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.     

The use of cranial variables for the estimation of body mass in fossil hominins

Estimating body mass/size/weight remains a crucial precursor to the evaluation of relative brain size and to achieving an understanding of brain evolution in fossil species. Despite the obvious close association between the metrics of postcranial elements and body mass a number of factors combine to reduce their utility. This study examines the feasibility of cranial variables for predicting body mass. The use of traditional regression procedures, independent contrasts analysis, and variance partitioning all support the hypothesis that cranial variables are correlated with body mass even when taking phylogeny into account, with r values typically ranging between 0.52 and 0.98. Body mass estimates derived for fossil hominins using cranial variables are similar to those obtained from previous studies using either cranial or postcranial elements. In particular, upper facial breadth and orbital height display strong predictive capability. Average body masses derived from Least Squares Regression (LSR) equations were used to calculate estimates of body mass for three hominin species. This resulted in estimates of between 30 kg and 47 kg for Australopithecus africanus, 48 kg and 52 kg for Paranthropus robustus, and 75 kg for Homo neanderthalensis. It is proposed that regression equations derived for the order primates are used to estimate body mass for archaic hominins, while hominoid based equations are most suited for Homo.     

Predicting body mass of bonobos (Pan paniscus) with human-based morphometric equations

A primate's body mass covaries with numerous ecological, physiological, and behavioral characteristics. This versatility and potential to provide insight into an animal's life has made body mass prediction a frequent and important objective in paleoanthropology. In hominin paleontology, the most commonly employed body mass prediction equations (BMPEs) are “mechanical” and “morphometric”: uni- or multivariate linear regressions incorporating dimensions of load-bearing skeletal elements and stature and living bi-iliac breadth as predictor variables, respectively. The precision and accuracy of BMPEs are contingent on multiple factors, however, one of the most notable and pervasive potential sources of error is extrapolation beyond the limits of the reference sample. In this study, we use a test sample requiring extrapolation—56 bonobos (Pan paniscus) from the Lola ya Bonobo sanctuary in Kinshasa, Democratic Republic of the Congo—to evaluate the predictive accuracy of human-based morphometric BMPEs. We first assess systemic differences in stature and bi-iliac breadth between humans and bonobos. Due to significant differences in the scaling relationships of body mass and stature between bonobos and humans, we use panel regression to generate a novel BMPE based on living bi-iliac breadth. We then compare the predictive accuracy of two previously published morphometric equations with the novel equation and find that the novel equation predicts bonobo body mass most accurately overall (41 of 56 bonobos predicted within 20% of their observed body mass). The novel BMPE is particularly accurate between 25 and 45 kg. Given differences in limb proportions, pelvic morphology, and body tissue composition between the human reference and bonobo test samples, we find these results promising and evaluate the novel BMPE's potential application to fossil hominins.     

Estimating the body mass of extinct ungulates: a study on the use of multiple regression

The correlation between body mass and both skeletal and dental measures in living mammals has enabled paleontologists to obtain reliable estimates of body size for extinct species, usually using log-transformed bivariate least-squares regression equations. Multiple regression, however, has rarely been used for estimating the mass of extinct species, although this technique can clearly improve the predictive equations compared with those adjusted by simple regression. However, the use of multiple regression is problematical, because even those functions explaining a high percentage of the variance of the dependent variable (i.e. body mass) can show a rather limited predictive power. After analyzing which factors determine the predictive ability of multiple regression equations, we propose a new set of algorithms that allow the estimation of the body mass of extinct ungulates. These algorithms are finally applied to three Miocene ungulate species, Dinohippus leidyanus , Stenomylus hitchcocki and Aletomeryx scotti .     

