After the fairly recent announcement of an amazing new species of theropod dinosaur, Yi qi, from China, I have been thinking about the evolution of flight and the prevalence of gliding behaviour in animals across all taxa.
Yi Qi fossil and artist reconstructions taken from the Telegraph. Photo: AFP PHOTO / NATURE / ZANG HAILONG IVPP
Without a doubt, Yi qi, is a remarkable specimen of a dinosaur and has generated a lot of excitement inpalaeontological circles (for example see Darren Naish’s excellent blog post). What makes Yi qi exceptional is it’s membranous wing surface similar to that of bats and pterosaurs. Crucially the wing surface is different from the feathered wings we are now used to seeing in some theropod dinosaurs. It highlights evolution’s ‘experimental’ approach to filling niches and additionally how often flight seems to have separately occurred in vertebrates.
In particular gliding flight appears time and time again. Indeed, across extant vertebrates there is an unbelievable diversity of gliding animals. Everything from the classic sugar gliders and flying squirrels, all the way to snakes, frogs, lizards and even fish and squids. Within the mammals alone, gliding flight is thought to have evolved separately approximately nine times.
Flying lizard ‘Draco taeniopterus’ taken from Wikipedia
The prevalence of gliding flight, shows how advantageous this mode of transport must be. Indeed, it is no hard to see that getting from tree to tree by gliding is energetically cheaper than climbing down to the ground and back up again. Additionally it keeps you out of the mouths of any ground dwelling predators, which can only be a good thing. The repeated evolution of gliding flight also has strong implications for the origins of powered flight in birds and bats, suggesting that their ancestor are likely to have been gliders. Although there are alternative hypotheses regarding the evolution of flight in birds, which argue for a ground-up evolution of flight (for example wing assisted incline running (WAIR)), I find these arguments far less persuasive than the typical tree-down argument. Within the bat community it is wildly accepted that bats evolved flight in a tree-down manner. This theory for bat is probably accepted in part due to the number of other gliding mammals that exist. And additionally, a ground-up evolution of flight in bats is very difficult to imagine. Not only are most bats not particularly mobile on the ground, but also unlike birds they use their wrists when running (see the fantastic video of a vampire bat running from Dan Riskin’s study), so can’t hold their wings out as they run up to flight speed.
Yi qi, I think only adds to the idea that the only sensible origin for flight in birds is a tree-down theory. With the membrane stretched out between elongated wings, it is difficult to see this structure having evolved in any other manner than a step-by-step improvement in glide performance. Whilst it has been suggested that feathers may have evolved for display or thermoregulation, before becoming flight apparatus, it is difficult to imagine any other purpose for Yi qi’s outstretched membrane than originally to help with gliding performance (caveat: not all structures have to have a ‘function’ at first, but can just be side-effects of selection due to other ecological pressures, before gaining a function secondarily) . Over the years it is easy to see the membrane getting larger and progressing on to fully formed wings. Whether or not Yi qi (and indeed Archaeopteryx) was a powerful flier, it is clear in my opinion that gliding flight must have come as the first step along the road to the fantastic aerobatic birds and bats we see today.
In future blog posts we’ll try to have a more in-depth look at all the different theories of the evolution of flight and look at the pros and cons of each. Spoiler: it is a complicated debated that still generates lots of controversy.
When you tell most people that you are interested in the aerodynamics of bat ears they give you a strange look presumably thinking that even by a scientist’s standards you are studying something weird and inconsequential. However, when you show them a picture of one of these enigmatic long-eared bats it starts to make (a bit more) sense!
Spotted bat (Euderma maculatum) showing off its frankly quite ridiculous ears!
Certainly when I first saw a picture of a long eared bat I couldn’t believe that any creature could have or need such large ears, never mind one that flies. But not only can they fly, some long-eared bats have remarkably large foraging ranges, with one female individual spotted bat (Euderma maculatum) repeatedly travel over 30km a day between roost and foraging site (Rabe et al. 1998). And once they get there they use their huge ears in a very unique way. Instead of echolocating their prey like most insectivorous bats, long-eared bats ‘glean’. Gleaning involves listening for the rustling sounds that insects make on the ground (or in the trees and bushes) and then using those sounds to locate the unlucky insect that is about to become dinner. Check out this lovely bit of footage from the BBC’s life of mammals series. Long eared bats can still echolocate but they tend to do so quietly and more for navigation and communication purposes. This sometimes earns them the nickname of ‘whispering’ bats.
