Elsevier

Journal of Human Evolution

Volume 115, February 2018, Pages 47-64
Journal of Human Evolution

A volumetric technique for fossil body mass estimation applied to Australopithecus afarensis

https://doi.org/10.1016/j.jhevol.2017.07.014Get rights and content

Abstract

Fossil body mass estimation is a well established practice within the field of physical anthropology. Previous studies have relied upon traditional allometric approaches, in which the relationship between one/several skeletal dimensions and body mass in a range of modern taxa is used in a predictive capacity. The lack of relatively complete skeletons has thus far limited the potential application of alternative mass estimation techniques, such as volumetric reconstruction, to fossil hominins. Yet across vertebrate paleontology more broadly, novel volumetric approaches are resulting in predicted values for fossil body mass very different to those estimated by traditional allometry. Here we present a new digital reconstruction of Australopithecus afarensis (A.L. 288-1; ‘Lucy’) and a convex hull-based volumetric estimate of body mass. The technique relies upon identifying a predictable relationship between the ‘shrink-wrapped’ volume of the skeleton and known body mass in a range of modern taxa, and subsequent application to an articulated model of the fossil taxa of interest. Our calibration dataset comprises whole body computed tomography (CT) scans of 15 species of modern primate. The resulting predictive model is characterized by a high correlation coefficient (r2 = 0.988) and a percentage standard error of 20%, and performs well when applied to modern individuals of known body mass. Application of the convex hull technique to A. afarensis results in a relatively low body mass estimate of 20.4 kg (95% prediction interval 13.5–30.9 kg). A sensitivity analysis on the articulation of the chest region highlights the sensitivity of our approach to the reconstruction of the trunk, and the incomplete nature of the preserved ribcage may explain the low values for predicted body mass here. We suggest that the heaviest of previous estimates would require the thorax to be expanded to an unlikely extent, yet this can only be properly tested when more complete fossils are available.

Introduction

Body mass is a critical constraint on an organism's ecology, physiology, and biomechanics, and is a required input parameter in many ecological and functional analyses. For paleontologists, it is thus highly desirable to reconstruct body mass for fossil species. Indeed, important studies concerning the evolution of brain size (McHenry, 1976), locomotor kinematics (Polk, 2004), and energetics (Steudel-Numbers, 2006) in hominins have all required reliable fossil body mass estimates.

The fossil record is, however, extremely fragmentary and the majority of specimens are known only from isolated elements. For this reason, the most common approach to mass estimation exploits a tight correlation between body mass and a given skeletal dimension or dimensions in a modern calibration dataset to derive a predictive equation. Within the field of physical anthropology, cranial metrics have been used in a predictive capacity, including orbital area (Kappelman, 1996), orbital height (Aiello and Wood, 1994), and facial breadth (Spocter and Manger, 2007). However, far more common are mass prediction equations based on postcranial elements, which Auerbach and Ruff (2004) subdivide into ‘mechanical’ and ‘morphometric’ methods on the basis of the chosen skeletal element. Mechanical techniques employ postcranial, mass supporting structures as a basis for predictive equations, including knee breadth (Squyres and Ruff, 2015), vertebral centrum area (McHenry, 1976), femoral head and neck breadth (Ruff et al., 1991), and humeral and radial head diameter (McHenry, 1992). Alternatively, morphometric techniques reconstruct fossil mass based on the direct assessment of body size and shape. For example, a series of studies (Ruff, 1994, Ruff, 2000, Ruff et al., 2005) have found the combination of stature and biiliac breadth to provide relatively accurate estimates of body mass when applied to modern humans. Footprint area (as measured from fossil trackways) has even been used as a means of reconstructing hominin body mass (Dingwall et al., 2013, Masao et al., 2016).

Whilst bivariate and multivariate mass predictive equations benefit from their applicability to fragmentary material and the ability to generate large modern comparative datasets, there are associated disadvantages: which skeletal element to use, extrapolation, biasing by robust/gracile elements, and mass and inertia properties.

