Estimating utilization distributions with kernel versus local convex hull methods

Estimates of utilization distributions (UDs) are used in analyses of home-range area, habitat and resource selection, and social interactions. We simulated data from 12 parent UDs, representing 3 series of increasingly intense space-use patterns (clustering of points around a home site, restriction of locations to a network of nodes and corridors, and dominance of a central hole in the UD) and compared the ability of kernel density estimation (KDE) and local convex hull (LCH) construction to reconstruct known UDs from samples of 10, 50, 250, and 1,000 location points. For KDE, we considered 4 bandwidth selectors: the reference bandwidth, least-squares cross-validation (LSCV), direct plug-in (DPI), and solve-the-equation (STE). For the sample sizes and UD patterns tested here, KDE achieved significantly higher volume-of-intersection (VI) scores with known parent UDs than did LCH; KDE also provided less biased home-range area estimates under many conditions. However, LCH minimized the UD volume that occurred outside the true home range boundary (V_out). Among the KDE bandwidth estimators, relative performance depended on the type and intensity of space use patterns, sample size, and the metric used to evaluate performance. Biologists should use KDE for UD and home range estimation within a probabilistic context, unless their objective is to exclude potentially unused areas by defining the area delimited by data. © 2011 The Wildlife Society.     

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.     

Testing for size and allometric differences in fossil hominin body mass estimation

Body size reconstructions of fossil hominins allow us to infer many things about their evolution and lifestyle, including diet, metabolic requirements, locomotion, and brain/body size relationships. The importance of these implications compels anthropologists to attempt body mass estimation from fragmentary fossil hominin specimens. Most calculations require a known “calibration” sample usually composed of modern humans or other extant apes. Caution must be taken in these analyses, as estimates are sensitive to overall size and allometric differences between the fossil hominin and the reference sample. Am J Phys Anthropol 151:215–229, 2013. © 2013 Wiley Periodicals, Inc.     

Craniodental body mass estimators in the dwarf bushbaby (Galagoides)

This study reports data on 17 craniodental body mass estimators in a sample (n = 38) of dwarf galagos (Galagoides). Correlation coefficients (r) range from a high of 0.64 for bizygomatic breadth and body mass to a low of 0.10 for M(3) length and body mass. Of the 17 variables studied, 7 exhibit significant (P < 0.05) correlation coefficients, with 5 of the 7 being multitooth (i.e., tooth row) or cranial variables. In contrast to the correlation coefficients of greater than 0.90 (e.g., Martin [1980] Z Morphol Anthropol 71:115-124; Steudel [1981] Int J Primatol 2:81-90; Gingerich et al. [1982] Am J Phys Anthropol 58:81-100; Conroy [1987] Int J Primatol 8:115-137) published for higher taxonomic level analyses (i.e., all-primate or prosimian) for many of the same variables studied here, the current data indicate weaker relationships when analyzed at the generic level. Possible explanations for the contrast in correlation coefficients between the current and many previous studies include the following: 1) individual variation due to a geographically dispersed sample, 2) individual body mass fluctuations due to seasonal food availability, and 3) individual variation within the sample due to variation in life-history parameters. Because the overall size range of the individuals in a specific or generic level analysis is smaller than that in an ordinal or subordinal sample, the individual variation normally masked when using species means represents a larger proportion of the total variation in a more limited sample. This may then be a cause of these weaker correlations.     