Multivariate analysis of neognath skeletal measurements: implications for body mass estimation in Mesozoic birds

The abundant fossils of avian stem taxa unearthed during the last years make it necessary to review and improve the models for estimating body mass used in palaeoecological studies. In this article, single and multiple regression functions based on osteological measurements were obtained from a large data set of extant flying birds for estimating the body mass of 42 Mesozoic specimens from stem taxa Archaeopterygidae, Jeholornithidae, Sapeornithidae, Confuciusornithidae, and Enantiornithes, and basal members of Ornithuromorpha. Traditionally, body mass has been estimated in fossil vertebrates using univariate scaling functions. In contrast, multiple regression functions have been used less frequently. Both predictive methods can be affected by different sources of error from statistics, phylogenetic relationships, ecological adaptations, and bone preservation; however, although some studies have addressed these biases, few have tested them within the context of a single data set. In our data set, we find that the models with greater predictive strength and applicability for new specimens, especially for stem taxa, are those derived from multiple regression analyses. For this reason, we suggest that multiple regression analyses may provide improved predictive strength for stem group specimens. Moreover, the methodology used for selecting variables allowed us to obtain specific sets of predictors for each fossil stem group that presumably minimized the variation resulting from historical contingency (i.e. differences in skeletal morphology arising from phylogeny), locomotor adaptations, and diagenetic compaction. The loss of generalizability in the multiple regression models resulting from collinearity effects was negligible on the body mass estimates derived from our data set. Therefore, the body mass values obtained for Mesozoic specimens are accurate and can be used in future studies in a number of palaeobiological and evolutionary aspects of extinct birds, particularly the first stages of avian flight. © 2015 The Linnean Society of London     

MRI-derived body segment parameters of children differ from age-based estimates derived using photogrammetry

Body segment parameters are required when researching joint kinetics using inverse dynamics models. However, the only regression equations for estimating pediatric body segment parameters across a wide age range were developed, using photogrammetry, based on 12 boys and have not been validated to date (Jensen, R.K., 1986. Body segment mass, radius and radius of gyration proportions of children. Journal of Biomechanics 19, 359–368). To assess whether these equations could validly be applied to girls, we asked whether body segment parameters estimated by the equations differ from parameters measured using a validated magnetic resonance imaging (MRI) method. If so, do the differences cause significant differences in joint kinetics during normal gait? Body segment parameters were estimated from axial MRIs of the left thigh and shank of 10 healthy girls (9.6±0.9 years) and compared to those from Jensen's equations. Kinematics and kinetics were collected for 10 walking trials. Extrema in hip and knee moments and powers were compared between the two sets of body segment parameters. With the exception of the shank mass center and radius of gyration, body segment parameters measured using MRI were significantly different from those estimated using regression equations. These systematic differences in body segment parameters resulted in significant differences in sagittal-plane joint moments and powers during gait. Nevertheless, it is doubtful that even the greatest differences in kinetics are practically meaningful (0.3%BW×HT and 0.7%BW×HT/s for moments and power at the hip, respectively). Therefore, body segment parameters estimated using Jensen's regression equations are a suitable substitute for more detailed anatomical imaging of 8–10-year-old girls when quantifying joint kinetics during gait.     

Cranial variables as predictors of hominine body mass

Body mass is a key variable in investigating the evolutionary biology of the hominines (Australopithecus, Paranthropus, and Homo). It is not only closely related to life-history parameters but also provides a necessary baseline for studies of encephalization or megadonty. Body mass estimates are normally based on the postcranial skeleton. However, the majority of hominid fossils are cranio-dental remains that are unassociated with postcranial material. Only rarely can postcranial material be linked with craniodentally defined hominid taxa. This study responds to this problem by evaluating body mass estimates based on 15 cranial variables to determine whether they compare in reliability with estimates determined from postcranial variables. Results establish that some cranial variables, and particularly orbital area, orbital height, and biporionic breadth, are nearly as good mass predictors for hominoids as are some of the best postcranial predictors. For the hominines in particular, orbital height is the cranial variable which produces body mass estimates that are most in line with postcranially generated estimates. Both orbital area and biporionic breadth scale differently in the hominines than they do in the other hominoids. This difference in scaling results in unusually large estimates of body mass based on these variables for the larger-sized hominines, although the three cranial variables produce equivalent predicted masses for the smaller-bodied hominines. © 1994 Wiley-Liss, Inc.     

