The relative body fat and anthropometric prediction of body density of South Australian females aged 17-35 years

One hundred and thirty-five females were tested in order to: produce some normative percentage body fat (% BF) data on an Australian sample which represented a cross-section of physical activity patterns, cross-validate existing multiple regression equations which predict body density (BD) from anthropometric measurements, and if necessary develop population specific equations. Measurements were taken of 10 girths, 3 widths and 7 skinfolds. Body density was measured by underwater weighing with the residual volume (RV) being determined by helium dilution. The Siri equation was then used to convert BD to % BF. The % BF scores had an overall mean of 23.4 (range 10.8-49.2). The very active group (n = 45) had a significantly lower (p less than 0.05) relative body fat (X = 20.6% BF) than either the active (n = 45; 23.5% BF) or sedentary groups (n = 45; 26.2% BF). Previously published equations were found to have limited applicability to Australian subjects. A stepwise multiple regression was therefore used to develop the following equation (R = 0.893): BD(g X cm-3) = 1.16957-0.06447 (log10 sigma triceps, subscapular, supraspinale, front thigh, abdominal and calf skinfolds in mm)-0.00081 (gluteal girth in cm) + 0.0017 (forearm girth in cm) + 0.00606 (biepicondylar humerus breadth in cm). Only those predictors which resulted in a statistically significant increase in r (p less than or equal to 0.05) were included. The standard error of estimate of 0.00568 g X cm-3 was equivalent to 2.6% BF at the mean.     

Validation of tetrapolar bioelectrical impedance method to assess human body composition

This study was conducted to validate the relationship between bioelectrical conductance (ht2/R) and densitometrically determined fat-free mass, and to compare the prediction errors of body fatness derived from the tetrapolar impedance method and skinfold thicknesses, relative to hydrodensitometry. One-hundred and fourteen male and female subjects, aged 18-50 yr, with a wide range of fat-free mass (34-96 kg) and percent body fat (4-41%), participated. For males, densitometrically determined fat-free mass was correlated highly (r = 0.979), with fat-free mass predicted from tetrapolar conductance measures using an equation developed for males in a previous study. For females, the correlation between measured fat-free mass and values predicted from the combined (previous and present male data) equation for men also was strong (r = 0.954). The regression coefficients in the male and female regression equations were not significantly different. Relative to hydrodensitometry, the impedance method had a lower predictive error or standard error of the estimates of estimating body fatness than did a standard anthropometric technique (2.7 vs. 3.9%). Therefore this study establishes the validity and reliability of the tetrapolar impedance method for use in assessment of body composition in healthy humans.     

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.     

Validity of leg-to-leg bioelectrical impedance measurement in highly active women

The aim of this study was to compare the validity of the leg-to-leg bioelectrical impedance analysis (BIA) method with that of anthropometry using hydrostatic weighing (HW) as the criterion test. A secondary objective was to cross-validate previously developed anthropometric regression equations as well as to develop a new regression equation formula based on the anthropometric data collected in this study. Three methods for assessing body composition (HW, BIA, and anthropometric) were applied to 60 women university athletes. The means and standard deviations of age, weight, height, and body mass index (BMI) of athletes were as follows: age, 20.70 +/- 1.43; weight, 56.19 +/- 7.83 kg; height, 163.33 +/- 6.11 cm; BMI, 21.01 +/- 2.63 kg x m(-2). Leg-to-leg BIA (11.82 +/- 2.39) has shown no statistical difference between percentage body fat determined by HW (11.63 +/- 2.42%) in highly active women (p > 0.05). This result suggests that the leg-to-leg BIA and HW methods were somewhat interchangeable in highly active women (R = 0.667; standard error of estimate [SEE] = 1.81). As a result of all cross-validation analyses, anthropometric and BIA plus anthropometric results have generally produced lower regression coefficients and higher SEEs for highly active women between the ages of 18 and 25 years. The regression coefficients (0.903, 0.926) and SEE (1.08, 0.96) for the new regression formulas developed from this study were better than the all the other formulas used in this study.     

