the australopithecines?

Stature of the African early hominids is estimated from most of the available fragments of fossil long bones by means of regression analysis. The average height of the South African gracile australopithecines is predicted to be 145.1 cm (4′9″) where n = 4 and of the South African robust forms, 152.7 cm (5′) where n = 3. The East African early hominids are somewhat taller (x = 163.0 cm or 5′4″, where n = 7). Variability in stature is high even within the same site which is probably a reflection of fairly strong sexual dimorphism in body size. Evidence is presented which suggests that at least in one form of early hominid the size proportions of fore- and hindlimbs are different than in modern man. There is also evidence that average stature may have increased through time. The most significant of these findings is that the two forms of early hominids in South Africa are possibly more similar in stature than is usually cited. This does not imply necessarily that the two forms did not differ significantly in robustness or weight.     

Stature in archeological samples from central Italy: methodological issues and diachronic changes

Stature reconstructions from skeletal remains are usually obtained through regression equations based on the relationship between height and limb bone length. Different equations have been employed to reconstruct stature in skeletal samples, but this is the first study to provide a systematic analysis of the reliability of the different methods for Italian historical samples. Aims of this article are: 1) to analyze the reliability of different regression methods to estimate stature for populations living in Central Italy from the Iron Age to Medieval times; 2) to search for trends in stature over this time period by applying the most reliable regression method. Long bone measurements were collected from 1,021 individuals (560 males, 461 females), from 66 archeological sites for males and 54 for females. Three time periods were identified: Iron Age, Roman period, and Medieval period. To determine the most appropriate equation to reconstruct stature the Delta parameter of Gini (Memorie di metodologia statistica. Milano: Giuffre A. 1939), in which stature estimates derived from different limb bones are compared, was employed. The equations proposed by Pearson (Philos Trans R Soc London 192 (1899) 169-244) and Trotter and Gleser for Afro-Americans (Am J Phys Anthropol 10 (1952) 463-514; Am J Phys Anthropol 47 (1977) 355-356) provided the most consistent estimates when applied to our sample. We then used the equation by Pearson for further analyses. Results indicate a reduction in stature in the transition from the Iron Age to the Roman period, and a subsequent increase in the transition from the Roman period to the Medieval period. Changes of limb lengths over time were more pronounced in the distal than in the proximal elements in both limbs.     

从中指骨长度推算身高的研究

作者对近年在华南地区收集的,已知生前身高的汉族成年男性骨骼的中指骨近节、中节进行了测量。用直线回归方程、多元回归方程对从中指骨长度推算身高进行了研究。并用50例国人骨骼标本对这些推算身高的方法作了检验。结果表明,中指骨与四肢大型长骨,以及从中指骨长度推算身高的直线回归方程与多元回归方程,对推算身高的价值都是相同的。     

Regression equations for estimating stature from long bones of early Holocene European samples

Regression equations for estimating living stature from long bone lengths have been calibrated on a sample of European Neolithic skeletons (33 males and 27 females) by using both least-squares (model I) and major-axis (model II) regression techniques. Stature estimates of the skeletal sample have been made by means of Fully's anatomical method, a procedure based on the sum of all osseous components of height, providing the best approximations to the actual stature. The calculated equations have been tested, along with those generally used to predict stature of earlier European remains, on a small, well-preserved sample including Late Upper Paleolithic, Mesolithic, and Neolithic skeletons. The results indicate that the model II equations are particularly useful when very short or very tall individuals are involved and, at the same time, are among the best predictors of stature in less extreme conditions. © 1996 Wiley-Liss, Inc.