Bioelectrical impedance estimation of fat-free body mass in children and youth: a cross-validation study.

The purposes of this study were to develop and cross-validate the "best" prediction equations for estimating fat-free body mass (FFB) from bioelectrical impedance in children and youth. Predictor variables included height2/resistance (RI) and RI with anthropometric data. FFB was determined from body density (underwater weighing) and body water (deuterium dilution) (FFB-DW) and from age-corrected density equations, which account for variations in FFB water and bone content. Prediction equations were developed using multiple regression analyses in the validation sample (n = 94) and cross-validated in three other samples (n = 131). R2 and standard error of the estimate (SEE) values ranged from 0.80 to 0.95 and 1.3 to 3.7 kg, respectively. The four samples were then combined to develop a recommended equation for estimating FFB from three regression models. R2 and SEE values and coefficients of variation from these regression equations ranged from 0.91 to 0.95, 2.1 to 2.9 kg, and 5.1 to 7.0%, respectively. As a result of all cross-validation analyses, we recommend the equation FFB-DW = 0.61 RI + 0.25 body weight + 1.31, with a SEE of 2.1 kg and adjusted R2 of 0.95. This study demonstrated that RI with body weight can predict FFB with good accuracy in Whites 10-19 yr old.     

New body mass estimates for Omomys carteri,a middle Eocene primate from North America

We report new body mass estimates for the North American Eocene primate Omomys carteri. These estimates are based on postcranial measurements and a variety of analytical methods, including bivariate regression, multiple regression, and principal components analysis (PCA). All body mass estimation equations show high coefficients of determination (R²), and some equations exhibit low prediction errors in accuracy tests involving extant species of body size similar to O. carteri. Equations derived from PCA-summarized data and multiple regression generally perform better than those based on single variables. The consensus of estimates and their statistics suggests a body mass range of 170–290 g. This range is similar to previous estimates for this species based on first molar area (Gingerich, J Hum Evol 10:345–374, 1981; Conroy, Int J Primatol 8:115–137, 1987). Am J Phys Anthropol 109:41–52, 1999. © 1999 Wiley-Liss, Inc.     

牛科(哺乳纲:偶蹄目)动物与生境利用有关的适应形态模式

对广义牛科动物颅后骨骼的多元变量分析揭示了牛科生境利用和体型之间的骨学特征。利用逐步分辨分析方法和一个基于机器学习的决策树方法鉴别了每种生境中牛科动物颅后解剖结构的形态特征。从110个广义牛科动物测量了43个指标进行了这项分析。利用所有主要肢骨测量值和以单根肢骨测量为主的测量值获得的分辨函数和决策树可以完美地区分适应开阔生境、森林和山地的牛科动物(在所有分析中得到了100 %正确的再分类)。由于调整的函数仅涉及到很小的颅后骨骼测量集,这些函数可以应用于研究考古学和古生物学发掘物中保存的不完整标本。这些表征生境利用的生态适应函数与那些用颅齿部性状建立、用于推测牛科动物食物选择的函数结合,具有刻画已灭绝的分类类群的古个体生态学和重建古环境的潜力。我们还分析了多元回归是否较单一因子回归表现出较高的预测能力,并提出了从每一种单根主要肢骨测量的颅后形态变量得到的最好代数函数     