Comparison of estimation accuracy of body density between different hydrostatics weighing methods without head submersion

This study compared the accuracy of body density (Db) estimation methods using hydrostatic weighing without complete head submersion (HW(withoutHS)) of Donnelly et al. (1988) and Donnelly and Sintek (1984) as referenced to Goldman and Buskirk's approach (1961). Donnelly et al.'s method estimates Db from a regression equation using HW(withoutHS), moreover, Donnelly and Sintek's method estimates it from HW(withoutHS) and head anthropometric variables. Fifteen Japanese males (173.8+/-4.5 cm, 63.6+/-5.4 kg, 21.2+/-2.8 years) and fifteen females (161.4+/-5.4 cm, 53.8+/-4.8 kg, 21.0+/-1.4 years) participated in this study. All the subjects were measured for head length, width and HWs under the two conditions of with and without head submersion. In order to examine the consistency of estimation values of Db, the correlation coefficients between the estimation values and the reference (Goldman and Buskirk, 1961) were calculated. The standard errors of estimation (SEE) were calculated by regression analysis using a reference value as a dependent variable and estimation values as independent variables. In addition, the systematic errors of two estimation methods were investigated by the Bland-Altman technique (Bland and Altman, 1986). In the estimation, Donnelly and Sintek's equation showed a high relationship with the reference (r=0.960, p<0.01), but had more differences from the reference compared with Donnelly et al.'s equation. Further studies are needed to develop new prediction equations for Japanese considering sex and individual differences in head anthropometry.     

Peak vertical jump power estimations in youths and young adults

The purpose of this study was to develop and validate a regression equation to estimate peak power (PP) using a large sample of athletic youths and young adults. Anthropometric and vertical jump ground reaction forces were collected from 460 male volunteers (age: 12-24 years). Of these 460 volunteers, a stratified random sample of 45 subjects representing 3 different age groups (12-15 years [n = 15], 16-18 years [n = 15], and 19-24 years [n = 15]) was selected as a validation sample. Data from the remaining 415 subjects were used to develop a new equation ("Novel") to estimate PP using age, body mass (BM), and vertical jump height (VJH) via backward stepwise regression. Independently, age (r = 0.57), BM (r = 0.83), and VJ (r = 0.65) were significantly (p < 0.05) correlated with PP. However, age did not significantly (p = 0.53) contribute to the final prediction equation (Novel): PP (watts) = 63.6 × VJH (centimeters) + 42.7 × BM (kilograms) - 1,846.5 (r = 0.96; standard error of the estimate = 250.7 W). For each age group, there were no differences between actual PP (overall group mean ± SD: 3,244 ± 991 W) and PP estimated using Novel (3,253 ± 1,037 W). Conversely, other previously published equations produced PP estimates that were significantly different than actual PP. The large sample size used in this study (n = 415) likely explains the greater accuracy of the reported Novel equation compared with previously developed equations (n = 17-161). Although this Novel equation can accurately estimate PP values for a group of subjects, between-subject comparisons estimating PP using Novel or any other previously published equations should be interpreted with caution because of large intersubject error (± >600 W) associated with predictions.     

New equations for estimating body cell mass from bioimpedance parallel models in healthy older Germans

The objectives of this study were to assess for elderly Germans the validity of existing equations for predicting body cell mass (BCM) and to develop from single- and multifrequency bioimpedance (SFBIA, MFBIA) models new prediction equations. In a data-splitting approach, validation and cross-validation were performed in 160 healthy elderly (60- to 90-yr) subjects. BCM was determined using a tetrapolar bioimpedance analyzer (800 microA; 4 fixed frequencies: 1, 5, 50, and 100 kHz; electrodes placed to hand, wrist, ankle, and foot) and whole body (40)K counting as a reference method. New prediction equations were derived by multiple stepwise regression analysis. The Bland-Altman procedure was used for methods comparison. Relative to whole body counting, the manufacturer's equation overestimated BCM by 9% in men (P < 0.0001, paired t-test) and 4% in women (P = 0.002). Compared with the manufacturer's equation, the newly derived equations (r = 0.92, RMSE = 6-9%) improved accuracy (pure error = 13 vs. 7-8%) and reduced bias and limits of agreement. SFBIA and MFBIA equations did not differ in precision or accuracy. We conclude that the newly derived equations improved BCM estimates in the elderly compared with existing equations. There was no advantage of MFBIA over SFBIA equations.     

Relative body fat and anthropometric prediction of body density of female athletes