Having such large ears, however, must inevitably come at an aerodynamic cost. With an increase in drag (like a parachute) making every wing beat more energetically costly than their small-eared cousins. Therefore, there clearly must be an evolutionary trade-off for gleaning bats between the increased cost of flight that the large ears cause and the ability to forage in a unique manner and exploit a resource unavailable to small-eared bats.
However, the trade-off might not be as unbalanced as it would first seem. It has been commonly been suggested that bats can use their ears to generate lift, like miniature wings in front of the main wings (Bullen and McKenzie 2001). In aeronautics these structures are often called ‘canard’ (French for duck) wings and are used as control surfaces.
A small aircraft with ‘canard’ wings, which are used to help control flight.
This might initially seem like a crazy idea. How can a bat possibly use its ears like wings! However, new research from Vanderelst et al. (2015) seems to back up this unlikely idea. Using simplified wind-tunnel models of seven different bat species they showed that the ears do indeed generate drag as expected, but also substantial lift. With most bat models lift-to-drag ratio being higher with ears than without! Therefore, it would seem that bats can offset the aerodynamic cost of their ears by using them as miniature wings and generating additional lift. I have to admit that the first time I saw a picture of long-eared bat I never would have thought that ears could do anything but generate drag. However, after seeing long-eared bats flying acrobatically in the flesh I now find it much less of a surprise that their ears are generating useful lift. Such are the joys of animals biomechanics.
A long night of bat catching and field work.
As a side note, if you ever get the chance to go out bat catching for the night, with some researchers I highly recommend it. The tiredness you will feel the next day will more than be offset by the fun of seeing these amazing, often overlooked and sadly misunderstood little creatures. Just remember to take insect repellant!
References
Bullen, R, and N L McKenzie. 2001. “Bat Airframe Design: Flight Performance, Stability and Control in Relation to Foraging Ecology.” Australian Journal of Zoology 49: 235–261. papers2://publication/uuid/FD05E232-A310-423F-B168-621A57E813CA.
Rabe, Michael J, Melissa S Siders, C Richard Miller, and Tim K Snow. 1998. “Long Foraging Distance for a Spotted Bat (Euderma Maculatum) in Northern Arizona.” The Southwestern Naturalist 43 (2): 266–269. http://www.jstor.org/stable/30055364.
Vanderelst, Dieter, Herbert Peremans, Norizham Abdul Razak, Edouard Verstraelen, and Greg Dimitriadis. 2015. “The Aerodynamic Cost of Head Morphology in Bats: Maybe Not as Bad as It Seems.” Plos One 10 (3): e0118545. doi:10.1371/journal.pone.0118545. http://dx.plos.org/10.1371/journal.pone.0118545.
Surrounding our stegosaur body mass paper, I had some interesting conversations with members of the public and other academics about scaling. And one of the recurring issues that kept cropping up was how fast we’d expect body mass to increase with the overall size of the animal.
For reasonably complete fossil skeletons, we tend to talk in terms of length.
‘Sue’ the T.rex is around 12m long, whereas ‘Jane’ the tyrannosaur (I’m not getting into the Nanotyrannus debate here!) is only 6-7m long. If we can imagine these animals as fearsome, blood-thirsty sugar cubes, Sue has sides of length twice those of Jane. Therefore we might expect Sue to have volume of 23, or 8-times.
What I’ve described above is termed ‘isometry’, and we tend to use this as our null hypothesis when studying how animals change in body shape with size. Isometry implies that larger animals are the same shape as smaller animals, which we intuitively know is rarely the case:
across lots of different species, an adult elephant is definitely not the same shape as an adult shrew. And an adult ostrich is not a perfect scaled up version of a hummingbird.
within one species, an adult does not have the same body shape as a juvenille. In human for example, babies are known to have relatively giant heads compared to adults
So when animals deviate from this idealised isometry, we refer to it as allometric scaling. From a shrew to an elephant, we know that mammals get relatively thicker limb bones for their overall body size. And in a growth series of one species, we know juvenilles ‘grow into’ their legs i.e. scale allometrically.
There’s two messages I want to get across here:
It’s important we take this allometric scaling of skeletons with age into account. Our recent work estimating the body mass of a Stegosaurus has shown that it makes a huge difference whether we consider a fossil fully-grown or subadult
But isometry is a really useful way of ‘eye-balling’ how much an animal should weigh
I spend a lot of time developing new techniques for estimating how heavy fossil species were. Some of these techniques are more involved than others. But it’s important that we don’t get so wrapped up in the technical details of our methods that we forgot to stop and check that our results make intuitive sense.