Allometric equations for predicting body mass of dinosaurs

We use data from the literature to compare two statistical procedures for estimating mass (or size) of quadrupedal dinosaurs and other extraordinarily large animals in extinct lineages. Both methods entail extrapolation from allometric equations fitted to data for a reference group of contemporary animals having a body form similar to that of the dinosaurs. The first method is the familiar one of fitting a straight line to logarithmic transformations, followed by back-transformation of the resulting equation to a two-parameter power function in the arithmetic scale. The second procedure entails fitting a two-parameter power function directly to arithmetic data for the extant forms by nonlinear regression. In the example presented here, the summed circumferences for humerus plus femur for 33 species of quadrupedal mammals was the predictor variable in the reference sample and body mass was the response variable. The allometric equation obtained by back-transformation from logarithms was not a good fit to the largest species in the reference sample and presumably led to grossly inaccurate estimates for body mass of several large dinosaurs. In contrast, the allometric equation obtained by nonlinear regression described data in the reference sample quite well, and it presumably resulted in better estimates for body mass of the dinosaurs. The problem with the traditional analysis can be traced to change in the relationship between predictor and response variables attending transformation, thereby causing measurements for large animals not to be weighted appropriately in fitting models by least squares regression. Extrapolations from statistical models obtained by back-transformation from lines fitted to logarithms are unlikely to yield reliable predictions for body size in extinct animals. Numerous reports on the biology of dinosaurs, including recent studies of growth, may need to be reconsidered in light of our findings.     

Estimating body mass in subadult human skeletons

Methods for estimating body mass from the human skeleton are often required for research in biological or forensic anthropology. There are currently only two methods for estimating body mass in subadults: the width of the distal femur metaphysis is useful for individuals 1–12 years of age and the femoral head is useful for older subadults. This article provides age‐structured formulas for estimating subadult body mass using midshaft femur cross‐sectional geometry (polar second moments of area). The formulas were developed using data from the Denver Growth Study and their accuracy was examined using an independent sample from Franklin County, Ohio. Body mass estimates from the midshaft were compared with estimates from the width of the distal metaphysis of the femur. Results indicate that accuracy and bias of estimates from the midshaft and the distal end of the femur are similar for this contemporary cadaver sample. While clinical research has demonstrated that body mass is one principle factor shaping cross‐sectional geometry of the subadult midshaft femur, clearly other biomechanical forces, such as activity level, also play a role. Thus formulas for estimating body mass from femoral measurements should be tested on subadult populations from diverse ecological and cultural circumstances to better understand the relationship between body mass, activity, diet, and morphology during ontogeny. Am J Phys Anthropol 143:146–150, 2010. © 2010 Wiley‐Liss, Inc.     

Brief communication: Artificial cranial modification in Kow Swamp and Cohuna

The crania from Kow Swamp and Cohuna have been important for a number of debates in Australian paleoanthropology. These crania typically have long, flat foreheads that many workers have cited as evidence of genetic continuity with archaic Indonesian populations, particularly the Ngandong sample. Other scientists have alleged that at least some of the crania from Kow Swamp and the Cohuna skull have been altered through artificial modification, and that the flat foreheads possessed by these individuals are not phylogenetically informative. In this study, several Kow Swamp crania and Cohuna are compared to known modified and unmodified comparative samples. Canonical variates analyses and Mahalanobis distances are generated, and random expectation statistics are used to calculate statistical significance for these tests. The results of this study agree with prior work indicating that a portion of this sample shows evidence for artificial modification of the cranial vault. Many Kow Swamp crania and Cohuna display shape similarities with a population of known modified individuals from New Britain. Kow Swamp 1, 5, and Cohuna show the strongest evidence for modification, but other individuals from this sample also show evidence of culturally manipulated changes in cranial shape. This project provides added support for the argument that at least some Pleistocene Australian groups were practicing artificial cranial modification, and suggests that caution should be used when including these individuals in phylogenetic studies. Am J Phys Anthropol 155:173–178, 2014. © 2014 Wiley Periodicals, Inc.     

Stature and body mass estimation from skeletal remains in the European Holocene

Techniques that are currently available for estimating stature and body mass from European skeletal remains are all subject to various limitations. Here, we develop new prediction equations based on large skeletal samples representing much of the continent and temporal periods ranging from the Mesolithic to the 20th century. Anatomical reconstruction of stature is carried out for 501 individuals, and body mass is calculated from estimated stature and biiliac breadth in 1,145 individuals. These data are used to derive stature estimation formulae based on long bone lengths and body mass estimation formulae based on femoral head breadth. Prediction accuracy is superior to that of previously available methods. No systematic geographic or temporal variation in prediction errors is apparent, except in tibial estimation of stature, where northern and southern European formulae are necessary because of the presence of relatively longer tibiae in southern samples. Thus, these equations should bebroadly applicable to European Holocene skeletal samples.     