When numerous skeletal elements are available for a particular fossil individual, it may be unclear which bony dimension ought to be used as a basis for mass prediction. If both a complete femur and tibia are available, for example, either could be considered a suitable mass-supporting structure upon which to base a fossil mass estimate. Yet previous research estimating body mass for non-primate fossil mammals demonstrates that estimates can span two orders of magnitude for the same individual depending on which limb bone or skeletal metric was used for prediction (Fariña et al., 1998). This example includes unusually proportioned mammals such as xenarthrans, and mass estimates for fossil hominins are not known to vary to such a degree (e.g., McHenry's [1992] estimates for the A. afarensis skeleton A.L. 288-1 based on different anatomical parts range between 11.8 and 37.1 kg). However, McHenry and Berger (1998) do highlight the potential for hominin mass estimates to vary considerably depending upon the use of forelimb or hind limb joint size as the basis for the predictive equation. Ultimately, a decision must still be made on which equation to use, taking into account the predictive power of the model (r2 or percentage prediction error) and the existence of taphonomic damage or unusual morphology, for example, that may otherwise bias the result.

Whilst typically less extreme in paleoanthropology compared to other disciplines of vertebrate paleontology, body mass estimations are often conducted on fossil specimens lying outside the range of body sizes occupied by the modern calibration dataset. Potential dwarfism (Brown et al., 2004, Vančata, 2005, Holliday and Fransiscus, 2009, Stein et al., 2010, Herridge and Lister, 2012) and gigantism (Millien and Bovy, 2010, Bates et al., 2015) are recurrent themes for fossil mass reconstructions, yet by their very nature they require an extrapolation of a predictive relationship beyond the modern range. In such instances, extrapolated predictions should be regarded as extremely speculative (Smith, 2002) due to a lack of evidence that the linear model holds beyond the extant dataset and a rapid widening of confidence intervals around the prediction.

Underlying the theory of bivariate/multivariate mass prediction is the assumption that the relationship between mass and a given skeletal dimension identified in modern species also holds for the fossil species of interest. In some instances, however, we can intuitively appreciate that species may be characterized by unusually proportioned skeletal elements (the elongated canines of sabertoothed cats or the robust hind the limb bones of some moa birds, for example). When placed into the context of the rest of the body, such enlarged/reduced features are obvious. Should such structures be used as a basis for mass estimation, however, unfeasibly large/small fossil species will be reconstructed (Braddy et al., 2008 versus Kaiser and Klok, 2008, Brassey et al., 2013). This is a particular concern when dealing with isolated elements in the absence of complete skeletons, where relative robustness/gracility cannot be known. In physical anthropology, for example, the mass estimation of Gigantopithecus on the basis of molar size (Conroy, 1987) or mandible size (Fleagle, 2013) is vulnerable to this problem.

Currently, traditional allometric predictive relationships produce a solely scalar value for body mass (i.e., X species weighed Y kg). Whilst these single values may be of use in subsequent ecological analyses or evolutionary models, they are not informative with regards to how said mass is distributed around the body. Inertial properties (including mass, center of mass, and moments of inertia) are essential when conducting biomechanical simulations such as multibody dynamic analyses of locomotion and feeding. Previous biomechanical analyses of fossil hominins have therefore reconstructed inertial parameters on the basis of modern human and chimpanzee values (Crompton et al., 1998, Kramer and Eck, 2000, Sellers et al., 2004), due to a lack of viable alternatives.

For the above reasons, volumetric mass estimation techniques have become increasingly popular within the field of vertebrate paleontology (see Brassey, 2017 and references therein). Historically, volume based estimates required the sculpting of scale models and the estimation of volume via fluid displacement (Gregory, 1905, Colbert, 1962, Alexander, 1985). However, as part of the recent shift towards ‘virtual paleontology’ (Sutton et al., 2014; as characterized by the increased application of digital imaging techniques such as computed tomography, laser scanning, and photogrammetry), three-dimensional (3D) computational modeling of fossil species is becoming increasingly common. As articulated skeletons are digitized faster and with greater accuracy, volumetric mass estimation techniques now involve the fitting of simple geometric shapes (Gunga et al., 1995, Gunga et al., 1999) or more complex contoured surfaces (Hutchinson et al., 2007, Bates et al., 2009) to digital skeletal models within computer-aided design (CAD) packages. Volumetric approaches overcome many of the limitations associated with traditional allometric mass estimation methods, including the need to extrapolate predictive models and rely upon single elements, whilst also allowing inertial properties to be calculated if desired.