In the case of Stegosaurus, for example, the really large individuals can reach up to 9m in length, and estimates for their body mass tend to fall somewhere between 3-6 tonnes. Sophie, the new Stegosaurus specimen on display at the NHM, looks a bit smaller than that. Depending on how we mount her, and how much space we leave in between her bones, Sophie is 6-7m long.
We recently published a mass estimate for Sophie of around 1.8 tonnes. Since then, I’ve had numerous people tell that me the NHM steg couldn’t possibly weigh so little as 1.8 tonnes as “she’s not that much smaller than other specimens”. But this is when stopping to eye-ball your data is important. Assuming the sugar-cube isometry described above, the linear dimensions of an animal would only need to increase by 26% in order to double it’s volume (and mass). So we’d actually expect a fairly low body mass estimate for this Stegosaurus. In reality, the story is a bit more complicated because Sophie hadn’t stopped growing, but these simple calculations are useful for double-checking that our values are falling vaguely in the right ballpark.
So the moral of the story is that small increases in body length can result in big increases in body mass. And while isometry is most often the exception, rather than the rule, when it comes to scaling of body shape, it can be a useful concept for quickly checking your data to make sure you’re on the right track.
The Internet was recently ablaze with the unbelievable picture of a green woodpecker flying with a weasel riding on its back. The so-called ‘peckerweasel’. Indeed more than one commenter doubted the validity of the picture, believing it impossible for a woodpecker to fly with such a load on its back. I for one believe the photo is real and shows an amazing natural predator-prey interaction. But for the sake of argument and amusement can some simple flight biomechanics shed any light on the problem? With more than a handful of assumptions, here we attempt to find the answer. Can a green woodpecker fly with a weasel on its back?
The incredible picture of a weasel riding a green woodpecker. The so-called ‘peckerweasel’. Copyright: Martin Le-May
Power required
To start, we can calculate the power required for a woodpecker (with hitchhiking weasel) to fly continuously horizontally using the methods describe in Pennycuick’s classic JEB paper (Pennycuick, 1968). Using aerodynamic theory Pennycuick showed that a u-shaped curve defines the power requirements for animal flight, with high powers required at both hovering and fast flight speeds, and a minimum power requirement inbetween. In our case we can estimate the curve that defines the power required for a peckerweasel to fly if we know some aerodynamic constants and a few important morphological parameter:
The combined mass of the woodpecker and weasel.
And the woodpecker’s wingspan and wing area.
For the mass of the peckerweasel, we can assume that the woodpecker weighs around 200g and the weasel around 50g (about the weight of a Mars bar). As for the wing parameters of the peckerweasel, luckily Tobalske has published scaling equations which describe just these parameters in woodpeckers (Tobalske, 1996). Therefore, with our 200g woodpecker we calculate a wingspan of 0.54m and a wing area of 0.057m2. We put these values into Pennycuick’s equations for a variety of flight speeds and plot the flight power requirement curve for our peckerweasel.
Power produced
This, however, is only half the story since it only tells us what is required from the peckerweasel not what it can actually achieve. To calculate what a peckerweasel can achieve we need to work out the maximum power its flight muscles can achieve. In the case of the peckerweasel I think it is safe to assume the woodpecker was putting in the absolute maximum effort it can possibly muster, before it becomes tea. To calculate the maximum power that the woodpecker can achieve we need to know its flight muscle mass and the maximum power output of flight muscles. Once again the Tobalske paper comes to our rescue as he provides a scaling relationship for woodpecker pectoralis (the main flight muscle) mass. The scaling relationship gives us a peckerweasel’s pectoralis mass of 29g. Based on figure 6a of Askew et al.’s paper (Askew et al., 2001) on flight power, most flying animals have a flight muscle power output of about 200W/kg. This then give us the maximum flight power that our peckerweasel could produce. If this crosses the powered required for flight curve then we have lift-off. If not that woodpecker is getting eaten.
The power requirement for flight in a peckerweasel. And the maximum power output of the flight muscles of a peckerweasel. As can be seen for a small range of speeds (5-12m/s) it looks likes the peckerweasel has enough power available to fly. Phew!