Adjusting powerlifting performances for differences in body mass

It has been established that, in the sports of Olympic weightlifting (OL) and powerlifting (PL), the relationship between lifting performance and body mass is not linear. This relationship has been frequently studied in OL, but the literature on PL is less extensive. In this study, PL performance and body mass, for both men and women, was examined by using data from the International Powerlifting Federation World Championships during 1995-2004. Nonlinear regression was used to apply 7 models (including allometric, polynomial, and power models) to the data. The results of this study indicate that the relationship between PL performance and body mass can be best modeled by the equation y = a - bx(-c), where y is the weight lifted (in kg) in the squat, bench press, or deadlift, x is the body mass of the lifter (in kg), and a, b, and c are constants. The constants a, b, and c are determined by the type of lift (squat, bench press, or deadlift) and the gender of the lifter and were obtained from the regression analysis. Inspection of the plots of raw residuals (actual performance minus predicted performance) vs. body mass revealed no body mass bias to this formula in contrast to research into other handicapping formulas. This study supports previous research that found a bias toward lifters in the intermediate weight categories in allometric fits to PL data.     

Estimation of body weights from craniometric variables in baboons

Body weights of adult baboons (genera Papio, Mandrillus, and Theropithecus) were gathered from notes of collectors and museum records. However, these data were insufficient to establish mean body weights for all baboon groups. Thus, log cube roots of mean body weights were regressed as functions of the logs of several cranial and dental variables. The resulting least squares regression coefficients were used to estimate weights for 503 adult baboons from cranial measurements. The ability of the various regression functions to assess baboon body weight was determined by comparing reported and estimated mean and individual body weights. The best estimator of baboon body weights was the function derived from the factor scores of a principal components analysis of seven craniometric variables regressed on body weight. However, each of these craniometric variables singly was nearly as precise an estimator of body weight as the multivariate combination of all seven. Other measurements such as dental dimensions and foramen magnum area estimated weight less accurately. Body weight estimates derived from the regression analyses coupled with museum and literature records allowed an assessment of size relationships among all baboon groups.     

Temporal change in the morphometry–body mass relationship of polar bears

Accurate information on animal body mass is often an essential component of wildlife research and management. However, for many large-bodied species, obtaining direct scale weights from individuals may be difficult. In these cases, morphometric equations (e.g., based on girth or length) may provide accurate and precise estimates of body mass. We developed predictive equations to estimate the body mass of free-ranging polar bears (Ursus maritimus) in western Hudson Bay, Canada. Using multiple linear and non-linear regression, we identified a strong relationship between polar bear body weight and linear measures of straight line length and axillary girth. The mass–morphometry relationship appeared to change over time and we developed separate equations for polar bears measured during 2 time periods, 1980–1996 and 2007–2009. Non-linear models were more accurate and provided body mass estimates within 5.8% (R² = 0.98) and 6.1% (R² = 0.98) of scale weight in the earlier and later time periods, respectively. Earlier equations developed for polar bears in this subpopulation performed poorly when applied to recently sampled individuals. In contrast, some contemporary equations from other regions performed reasonably well, suggesting that temporal changes within a subpopulation may be more pronounced than regional differences and can render earlier predictive equations obsolete. Our results have important implications for current and future studies of polar bear body condition and the effects of ongoing climate warming. © 2011 The Wildlife Society.     