Body mass estimates of an exceptionally complete Stegosaurus (Ornithischia: Thyreophora): comparing volumetric and linear bivariate mass estimation methods

Body mass is a key biological variable, but difficult to assess from fossils. Various techniques exist for estimating body mass from skeletal parameters, but few studies have compared outputs from different methods. Here, we apply several mass estimation methods to an exceptionally complete skeleton of the dinosaur Stegosaurus. Applying a volumetric convex-hulling technique to a digital model of Stegosaurus, we estimate a mass of 1560 kg (95% prediction interval 1082–2256 kg) for this individual. By contrast, bivariate equations based on limb dimensions predict values between 2355 and 3751 kg and require implausible amounts of soft tissue and/or high body densities. When corrected for ontogenetic scaling, however, volumetric and linear equations are brought into close agreement. Our results raise concerns regarding the application of predictive equations to extinct taxa with no living analogues in terms of overall morphology and highlight the sensitivity of bivariate predictive equations to the ontogenetic status of the specimen. We emphasize the significance of rare, complete fossil skeletons in validating widely applied mass estimation equations based on incomplete skeletal material and stress the importance of accurately determining specimen age prior to further analyses.     

黎族人的瘦体与脂肪质量指数

2014年11月在海南省五指山市5个黎族村寨测量了607例(男为308例,女为299例)黎族人体质量、身高等6项体成分指标值,计算了黎族人的体脂率(P_(bf))、瘦体质量(m_l)、脂肪质量(m_f)、瘦体质量指数(I_(lm))、脂肪质量指数(I_(fm))。研究发现,女性体脂率、脂肪质量、脂肪质量指数都明显大于男性,瘦体质量、瘦体质量指数均明显小于男性。随年龄增长,黎族人身高、瘦体质量逐渐减小,体脂率、脂肪质量、脂肪质量指数逐渐增大。受试者特征曲线显示身体质量指数、脂肪质量指数都可以适宜评价黎族人的体脂率,而且脂肪质量指数对体脂率的估算准确性比身体质量指数更高。这也提示脂肪质量指数是比身体质量指数评价肥胖更好的指标。     

Age variations in the relation of body mass indices to estimates of body fat and muscle mass

In some chronic disease studies, distinctions have been made regarding the importance of body mass index (BMI) as a risk factor in younger versus older men and women. In order to determine the significance of these differences in BMI-disease associations, we determined the extent of age-dependent variations in the relation of BMIs to body composition in large probability samples of U.S. men and women from the First and Second U.S. National Health and Nutrition Examination Surveys (NHANES I and II). BMIs are more highly correlated with estimates of body fat in younger than in older men and women, and with muscle mass in older than in younger adults. Caution should be exercised in interpreting the significance of BMI as a risk factor for chronic disease, particularly in comparison of age groups.     

Estimating fossil hominin body mass from cranial variables: An assessment using CT data from modern humans of known body mass

Body mass estimates are integral to a wide range of inferences in paleoanthropology. Most techniques employ postcranial elements, but predictive equations based on cranial variables have also been developed. Three studies currently provide regression equations for estimating mass from cranial variables, but none of the equations has been tested on samples of known mass. Nor have the equations been compared to each other in terms of performance. Consequently, this study assessed the performance of existing cranial equations using computed tomography scans from a large, documented sample of modern humans of known body mass. Virtual models of the skull were reconstructed and measured using computer software, and the resulting variables were entered into three sets of published regression equations. Estimated and known body masses were then compared. For most equations, prediction errors were high and few individuals were estimated within ±20% of their known mass. Only one equation satisfied the accuracy criteria. In addition, variables that had been previously argued to be good predictors of mass in hominins, including humans, did not estimate mass reliably. These results have important implications for paleoanthropology. In particular, they emphasize the need to develop new equations for estimating fossil hominin body mass from cranial variables. Am J Phys Anthropol 154:201–214, 2014. © 2014 Wiley Periodicals, Inc.     

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.     

Scaling of the limb long bones to body mass in terrestrial mammals

Long‐bone scaling has been analyzed in a large number of terrestrial mammals for which body masses were known. Earlier proposals that geometric or elastic similarity are suitable as explanations for long‐bone scaling across a large size range are not supported. Differential scaling is present, and large mammals on average scale with lower regression slopes than small mammals. Large mammals tend to reduce bending stress during locomotion by having shorter limb bones than predicted rather than by having very thick diaphyses, as is usually assumed. The choice of regression model used to describe data samples in analyses of scaling becomes increasingly important as correlation coefficients decrease, and theoretical models supported by one analysis may not be supported when applying another statistical model to the same data. Differences in limb posture and locomotor performance have profound influence on the amount of stress set up in the appendicular bones during rigorous physical activity and make it unlikely that scaling of long bones across a large size range of terrestrial mammals can be satisfactorily explained by any one power function. J. Morphol. 239:167–190, 1999. © 1999 Wiley‐Liss, Inc.     