Ninety-one percent (n = 182) of the female members of South Australian representative squads in 14 sports volunteered to act as subjects. Twenty-seven percent of them had represented Australia. The underwater weighing method together with the measurement of residual volume (RV) by helium dilution were used to determine body density (BD); the percent body fat (% BF) was then computed according to Siri. A stepwise multiple regression analysis yielded a correlation coefficient (R) of 0.863 between the criterion (BD) and the best weighted sum of predictors (anthropometric variables): BD (g X cm-3) = 1.14075-0.04959 (log10 sigma triceps, subscapular, supraspinale and calf skinfolds in mm) + 0.00044 (age in decimal years)-0.000612 (waist girth in cm) + 0.000284 (height in cm)-0.000505 (gluteal girth in cm) + 0.000331 (breast girth in cm). Only those predictors which resulted in a statistically significant increase in R (p less than or equal to 0.05) were included. The standard error of estimate of 0.00597 g X cm-3 was equivalent to 2.7% BF at the mean. This equation was shown to be largely population specific. There was a range of 7.6-35.8% of BF and the overall mean 18.5% was significantly lower (p less than 0.001) than that of 23.4% obtained on a moderately active reference sample of similar age (n = 135). If group sizes of only one or two are regarded as too small for meaningful comparison, then the lowest mean of 13.5% was achieved by the long-distance runners (n = 14). The highest averages were registered by the heavyweight rowers (24.2%; n = 7) and soccer players (22.0%; n = 11). The overall average for games players (n = 107) was 19.4%.     

Prediction of metabolisable energy value of broiler diets and water excretion from dietary chemical analyses

Thirty various pelleted diets were given to broilers (8/diet) for in vivo measurements of dietary metabolisable energy (ME) value and digestibilities of proteins, lipids, starch and sugars from day 27 to day 31, with ad libitum feeding and total collection of excreta. Water excretion was also measured. Amino acid formulation of diets was done on the basis of ratios to crude proteins. Mean in vivo apparent ME values corrected to zero nitrogen retention (AMEn) were always lower than the AMEn values calculated for adult cockerels using predicting equations from literature based on the chemical analyses of diets. The difference between mean in vivo AMEn values and these calculated AMEn values increased linearly with increasing amount of wheat in diets (P = 0.0001). Mean digestibilities of proteins, lipids and starch were negatively related to wheat introduction (P = 0.0001). The correlations between mean in vivo AMEn values and diet analytical parameters were the highest with fibre-related parameters, such as water-insoluble cell-walls (WICW) (r = −0.91) or Real Applied Viscosity (RAV) (r = −0.77). Thirteen multiple regression equations relating mean in vivo AMEn values to dietary analytical data were calculated, with R² values ranging from 0.859 to 0.966 (P = 0.0001). The highest R² values were obtained when the RAV parameter was included in independent variables. The direct regression equations obtained with available components (proteins, lipids, starch, sucrose and oligosaccharides) and the indirect regression equations obtained with WICW and ash parameters showed similar R² values. Direct or indirect theoretical equations predicting AMEn values were established using the overall mean in vivo digestibility values. The principle of indirect equations was based on the assumption that WICW and ashes act as diluters. Addition of RAV or wheat content in variables improved the accuracy of theoretical equations. Efficiencies of theoretical equations for predicting AMEn values were almost the same as those of multiple regression equations. Water excretion was expressed either as the water content of excreta (EWC), the ratio of water excretion to feed intake (WIR) or the residual value from the regression equation relating water excretion to feed intake (RWE). The best regression predicting EWC was based on sucrose, fermentable sugars (lactose + oligosaccharides) and chloride variables, with positive coefficients. The best equations predicting WIR or RWE contained the sugar and chloride variables, with positive coefficients. Other variables appearing in these equations were AMEn or starch with negative coefficients, WICW, ‘cell-wall-retained water’, RAV or potassium with positive coefficients.     

Adipose tissue volume measured by magnetic resonance imaging and computerized tomography in rats

The primary purpose of this study was to investigate the viability of magnetic resonance imaging (MRI) as a means of measuring the body composition of rodents. To do so we compared adipose tissue (AT) volumes measured by MRI with those obtained by X-ray computerized tomography (CT) in a group of rats (n = 17) varying in weight (465-815 g) and percent body fat (5.4-31.1%), with the latter determined by chemical analysis. For both MRI and CT, AT volumes (cm3) per transverse slice (3-mm thickness, 21-mm centers) were determined using a computer-based image analysis system that permitted detailed comparisons of both visceral and subcutaneous AT depots. Total AT volumes were calculated using a linear interpolation of AT areas obtained on consecutive slices. Correlation coefficients between MRI and CT for visceral [r = 0.98, standard error of estimate (SEE) = 6.8 cm3], subcutaneous (r = 0.98, SEE = 6.5 cm3), and total AT volumes (r = 0.99, SEE = 9.0 cm3) were highly significant (P less than 0.001). Both MRI- and CT-predicted AT mass (assuming fat density = 0.90 g/ml) correlated strongly with chemically extracted lipid (grams) values (r = 0.98, SEE 9.6 g and r = 0.99, SEE = 6.9 g, respectively). Post hoc Scheffé contrasts demonstrated that the mean AT and lipid mass values derived by the three methods were not significantly different (P = 0.01). No systematic differences were observed because the regression lines derived for either MRI or CT vs. chemical analysis were not significantly different from the identity line.(ABSTRACT TRUNCATED AT 250 WORDS)     