Conclusions
As you can see from the figure, we can breathe a sigh of relief since it appears that a green woodpecker should just be able to fly with a weasel of about 50g on its back as per the photo, but would it would probably struggle to carry anything much larger. This is of course quite a silly example of the application of power curves to animal flight. However, this technique gets used in a whole range of scientific papers, from the migrating flight of birds to the understanding the flight morphology of bats.
Caveats/assumptions/mistakes
As with any scientific calculation, we’ve made numerous assumptions to simplify the problem, and this blog post should be taken with more than a pinch of salt. Here are a few that I can think of straight away.
The flight power required is based on aerodynamic theory that was originally developed for aircraft and helicopters and only has limited application to animal flight especially since most flying animals are much smaller than aircraft.
Additionally the flight power curves are for continuous horizontal flight and don’t tell us anything about how the woodpecker took off with the weasel on its back. That is a different and possibly harder question to investigate.
We’ve made quite a few assumptions about the size and shape of both the woodpecker and weasel, and even small changes in these values can quickly change the shape of the curves produced.
The maximum output of muscle power is based on a figure from Askew et al.’s paper and may not indeed accurately represent the power output of a green woodpecker.
Plus I’m sure quite a few other oversights and simplifications contained in this blog post.
References
Askew, G. N., Marsh, R. L. and Ellington, C. P. (2001). The mechanical power output of the flight muscles of blue-breasted quail (Coturnix chinensis) during take-off. J. Exp. Biol.204, 3601–3619.
Pennycuick, C. J. (1968). Power requirements for horizontal flight in the pigeon Columba livia. J. Exp. Biol.49, 527–555.
Tobalske, B. W. (1996). Scaling of Muscle Composition, Wing Morphology, and Intermittent Flight Behavior in Woodpeckers. Auk113, 151–177.
Last week, myself (along with Paul Barrett of the NHM and Susie Maidment of Imperial College) published a paper comparing various techniques used to estimate the body mass of extinct animals. We’ve applied it to ‘Sophie’ the Stegosaurus, an exceptionally complete dinosaur fossil that has occupied the majority of my time at the NHM over the last year.
Why bother?
The first question I often get asked is “Why do we need to know how heavy these extinct animals were?”. Apart from being declared ‘an awesome pub quiz fact’ live on national TV (thanks BBC…I think??), body mass is actually really important for many of the analyses I’m interested in carrying out. In the same week that our body mass paper was published, ‘peckerweasel’ hit the headlines. Debate raged over whether a green woodpecker really could fly with a weasel on its back, and lots of attention was paid to the body mass of said weasel (about the same as a Mars Bar apparently…).
This is just one instance in which body mass is required as in input into a biomechanical model, which can be subsequently applied to tell us something useful about how the animal was moving. In the case of ‘Sophie’, we would eventually like to reconstruct how Stegosaurus moved, especially given the bizarre forelimb:hindlimb ratio of leg lengths. The ancestor of Sophiewas actually bipedal (walked on two legs), making Stegosaurus one of a very limited number of ‘secondary quadrupeds’. If we want to simulate how Sophie walked, we need an idea of both how much she weighed, and how this weight was distributed around her skeleton.
Stegosaurs have unusually short forelimbs compared to their hindlimbs, probably as a result of evolving from an ancestor that walked on two legs. We plan on reconstructing locomotion in Stegosaurus to understand what effect these unusual limb proportions would have on gait. Image Copyright: Natural History Museum, London
How do we reconstruct the body mass of an extinct animal?
Historically, the body mass of dinosaurs was simply estimated using Archimedes’ principal. Scale models of fleshed-out dinosaurs would be sculpted in clay, and dunked into water to estimate their volume. This volume would be multiplied by an ‘average’ value for body tissue density (1000kg/m3 is typically taken for mammals, but more on this later) to get body mass. The advantage of this approach is that it also allows us to calculate properties such as the ‘center of mass’ of the animal in addition to just the total mass. Yet there is obviously some degree of artistic licence involved in sculpting, and this technique has been criticised as being very ‘user-subjective’ and is not easily reproducible. And in order to sculpt a reliable scale model, you need a decent proportion of the fossil skeleton to be preserved in the first place.
