Body mass is so fundamental to an organism that it is often overlooked, yet it has considerable importance in animal biology. It is, quite literally, the amount of matter making up an individual. On a day-to-day basis, we encounter values for body mass as we step onto our bathroom scales and are encouraged to maintain a healthy weight (not too heavy or too light). Veterinarians are interested in body mass for much the same reason: the weight of an animal can provide an indication of its health and is commonly used to plan medical treatments. Body mass is also tied to an animal’s physiology (including speed of metabolism and length of pregnancy), ecology (diet, home-range size) and behaviour (social status, aggression). For these reasons, zoologists are often interested in determining the mass of the species that they study (Fig. 1).
In modern animals, it is easy enough to find body mass by weighing individuals in captivity or the wild (exceptionally large and/or rare species notwithstanding). In palaeontology, however, it is not possible to measure mass directly. Even when very complete fossils are found (the intact shell of an ammonite, for example), the process of mineralization and the filling of void spaces ensures that the mass of the fossil is very different from that of the live animal. Palaeontologists have therefore developed techniques to reconstruct ‘live’ body mass on the basis of fossilized remains.
The importance of body mass in the fossil record
Palaeontologists have been estimating body masses of extinct organisms for more than 100 years. Occasionally, the reconstruction of mass is the sole purpose of a palaeontological study — particularly with very small species or extremely large ones, such as huge sauropod dinosaurs. More often, body mass is not the end goal, but it is necessary to know it before you can do further studies. Masses are required for biomechanical analyses (such as determining whether groups could fly or how fast they could run), or for reconstructing the physiology of extinct species (predicting metabolic rate or required daily food intake). In several mass extinctions, body size has been correlated with the risk of extinction , and to analyse them, researchers must be able to estimate the masses of species from a very large number of fossil groups. Importantly, estimates of fossil body mass also inform museum exhibitions and popular media, and ensure that reconstructions of extinct species are up to date.
Methods of estimating fossil body mass
The fossil record is notoriously fragmentary. Finding a complete skeleton is incredibly rare, and most species are known only from a few scraps of bone. Because of this, the most popular techniques for reconstructing body mass in palaeontology operate on individual bones of the skeleton.
Generally, the larger the animals, the larger its bones. In many species, the mass of the animal is tightly correlated to certain dimensions of bones (length or circumference, for example (Fig. 2A). This is particularly true for the limb bones responsible for supporting the weight of the animal.
This relationship (represented on a graph by the line of best fit) can be used to predict mass. Figure 2A illustrates the relationship between the mass of a range of modern rodents and rabbits and the length of their thigh bones (closed circles). Using the line of best fit, one could estimate that a fossil giant rodent with a thigh bone 400 millimetres long would have a body mass of approximately 140 kilograms (open circles).
There are several advantages to this approach. Gathering data on modern species is straightforward. The data required for the model in Figure 2A can be collected very easily from a museum collection, with minimal training or equipment. This ensures that a large number of individuals can be sampled and that we can be confident that the predictive relationship holds true. By basing our mass estimates on individual bones, we do not need to reconstruct the external appearance of the fossil animal.
There are also downsides to this approach. When several bones are preserved, it can be difficult to decide which to use to predict the body mass. In extreme cases, predicted mass can vary by an order of magnitude, depending on which bone is chosen for the calculation. For the giant ground sloth Megatherium (Fig. 2B), predicted mass ranges from 0.5 tonnes (based on the lower arm bone) to 97 tonnes (based on the thigh bone). In this situation, we must decide which bone will produce the most reliable estimates using our understanding of modern and fossil species.
Often we are interested in estimating the mass of very large or small fossil species, particularly those that are a very different size from their modern relatives. Indeed, their unusual size is often one of the main reasons why palaeontologists are interested in studying a particular species. Classic examples include sauropod dinosaurs, the ‘hobbit’ hominin Homo floresiensis, giant rodents and dwarf deer (Fig. 3). However, this requires us to extrapolate beyond the range of modern species (as shown in Figure 2A). When we do this, the confidence interval (the range of values within which we can be confident the ‘true’ value lies) becomes much wider.
Finally, the approach outlined above provides a single value for body mass: Tyrannosaurus rex weighed 6 tonnes, for example. This tells us nothing about how that mass was distributed around the animal. Did T. rex have a larger rear end because of its extensive leg and tail muscles? Did Triceratops have more mass towards the front of its body owing to its large skull? Properties such as the centre of mass and the distribution of mass between body segments are particularly important when running biomechanical analyses. In a fossil species that walked on two legs, for example, the centre of mass of the animal must be located near the hind legs, or it would topple over. For such analyses, straightforward values for body mass are important but are not the end of the story.
For the above reasons, there is considerable interest in alternative techniques for reconstructing fossil species that rely on more than a single bone, and that estimate the distribution of mass around the body.
Early sculpting techniques
In 1905, a skeleton of the sauropod Brontosaurus excelsus went on display at the American Museum of Natural History in New York (Fig. 4A). To accompany this, Henry Fairfield Osborn (vertebrate palaeontology curator and later president of the AMNH) asked his graduate student William Gregory to estimate the “probable weight in the flesh” of the animal. Gregory sculpted a 1:16 scale model of the animal, plumping out the skeleton to reconstruct a ‘lifelike’ representation. The model was submerged in water to determine its volume, and this figure was scaled back up to give the volume of the ‘live’ animal.