Predicting euarchontan body mass: A comparison of tarsal and dental variables

Objective: Multiple meaningful ecological characterizations of a species revolve around body mass. Because body mass cannot be directly measured in extinct taxa, reliable body mass predictors are needed. Many published body mass prediction equations rely on dental dimensions, but certain skeletal dimensions may have a more direct and consistent relationship with body mass. We seek to evaluate the reliability of prediction equations for inferring euarchontan body mass based on measurements of the articular facet areas of the astragalus and calcaneus. Methods: Surface areas of five astragalar facets (n = 217 specimens) and two calcaneal facets (n = 163) were measured. Separate ordinary least squares and multiple regression equations are presented for different levels of taxonomic inclusivity, and the reliability of each equation is evaluated with the coefficient of determination, standard error of the estimate, mean prediction error, and the prediction sum of squares statistic. We compare prediction errors to published prediction equations that utilize dental and/or tarsal measures. Finally, we examine the effects of taxonomically specific regressions and apply our equations to a diverse set of non‐primates. Results: Our results reveal that predictions based on facet areas are more reliable than most linear dental or tarsal predictors. Multivariate approaches are often better than univariate methods, but require more information (making them less useful for fragmentary fossils). While some taxonomically specific regressions improve predictive ability, this is not true for all primate groups. Conclusions: Among individual facets, the ectal and fibular facets of the astragalus and the calcaneal cuboid facet are the best body mass predictors. Since these facets have primarily concave curvature and scale with positive allometry relative to body mass, it appears that candidate skeletal proxies for body mass can be identified based on their curvature and scaling coefficients. Am J Phys Anthropol 157:472–506, 2015. © 2015 Wiley Periodicals, Inc.     

Evolutionary dynamics of vertebrate body mass range

Change in body mass with time has been considered for many clades, often with reference to Cope's rule, which predicts a tendency to increase in body size. A more general rule, namely increase in the range of body mass with time, is analyzed here for vertebrates. The log range of log vertebrate body mass is shown to increase linearly and highly significantly with the log of duration of clade existence. The resulting regression equations are used to predict the origin age, initial body mass, and subsequent dynamics of body mass range for primate clades such as the New World monkeys (Platyrrhini, 32 million years ago, initial mass of 1.7 kg) and the Anthropoidea (57 million years ago, initial mass of 0.12 kg), tested against the primate fossil record. Using these methods, other major primate clades such as Lemuriformes and Adapoidea are also estimated to have originated in the Tertiary (63 and 64 million years ago, respectively), with only the Plesiadapiformes originating in the Cretaceous (83 million years ago). Similarities of body mass range between primate and other vertebrate sister groups are discussed. Linear relationships of log range and log duration are considered with respect to Brownian processes, with the expected regression coefficients from the latter explored through simulations. The observed data produce regression coefficients that overlap with or are higher than those under Brownian processes. Overall, the analyses suggest the dynamics of vertebrate body mass range in morphologically disparate clades are highly predictable over many tens of million years and that the dynamics of phenotypic characteristics can assist molecular clock and fossil models in dating evolutionary events.     

Validity of bioelectric impedance for body composition assessment in children

Whole-body bioelectrical impedance analysis (BIA) was evaluated for its reliability and accuracy in estimating body composition in children. The hypothesis that the index, body height2 divided by resistance (RI), can accurately predict fat-free body mass (FFB) and percent fat (%FAT) in children was tested on 94 caucasian children 10-14 yr old. Criterion variables were FFB and %FAT estimated using multicomponent equations developed for children. BIA measurements (resistance and reactance) were found to be reliable. Prediction accuracy (standard error of the estimate, SEE) for FFB from RI alone was 2.6 kg and for %FAT from RI and body weight was 4.2%. For RI, anthropometric variables and reactance, the SEE improved to 1.9 kg FFB. For RI and anthropometric variables, the SEE was 3.3% FAT. For anthropometric variables alone, the SEE's were 2.1 kg FFB and 3.2% FAT. Adult FFB and %FAT prediction equations cross-validated with this sample resulted in SEE's similar to those for adult samples. We conclude that RI together with anthropometry is a reliable and an acceptably accurate method of estimating FFB mass and %FAT in children.