Both physical sculpting and digital CAD ‘sculpting’ of 3D models inevitably involves some degree of artistic interpretation, however. By attempting to reconstruct the external appearance of an extinct species, assumptions must be made regarding the volume and distribution of soft tissues beyond the extent of the skeleton. Whilst those undertaking such modeling necessarily rely upon their experience as anatomists to inform reconstructions, previous research has found resulting mass estimates to be sensitive to the individual carrying out the procedure (Hutchinson et al., 2011). The convex hulling technique applied in the present paper was therefore developed with the aim of incorporating many of the benefits associated with volumetric mass estimation, whilst overcoming the subjectivity inherent in ‘sculpted’ models (Sellers et al., 2012).

A convex hull is a geometric construct commonly used within mathematical sciences. The convex hull of n points is simply the minimum size convex polytope that still contains n (Fig. 1). In two dimensions, the process is analogous to stretching an elastic band around a series of points, with the band ‘snapping-to’ the outermost points. The ultimate form of the hull is dictated by a small number of points lying at the extremities, and for a given set of points, there is a unique convex hull. Two-dimensional (2D) convex hulls have often been applied in ecology as a means of defining the range size of wild animals (Harris et al., 1990 and references therein) or quantifying population niche width around stable isotopic data (Syväranta et al., 2013). A 3D convex hull can, likewise, be fitted to a suite of x, y, z coordinates to form a tight-fitting 3D polyhedron (Fig. 2). Three-dimensional convex hulls are more commonly applied within the fields of robotics and computer games design to rapidly detect potential collisions between objects (Jiménez et al., 2001), but have also been applied in the biological sciences to estimate volume of crop yield (Herrero-Huerta et al., 2015) or canopy foliage (Cheein and Guivant, 2014).

Sellers et al. (2012) initially developed the convex hull mass prediction technique on a dataset of modern quadrupedal mammals. Using a light detection and range (LiDAR) scanner, the articulated skeletons of 14 mammals located within the main gallery of the Oxford University Museum of Natural History (OUMNH) were digitized. Point clouds corresponding to individual skeletons were isolated from the larger gallery scan and each skeleton subdivided into functional units (e.g., head, neck, thigh, shank, and trunk). Convex hulls were fitted to the point clouds representing all functional units, and the total convex hull volume of the skeleton was calculated as the sum of individual segments (Fig. 2). Total convex hull volume was subsequently multiplied by a literature value for body density to produce a convex hull mass and regressed against body mass to produce a linear bivariate predictive equation. The model was characterized by a high correlation coefficient and percentage standard error of the estimate (%SEE) of approximately 20%.

In some respects, convex hulling is a hybrid technique, combining volumetric data from an articulated skeletal model with the more traditional allometric mass estimation approach. By incorporating data from the entire skeleton, the technique may be less sensitive to particularly robust or gracile elements than previous approaches, and no decision need be made regarding which particular bone to base estimates upon. As a volumetric technique, convex hulling may also provide values for segment inertial properties whilst avoiding the subjectivity inherent within previous sculpting techniques. The initial Sellers et al. (2012) application of convex hulling did, however, require a literature value for body density to be assigned to the modern dataset, which was itself heavily dominated by ungulates.

Subsequent applications of the convex hulling procedure have sought to overcome some of the above concerns. Brassey and Sellers (2014) directly regressed convex hull volume against body mass to generate scaling equations for both mammals (including primates) and birds, without the requirement to assign a literature value for body density. There is an inherent assumption, however, that the body density of the fossil species falls within the range of values occupied by the modern taxa. Furthermore, Brassey et al., 2013, Brassey et al., 2016 produced additional convex hull predictive equations based upon modern ratites and pigeons for application to the mass estimation of the extinct moa and dodo, respectively.