Predicting anaerobic capabilities in 11-13-year-old boys

Anaerobic exercise is involved in many recreational and competitive sport activities. This study first established regression equations to predict maximal anaerobic power and then cross-validated these prediction equations. Using stepwise multiple regression analysis prediction equations for relative (watts per kilogram of body mass) and absolute (watts) mean and peak anaerobic power using the 30-second Wingate Test as the power measure were determined for 40 boys (age, 11-13 years). Percentage of body fat, free-fat weight, midthigh circumference, and 30-m dash were the independent predictive variables with the generated regression equations subsequently cross-validated using 20 different boys (age, 11-13 years). Significant correlations (Pearson r) were found for the cross-validation subjects between the measured power outputs and predicted power outputs for relative mean power (r = 0.48, p < 0.05), absolute mean power (r = 0.77, p < 0.01), and absolute peak power (r = 0.76, p < 0.01). Using paired t-tests, no significant mean differences (p > 0.05) were found for the same subjects between actual and predicted power outputs for relative mean power, absolute mean power, and absolute peak power. Prediction of maximal anaerobic power from selected anthropometric measurements and 30-m dash appears tenable in 11-13-year-old boys and can be accomplished in a simple cost- and time-effective manner.     

大兴安岭东部主要林分类型乔木层生物量估算模型

大尺度森林生物量的估算方法是人们目前关注的焦点,建立林分生物量模型成为一种趋势.本研究以大兴安岭东部6个主要林分类型为研究对象,构建了其总量及各分项一元、二元可加性林分生物量模型.采用似然分析法判断总量及各分项生物量异速生长模型的误差结构(可加型或相乘型),采用非线性似乎不相关回归模型方法估计模型参数.结果表明: 经似然分析法判断,大兴安岭东部6个主要林分类型总量及各分项生物量异速生长模型的误差结构都是相乘型的,对数转换的可加性生物量可以被选用.各林分类型可加性生物量模型的调整后确定系数为0.78～0.99,平均相对误差为-2.3%～6.9%,平均相对误差绝对值6.3%～43.3%.增加林分平均高可以提高绝大多数生物量模型的拟合效果和预测能力,而且总量、地上和树干生物量模型效果较好,树根、树枝、树叶和树冠生物量模型效果较差.为了使模型参数估计更有效,所建立的生物量模型应当考虑林分总生物量及各分项生物量的可加性.本研究建立的林分总量与各分项生物量模型都能对大兴安岭东部6个主要林分类型生物量进行较好的估计.     

Total lung capacity of baboons and humans determined by planimetry of radiographs.

Total lung capacity and radiographic lung area of 25 young and 7 aged baboons (Papio cynocephalus) and seven nonsmoking young adult men were measured. For all subjects, total lung capacity and radiographic lung area raised to the 3/2 power were shown to be highly correlated (r = 0.995). The regression equation for this relationship was total lung capacity (ml) = 78 + 0.234 x radiographic lung area (1.5) (cm2). A more useful regression equation for predicting values of total lung capacity was found to be log total lung capacity = -0.3819 + 1.4153 x log radiographic lung area (r = 0.993), because the standard error of estimate remains a constant percentage of Y values (+/- 12%). Total lung capacity and radiographic lung area were also highly correlated with height, weight and arm span of young baboons and men (r greater than 0.92), but the lungs of aged baboons were disproportionately larger.     

东北林区4个天然针叶树种单木生物量模型误差结构及可加性模型

基于276株实测生物量数据,构建了东北林区红松、臭冷杉、红皮云杉和兴安落叶松4个天然针叶树种总量及各分项生物量一元、二元可加性生物量模型.采用似然分析法判断总量及各分项生物量异速生长模型的误差结构(可加型或相乘型),而模型参数估计采用非线性似乎不相关回归模型方法.结果表明: 经似然分析法判断,4个天然树种总量及各分项生物量异速生长模型的误差结构都是相乘型的,对数转换的可加性生物量可以被选用.各树种可加性生物量模型的调整后确定系数R_a²为0.85～0.99,平均相对误差为-7.7%～5.5%,平均相对误差绝对值<30.5%.增加树高可以显著提高各树种可加性生物量模型的拟合效果和预测能力,而且总量、地上和树干生物量模型效果较好,树根、树枝、树叶和树冠生物量模型效果较差.所建立的可加性生物量模型的预测精度为77.0%～99.7%(平均92.3%),可以很好地预估东北林区天然红松、臭冷杉、红皮云杉和兴安落叶松的生物量.
     