The relationship between body mass and relative investment in testes mass in cetaceans: Implications for inferring interspecific variations in the extent of sperm competition

Based on sperm competition theory, percentage testes mass (% of total body mass) has been used to infer variations in the extent of sperm competition within mating systems of cetaceans. However, in most amniote taxa, including mammals, there is an underlying negative relationship between body mass and relative investment in testes mass, which must first be taken into account. Here, I identify a very strong nonlinear, negative relationship between body mass in cetaceans and relative investment in testes mass based on data from 31 species. As a result, if percentage testes mass alone is used to infer the relative extent of sperm competition in cetaceans, its importance in mating systems of smaller species is likely to be overestimated, whereas its role in larger species is likely to be underestimated. Similarly, there will also be systematic biases if this relationship is assumed to be linear when it is not. Therefore, it is essential that the underlying, nonlinear body mass–testes mass relationship is correctly taken into account when using relative investment in testes mass to estimate the relative levels of sperm competition in cetaceans. This is particularly important if such inferences are used to inform conservation strategies for endangered cetacean species.     

The influence of body size on adult skeletal age estimation methods

Accurate age estimations are essential to archaeological and forensic analyses. However, reliability for adult skeletal age estimations is poor, especially for individuals over the age of 40 years. This is the first study to show that body size influences skeletal age estimation. The ??can et al., Lovejoy et al., Buckberry and Chamberlain, and Suchey‐Brooks age methods were tested on 764 adult skeletons from the Hamann‐Todd and William Bass Collections. Statures ranged from 1.30 to 1.93 m and body masses ranged from 24.0 to 99.8 kg. Transition analysis was used to evaluate the differences in the age estimations. For all four methods, the smallest individuals have the lowest ages at transition and the largest individuals have the highest ages at transition. Short and light individuals are consistently underaged, while tall and heavy individuals are consistently overaged. When femoral length and femoral head diameter are compared with the log‐age model, results show the same trend as the known stature and body mass measurements. The skeletal remains of underweight individuals have fewer age markers while those of obese individuals have increased surface degeneration and osteophytic lipping. Tissue type and mechanical loading have been shown to affect bone turnover rates, and may explain the differing patterns of skeletal aging. From an archaeological perspective, the underaging of light, short individuals suggests the need to revisit the current research consensus on the young mortality rates of past populations. From a forensic perspective, understanding the influence of body size will impact efforts to identify victims of mass disasters, genocides, and homicides. Am J Phys Anthropol 156:35–57, 2015 © 2014 Wiley Periodicals, Inc.     

Satellite‐derived estimations of spatial and seasonal variation in tropospheric carbon dioxide mass over China