An alternative approach is to base our mass estimates of dinosaurs on the dimensions of individual bones within their skeleton. The circumference of the thigh bone and upper arm bone, for example, has been found to be a very good predictor of body mass in modern birds and mammals. Once we understand how this relationship between bony dimension and body mass works in modern animals, we can apply it to fossil animals. The nice thing about this approach is that it can be applied to very fragmentary skeletal remains. Most of the fossil species ever discovered consist of small scraps of bone. Complete skeletons, such as Sophie, are actually incredibly rare. By developing a technique to estimate body mass based on individual bits of limb bone, it means large-scale studies of body size can be carried out. These studies are extremely important for developing our understanding of broad patterns in evolution and extinction across massive periods of time, and would be impossible if they required complete fossil skeletons. Yet this approach tells us nothing about how the mass of the animal is distributed around the skeleton, which is often a prerequisite for our simulations of animal walking.
Recently, the field has seen an interesting return to the traditional Archimedes’ volumetric approach to mass estimation, with the adoption of 3D digital computer modelling. Virtual skeletons of fossils can be created using laser scanning or photogrammetry, and soft tissue outlines placed around the digital model to reconstruct its former fleshed-out volume. Whilst this method still arguably involves some degree of ‘sculpting’, it does allow for lung space to be included in the 3D models, and the digital files are more amenable to data sharing.
Convex hulling
During my PhD in Manchester, we published on a new technique for estimating body mass from digital 3D models of fossils that is arguably less subjective than previous methods. ‘Convex hulling’ is a hybrid of both the volumetric 3D approach and the simple scaling models. We laser scanned the skeletons of lots of modern mammals on display at Oxford Museum, and created digital models of their skeletons. Using ‘convex hulling’, we then fitted ‘shrink-wrapped’ shapes around the models to calculate the minimum volume defined by their skeletons. To reiterate, we make no attempt to reconstruct the soft tissue outline of the animal, everything is solely based on the bare bones.
Convex hulling applied to a human skull. A, point cloud representing the original surface of the skull; B, illustrates the fit of the convex hull around the contours of the skull; C, shows the watertight convex hull.
Once we’ve estimated the minimum volume of each animal’s skeleton, we calculate the relationship between volume and body mass for this dataset of modern mammals. And when we understand this relationship in living animals, we can create a 3D model of our fossil dinosaur, wrap convex hulls around its skeleton and estimate its mass using this model. Simples…
So how much did Stegosaurusweigh?
First of all, the crucial question is actually “How much did this Stegosaurus weigh?“. When we run simulations of dinosaur locomotion, feeding or breathing, we are usually basing our models on the skeleton of one individual. Therefore it’s important that we estimate the mass of that particular individual, and not use an average value for the species. Intuitively we understand that amongst humans, there is a lot of variation in body size. The same was almost certainly true for dinosaurs. So we set about estimating the body mass of our particular specimen, ‘Sophie’ the Stegosaurus.
We wanted to compare the mass estimates generated using the volumetric ‘convex hull’ method against those generated from traditional scaling studies. I spent a considerable amount of time creating 3D models of every bone in Sophie’s body, and rearticulating the bones into a 3D digital model of the skeleton. Because we were unsure about exactly how the skeleton fitted together (the process of fossilisation can distort the skeleton, and areas of soft tissue that once spaced apart the bones has disappeared), we also created a ‘skinny’ and a ‘fat’ version of the skeleton to act as our lower and upper limits of likely body size. I fitted shrink-wrap convex hulls to the skeleton to calculate mass volumetrically, and also used the R package ‘MASSTIMATE’ to calculate her mass using models based on her limb bone circumferences.
3D reconstructions of Sophie the Stegosaurus and the associated convex hulls. A-B, ‘skinny’ model; C-D, ‘best-guess’ model; E-F, ‘fat’ model.
Initially, we found a huge difference between the volumetric results and the traditional scaling results. Convex hulling suggested Sophie had a body mass around 1560kg (with big error bars stretching from 1082–2256kg), whereas predictions based on her limb bones suggested a mass between 2400-3800kg. Such a difference is worrying when both of these techniques are frequently applied in the palaeontology literature, and we had no good explanation for what was causing this discrepancy. Fortunately, thanks to a tip-off from colleague, we went back to review more about Sophie’s life history.
How old was Sophie when she died?