Does the weight of the brain depend on the body height?]

Brains of 1664 subjects (895 males and 769 females) aged from 20 to 89 years have been studied. The whole material being investigated was divided, within sex groups, into body-height classes and age classes. The class interval within the age classes was 10 years, that in height classes 5 cm. Mean arithmetics, standard deviations, standard error as well as coefficients of variation and correlation for respective classes have been calculated. It has been ascertained that the brain weight depends on the body height. In tall subjects no brains of extremely low absolute weight are encountered and, adversely, high brain weight is seldom met in short individuals. The body height also exerts certain influence upon the relative weight of the brain. More favourable proportion between the brain weight and the body length has been revealed in short subjects. Tall individuals are characterized by a low relative weight of the brain. It should be supposed that the spinal cord weight is higher in the latter subjects. The differences between the mean absolute weight of women's brains and that in men of the same age class are conditioned by the difference in the body length. A constant magnitude of difference in the mean brain weight in subjects of the same body height claims 100 g. The paper provides 2 enclosed tables representing obtained results for arithmetic mean of the absolute brain weight both in the age classes and body height classes. The differences between the mean weights of brains in women as well as in men are not significant. The coefficient of correlation between the brain weight and the body height is for men r male1 = 0.2008 for women r female1 = 0.2630, wherease the coefficient of regression for the brain weight is r male2 = 3.67 and r female2 = 3.906 respectively.     

A new non-exercise-based Vo2max prediction equation for aerobically trained men

The purposes of the present study were to (a) modify previously published Vo(2)max equations using the constant error (CE = mean difference between actual and predicted Vo(2)max) values from Malek et al. (28); (b) cross-validate the modified equations to determine their accuracy for estimating Vo(2)max in aerobically trained men; (c) derive a new non- exercise-based equation for estimating Vo(2)max in aerobically trained men if the modified equations are not found to be accurate; and (d) cross-validate the new Vo(2)max equation using the predicted residual sum of squares (PRESS) statistic and an independent sample of aerobically trained men. One hundred and fifty-two aerobically trained men (Vo(2)max mean +/- SD = 4,154 +/- 629 ml.min(-1)) performed a maximal incremental test on a cycle ergometer to determine actual Vo(2)max. An aerobically trained man was defined as someone who had participated in continuous aerobic exercise 3 or more sessions per week for a minimum of 1 hour per session for at least the past 18 months. Nine previously published Vo(2)max equations were modified for use with aerobically trained men. The predicted Vo(2)max values from the 9 modified equations were compared to actual Vo(2)max by examining the CE, standard error of estimate (SEE), validity coefficient (r), and total error (TE). Cross-validation of the modified non-exercise-based equations on a random subsample of 50 subjects resulted in a %TE > or = 13% of the mean of actual Vo(2)max. Therefore, the following non-exercise-based Vo(2)max equation was derived from a random subsample of 112 subjects: Vo(2)max (ml.min(-1)) = 27.387(weight in kg) + 26.634(height in cm) - 27.572(age in years) + 26.161(h.wk(-1) of training) + 114.904(intensity of training using the Borg 6-20 scale) + 506.752(natural log of years of training) - 4,609.791 (R = 0.82, R(2) adjusted = 0.65, and SEE = 378 ml.min(-1)). Cross-validation of this equation on the remaining sample of 40 subjects resulted in a %TE of 10%. Therefore, the non-exercise-based equation derived in the present study is recommended for estimating Vo(2)max in aerobically trained men.     

Validity of two-component models for estimating body fat of black men.

Commonly used two-component model conversion formulas that estimate relative body fat (%BF) from body density (Db) were cross-validated on a heterogeneous sample of black men (n = 30; age = 19--45 yr). A four-component model was used to obtain criterion measures of %BF, and linear regression and analysis of individual residual scores were conducted to assess the predictive accuracy of the formulas under investigation. The two-component formula commonly used to estimate %BF of black men (Schutte JE, Townsend EJ, Hugg J, Shoup RF, Malina RM, and Blomqvist CG. J Appl Physiol 56: 1647-1649, 1984) significantly (P < or = 0.01) and systematically (87% of sample) overestimated %BF (-1.28%); thus we developed the following two-component Db conversion formula: %BF = [(4.858/Db) - 4.394] x 100. Because our formula was derived from a four-component model and a larger, more heterogeneous sample than the commonly used two-component formula, we recommend using it to convert Db to %BF for black men. Additionally, there was good agreement between dual-energy X-ray absorptiometry and the four-component model, making this a suitable alternative for estimating the %BF of black men.     

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.