China has frequently been questioned about the data transparency and accuracy of its energy and emission statistics. Satellite‐derived remote sensing data potentially provide a useful tool to study the variation in carbon dioxide (CO₂) mass over areas of the earth's surface. In this study, Greenhouse gases Observing SATellite (GOSAT) tropospheric CO₂ concentration data and NCEP/NCAR reanalysis tropopause data were integrated to obtain estimates of tropospheric CO₂ mass variations over the surface of China. These variations were mapped to show seasonal and spatial patterns with reference to China's provincial areas. The estimates of provincial tropospheric CO₂ were related to statistical estimates of CO₂ emissions for the provinces and considered with reference to provincial populations and gross regional products (GRP). Tropospheric CO₂ masses for the Chinese provinces ranged from 53 ± 1 to 14,470 ± 63 million tonnes were greater for western than for eastern provinces and were primarily a function of provincial land area. Adjusted for land area troposphere CO₂ mass was higher for eastern and southern provinces than for western and northern provinces. Tropospheric CO₂ mass over China varied with season being highest in July and August and lowest in January and February. The average annual emission from provincial energy statistics of CO₂ by China was estimated as 10.3% of the average mass of CO₂ in the troposphere over China. The relationship between statistical emissions relative to tropospheric CO₂ mass was higher than 20% for developed coastal provinces of China, with Shanghai, Tianjin, and Beijing having exceptionally high percentages. The percentages were generally lower than 10% for western inland provinces. Provincial estimates of emissions of CO₂ were significantly positively related to provincial populations and gross regional products (GRP) when the values for the provincial municipalities Shanghai, Tianjin, and Beijing were excluded from the linear regressions. An increase in provincial GRP per person was related to a curvilinear increase in CO₂ emissions, this being particularly marked for Beijing, Tianjin, and especially Shanghai. The absence of detection of specific elevation of CO₂ mass in the troposphere above these municipalities may relate to the rapid mixing and dispersal of CO₂ emissions or the proportion of the depth of the troposphere sensed by GOSAT.     

Evaluation of juvenile stature and body mass prediction

This investigation evaluates the performance of juvenile stature (from tibia and radius lengths) and body mass (from breadth of the femoral distal metaphysis) prediction equations based on the Denver Growth Study sample (Ruff C. 2007. Am J Phys Anthropol 133 698-716). The sample used here for evaluation is an independent sample of juveniles brought to the Franklin County (Ohio) Coroner in 1990-1991. The Ohio sample differs somewhat from the Denver reference sample: it includes approximately 25% African-Americans (rather than all European-Americans), a significant number of right limb bones were measured (rather than all left side), it includes a wider range of economic statuses and it includes individuals who died from disease and trauma. As such the composition and measures of the Ohio sample correspond more generally to that seen in skeletal samples so that the accuracy of the estimates from the present sample should approach those found in practical applications of these methods. Results indicate that both juvenile body mass and stature are estimated relatively accurately. Accuracy of body mass estimates for 1-13-year-old juveniles is similar for African-American and European-American males and females. The least accurate estimates are for individuals in the 8-13 years age class (excluding individuals with body mass indices greater than the age specific 95th percentile): n = 9, +/- 2.9 kg, 95% confidence interval 1.4-4.4 kg. Accuracy of stature estimates for 1-17-year-old juveniles is comparable for the tibia and radius and, as with body mass estimates, are similar for African-American and European-American males and females. For combined age, sex, and ancestry groups average accuracies are in the +/-3.5 to +/-6.5 cm range. Some limitations of the methods are discussed.     

Estimating the critical body mass of king penguins

King penguins (Aptenodytes patagonicus) can fast for over a month. However, they return to sea to forage before their body mass reaches a critical value (cMb), beyond which there is an increase in rate of mass loss and in protein catabolism, termed phase III of fasting. Thus when studying king penguins onshore, accurate estimation of their cMb and, in turn, the date at which that body mass would be reached, will be informative to behavioural and physiological data being collected. For penguins being studied during fasts in captivity, knowing cMb is particularly important because of the need to release the birds back into their colony while they are still in good nutritional condition. The present study investigates the validity of using measures of beak, flipper and foot length together to estimate cMb in king penguins and provides a simple and effective prediction equation for researchers. The three morphometric measurements, along with body mass just prior to going to sea after the moult fast (taken to represent cMb), were obtained for nine king penguins in a colony at the Crozet Archipelago. A multiple linear regression of the three morphometric measurements against cMb provided an R ² of 71.2%. Mean absolute percentage error of the estimate of cMb over the nine birds was 8.82 ± 1.20%. The described technique could probably be employed for estimating cMb in other long-fasting seabirds.     

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.