The partial A. afarensis skeleton A.L. 288-1 (‘Lucy’) is one of the most complete Pliocene hominin skeletons found to date, with over 40% of the skeleton preserved, including the pelvis and most of the upper and lower limbs represented by at least one side (Johanson and Edey, 1981; Johanson et al., 1982a, Johanson et al., 1982b). The only other A. afarensis remains approaching such percentage preservation is the Woranso-Mille specimen (Haile-Selassie et al., 2010a, Haile-Selassie et al., 2010b), with other relatively complete specimens including the Australopithecus sediba remains from Malapa (Berger et al., 2010) and the ‘Little Foot’ skeleton, attributed to Australopithecus prometheus (Clarke, 1998). Unsurprisingly, A.L. 288-1 has therefore been subject to a wealth of mass estimation studies spanning the last 35 years (Fig. 3).

Due to the relative completeness of the specimen, previous mass estimates of A.L. 288-1 have been based upon axial, sacral, forelimb, and hind limb elements, and indeed multivariate models incorporating several elements. Table 1 details the results of McHenry's (1992) often-cited study, in which the body mass of A.L. 288-1 was estimated on the basis of several skeletal elements using both an ape- and human-based predictive equation. As can be seen in Table 1, estimated body mass ranged between 13 and 37 kg within a single study (based on the radial head and femoral shaft respectively). More broadly, across the gamut of previous mass estimates for A.L. 288-1 (including predictive intervals when calculated), published values range from 13 to 42 kg (Fig. 3), with studies diverging in their choice of reference dataset, skeletal metric, and Type I versus Type II regressions. It should be noted, however, that the mass estimates in Figure 3 represent the extreme upper and lower values of each publication and do not account for any author preference stated with regards to which estimate is most appropriate. McHenry (1992) favors the human-based predictive equation for example, narrowing the range to 17–37 kg. Likewise, Squyres and Ruff (2015) present results from both Type I and Type II regressions, but consider the results of the ordinary least squares (OLS) analysis inappropriate and favor reduced major axis (RMA). Yet despite three decades' worth of debate regarding the appropriate choice of skeletal element, dimension, modern calibration dataset, and regression type, Figure 3 suggests most studies do indeed overlap in the area of 25–37 kg.

Although A.L. 288-1 has frequently been the subject of fossil hominin mass prediction studies, a volumetric reconstruction has never been attempted. Numerous dynamic analyses of locomotion in A. afarensis have required values for center of mass and segment inertial properties for the specimen (Crompton et al., 1998, Kramer, 1999, Kramer and Eck, 2000, Sellers et al., 2004, Wang et al., 2004, Nagano et al., 2005, Sellers et al., 2005). In all instances, however, body mass has been assigned a priori on the basis of previously published estimates, with the mass subsequently distributed around the skeleton via scaling of human and/or chimpanzee inertial properties. The slow adoption of volumetric mass estimation in physical anthropology compared to other paleontological disciplines (Brassey, 2017) may be attributed partly to the relative paucity of complete skeletons. Whilst A.L. 288-1 is indeed one of the most complete Pliocene hominins ever found, large portions of the skeleton were not recovered. Most notably, the vertebral column and shoulder girdle is poorly represented, with considerable portions missing. The rib cage is relatively well represented, with material available for all ribs barring ribs 2 and 12. Due to the fragmentary nature of the costal remains, a good deal of reconstruction and interpolation is required however. This is particularly problematic when conducting volumetric mass estimation, as the vast majority of total body volume resides within the trunk.

A volumetric reconstruction of A. afarensis A.L. 288-1 is a worthwhile endeavor on several grounds however. Recent studies of non-hominin fossil skeletons have found traditional bivariate mass predictions to be unfeasibly high (Brassey et al., 2013, Bates et al., 2015), but such insight may only be gained via attempting to fit volumetric shapes around the skeleton to simulate the extent of soft tissue required to achieve said mass values. Whilst the wealth of pre-existing mass estimates of A.L. 288-1 is commendable, they are heavily skewed towards hind limb and pelvis based regressions. Although this may be justifiable on mechanical grounds, it would seem prudent to also approach the problem of mass estimation from an alternative and innovative direction incorporating information from across all available skeletal material.