The age (or ontogenetic status) of an animal can be determined from the skeleton in a couple of ways. The bones of your skeleton fuse together as you grow. A classic example is the fontanelle (or soft spot) on the top of a baby’s skull, which gradually closes as the skull bones fuse together with age. In modern birds and reptiles, we see a similar pattern of bones fusing with age, and we can infer that the same process occurred in dinosaurs. In the case of Sophie’s skeleton, we see a confusing mix of features. In some places, the bones are completely fused together, as would be expected in an adult. In other regions (particularly the hips) there are still noticeable gaps between the bones, characteristic of juveniles. This highlights the importance of finding complete skeletons such as Sophie. Depending on which particular bone we might have pulled from the ground, we could have confidently assumed she was either an adult or a juvenile.
Alternatively, we can look at the microstructure of fossil bone under a microscope to determine age. When adult dinosaurs approach their maximum body size and their growth rate becomes negligible, a distinct band of bone is formed on the outer surface of the limb bones. When palaeontologists had previously studied Sophie’s bones, they did not find this feature, suggesting this Stegosaurus was still growing. Based on all this evidence we concluded that Sophie was a ‘young adult’, but still had not reached her maximum body size.
What does this mean for body mass?
Intuitively, we understand that human babies do not resemble miniaturised adults. Our body proportions change as we age. Babies have a relatively giant head compared to adults, for example. The same is true of leg bones, and animals are said to ‘grow into’ their limbs. The traditional scaling studies of limb bone circumference are based on modern adult specimens, and should only be applied to adult fossil specimens. If we apply them to juvenilles, we risk confusing interspecific scaling (scaling between different species) with ontogenetic scaling (scaling within one species with age). By applying the traditional scaling equations to Sophie in this manner, we were reconstructing an erroneously large individual due to her still-changing limb proportions.
To correct for the fact that Sophie was still growing, we applied a technique called ‘Developmental Mass Extrapolation’ (DME). Using DME, we calculated the body mass of a ‘known’ adult Stegosaurus specimen (as judged by bone microstructure). We then scaled down this body mass on the basis of thigh bone length (femur length is assumed to scale isometrically through growth, whereas circumference scales allometrically) to give an age-corrected value for Sophie’s body mass. This value neatly overlapped those predicted by our volumetric convex hulling.
So mystery solved? Perhaps the disagreement in mass estimates between 3D volumetric models and traditional scaling studies is due to the growth stage of the specimen? In the case of this particular Stegosaurus, that seems to be the case. However, more studies are needed to look at this phenomena in other groups of fossil animals, and at other ontogenetic stages.
Where to go from here?
Whilst it’s encouraging that two independent methods have converged to give roughly the same result, the possibility always exists that the two techniques are just equally wrong! Invariably, our mass estimates will be ‘wrong’ as they are just that…estimates. It’s highly unlikely that we’ve hit the nail on the head and got it exactly right. There are still uncertainties and assumptions inherent in our models that are worth pointing out, and we’d like to move forward and think about how we improve on them:
Our convex hull model is based on modern quadrupedal mammals. We therefore have to assume that the body density of Stegosaurus fell somewhere within the range of those of modern mammals. This would be problematic for theropod and sauropod dinosaurs, as their skeletons were permeated by air-sacs which would have acted to lower the overall body density of the animal. Yet no evidence has been found for these air-sacs existing in ornithischian dinosaurs, to which Stegosaurus belongs.
Based on modern mammals, our convex hull model assumes that an extra 21% of mass was distributed outside the confines of the convex hull. Yet dinosaurs were characterised by possessing a considerable bulk of muscle stretching from the back of the thigh to the tail (the M. Caudofemoralis), which is not present in modern mammals. Our mass estimates are therefore probably lower than would be expected if we accounted for their muscled rear-end. One way to account for this would be to generate a convex hull model for modern reptiles which do possess bulky tails (This work is already underway I believe…)
We’ve also made no attempt to correct our convex hull model for the possible effects of ontogeny. We’re assuming that this Stegosaurus had the same proportion of soft tissue held outside its skeleton as adult modern mammals. But we have very little information about how the distribution of soft tissues around the skeleton changes with age in modern animals. It would be interesting to look at how convex hull volume scales with body mass through ontogeny in a modern species. Any volunteers?
I still have some reservations about DME as a means of correcting for ontogenetic scaling. DME assumes femur length scales isometrically with age. A quick Google search throws up as many exceptions to this rule as there are confirmations in modern animals. It also places a hefty burden on accurately determining the ontogenetic status and body mass of a totally different fossil specimen, for which you may have limited access and/or information. And the DME-corrected mass you ultimately determine for your individual is dependent upon which ‘known’ adult specimen you’ve chosen.
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