Because mass = volume × density, an estimate of sauropod density was needed to predict mass. In 1905, the received wisdom was that sauropods were aquatic, and needed a body density greater than water to walk along the bottom of lakes (Fig. 5A). Gregory multiplied total volume by a density of 1,100 kilograms per metre cubed to produce an estimated mass of 38 tonnes. This ‘sculpting’ approach remained common for the next 80 years, with slight modifications to the modelling medium and apparatus for estimating volume (Fig. 4B–C).
This approach was appealing for several reasons. Sculpting clay models is straightforward and does not require the use of statistical models, avoiding the problems of extrapolation when focusing on very small or large species. The scale models use information from across the whole skeleton (rather than depending on a single bone) and give values for the distribution of mass around the body. However, the technique does require an estimate of body density, and these can depend on our guesses about how the fossil species lived. Although aquatic sauropods might have needed high body density, we now believe that sauropods lived on land, and recent reconstructions (Fig. 5B) assume a low density (typically 850–900 kg m−3) and the presence of air-filled cavities around the body. The process of ‘sculpting’ is also open to the interpretation of the person creating the model, in terms of how much soft tissue is placed around the skeleton. One researcher may build a slender model, whereas another may produce a more corpulent version on the basis of the same skeleton.
Palaeontologists have more recently adopted computer-aided design (CAD) to reconstruct fossil species. One popular approach uses ‘slices’, 2D images of an animal. In Figure 6A–B, a side and top-down view of the body of T. rex is subdivided by several straight lines. These lines define a series of ellipses, joined together as 3D ‘slabs’ along the body. The slabs are simple shapes, so their volume is straightforward to calculate. In this case, the total volume of the torso of T. rex is all the volumes of the slabs added together.
Early models were simple, but later reconstructions included complex body shapes and internal details, improving our understanding of mass distribution around the body. In Figure 6C, the body outline of Diplodocus carnegii is shown. Ellipsoids have been added to the model to represent lung cavities and air spaces present within the vertebrae; these spaces have zero density. Although an improvement over clay-based sculpting, this method relies on an accurate reconstruction of the skeleton (typically based on photographs), and assumes that animals have an elliptical cross-section throughout their body.
Recent digital-sculpting studies have used advanced CAD tools to create curves and surfaces of a more ‘organic’ shape, no longer simplifying the body into basic geometric objects. In these studies, a 3D model of the fossil skeleton acts as the starting point (Fig. 7A). Smoothed, contoured shapes are then fitted around the skeleton to represent soft tissues (Fig. 7B). Density values are assigned and total body mass is calculated on the basis of volume.
As well as letting users construct complex shapes and internal air cavities, recent CAD models also allow them to create several versions of the same fossil species (for example, fat, average and slim). This approach is called sensitivity analysis, and is often used alongside body-mass estimates to explore the sensitivity of our predictions to uncertainties in the model. In Figure 7C, the volume of extra soft tissue around the skeleton is modified to create ‘fatter’ and ‘thinner’ versions and bracket predicted body mass.
Lastly, convex hulling is an increasingly popular technique. It can be thought of as shrink-wrapping an object. In two dimensions, a convex hull shrink-wrapped around a set of points creates a 2D polygon (Fig. 8A). In three dimensions, it can be fitted around a set of points in space to create a 3D polyhedron (Fig. 8B).
To estimate mass, convex hulls have been wrapped around 3D models of modern animal skeletons (Fig. 8C–D). Skeletons are subdivided into regions (head, torso, thigh, etc) and convex hulls are fitted around each region. The total convex-hull volume of the model is found by adding together the volumes of each region. This shrink-wrapped volume is much lower than the ‘live’ volume of the animal, because convex hulls are fitted without adding soft tissues. When this process is repeated on several modern animals, a predictive relationship similar to that in Figure 2 can generated, replacing ‘bone length’ with ‘convex-hull volume’. The last step involves fitting convex hulls around the digital skeleton of a fossil species, and using this predictive relationship to estimate mass.
Convex hulling is therefore a hybrid, combining volume-based modelling with traditional predictive relationships. Unlike the ‘sculpting’ techniques discussed above, convex hulling does not require users to reconstruct soft tissues, so it removes the potential for artistic licence. The process of fitting convex hulls around skeletons is straightforward, so this technique is also very rapid and easy to learn. Importantly, it is also highly repeatable, meaning that one group of palaeontologists should be able to repeat the calculations of another group to confirm its results (a fundamental feature of all science). The major drawback of convex hulling is that a complete digital model of the skeleton is needed, preventing this technique from being applied to incomplete skeletons. Additionally, the results can be very sensitive to how the skeleton is rebuilt, which can be problematic when we are unsure about how much space to leave between bones, or exactly what shape the ribcage might have been. And because the technique relies on a predictive equation, it also requires 3D models of the skeletons of many modern animals, which can be difficult or costly to get.
In the current era of ‘virtual palaeontology’, we have become much better at estimating how extinct species fed, moved, breathed and reproduced. And although these advances are extremely exciting, it is important to ensure that the basic parameters that we use to make these models, such as body mass, are as reliable as possible. There is no single perfect solution to the problem of fossil mass estimation, and the most appropriate technique will vary depending on both the species and the condition of the fossil. Furthermore, it is worth emphasizing that all our estimates are likely to be wrong to some extent. Once we accept this, it becomes more useful to explore why different techniques produce contrasting estimates, and how we can begin to narrow down the range of values within which the ‘true’ values for body mass sit.
1Faculty of Life Sciences, University of Manchester, M13 9PL