As a volumetric technique, convex hulling is well suited to the reconstruction of specimens characterized by incomplete thoracic material. The extent of an object's convex hull is dictated by its geometric extremes (Fig. 1), ensuring the presence of ‘missing data’ within the bounds of the hull does not impact upon its ultimate volume. As such, absence of or damage to vertebrae or ribs lying within the bounds of the ‘trunk’ functional unit will not negatively impact resulting mass estimates. A corollary, however, is this makes it even more essential that the placement of geometric extremes (and any additional spacing to account for missing elements) is reliable.

In this paper, we use convex hulling to estimate the body mass of the (reconstructed) A.L. 288-1 skeleton. In doing so, we also explore the effect of uncertainty in the articulation of the thorax and reconstruction of the pelvis on resulting mass estimates. In the past, the form of the A. afarensis ribcage has been debated, typically falling into a dichotomy of an ape-like ‘funnel shape’ versus human-like ‘barrel shape’ (Latimer et al., 2016 and references therein). Despite this interest, relatively little is known of the effect thoracic morphology may have upon resulting mass estimates and inertial properties. The novel application of convex hulling to the mass estimation of A. afarensis will act as an independent check on the validity of previous allometry based mass predictions and going forward will further inform discussions on the nature of australopith locomotion and sexual dimorphism that are themselves heavily reliant upon values for body mass.

Here, we choose to focus on just one hominin specimen as a case study of the convex hulling methodology. In doing so, we accompany our mass estimates with the most transparent and rigorous 3D reconstruction of A.L. 288-1 to date. We aim to equip the reader with the methodological tools necessary to expand this technique, as well as a grounding in its current benefits and limitations. Given the ongoing discovery of exceptional specimens and the rapidly declining costs of digitization, we are optimistic that this technique can be more broadly applied within the field of human evolution. Of course, this will be facilitated by a shift towards authors making underlying digital datasets freely available (Davies et al., 2017), a practice from which we all stand to benefit greatly.

Section snippets

Modern calibration dataset

There is considerable debate in the literature regarding the appropriate choice of reference population when applying predictive equations to fossil hominins. Typically, calibration datasets comprise modern humans, modern human populations of small stature, African great apes (Jungers, 1990, Hens et al., 2000, Grabowski et al., 2015), or a combination of the above. When deriving mass prediction equations based on hind limb dimensions, human based models are often preferred due to a perceived

Predictive model

The results of the regression analyses can be seen in Table 8 and Figure 6A. The OLS fit is characterized by a high correlation coefficient (r2 = 0.988) and a %SEE of 20%, whilst the type-II RMA regression has a %SEE of 14%. When phylogenetic non-independence was taken into account by conducting PGLS, %SEE increased to 26%. Ordinary least squares is typically the preferred regression type when used in a predictive capacity (Smith, 1994, Smith, 2009) and is therefore reported throughout.

Discussion

The volumetric model of A. afarensis (A.L. 288-1) presented here results in an average body mass estimate of 20.4 kg. This figure is lower than several mass estimates published elsewhere for this specimen (Fig. 3), although the sizeable 95% prediction intervals overlap many previous studies and suggest a mass up to 31 kg is statistically supported. When compared with previous studies, the lower average mass estimate calculated here may be consistent with three alternative explanations: (1) that

Conclusions

The method presented here suggests that based on a complete reconstruction of the skeleton, we should expect the body mass of A.L. 288-1 to be 20.4 kg. This is considerably lower than predicted by most published sources although still within the previously published range. This reduction is very much in line with the reductions in body mass estimates seen in other paleontological studies when volumetric approaches are used and may well reflect the fact that A.L. 288-1 is a considerably lighter

Acknowledgments

We would like to thank the editor, guest editor, and two anonymous reviewers for their suggested improvements to the manuscript. The authors would like to acknowledge the Kyoto Primate Research Institute (KUPRI), the Visible Human Project, the Cancer Imaging Archive, CARTA, and Morphosource.org for access to datasets. We also thank Doug Boyer (Duke University) for making scans of the A.L. 333 composite skull and AL288-1 pelvis and sacrum available to us. We acknowledge Andrew Kitchener

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