Finite element analyis: the importance of being valid

On the back of finally getting another paper out:

Cuff AR, Bright JA, Rayfield EJ. (2015) Validation experiments on finite element models of an ostrich (Struthio camelus) cranium.PeerJ 3:e1294 https://dx.doi.org/10.7717/peerj.1294

it required another blog post. I won't over blog it as it is open access and apparently far clearer than some of my other papers to my parents (my metric for how overly complicated I've made things). This one is about the importance of validating finite element analyses (see FEA for "dummies"), but will also touch on the joys of trying to publish negative results (i.e. when experiments don't match computer models). A quick background for those who don't want to read the previous post, finite element analysis (FEA) is a method for analysis how complex structures deform under loads, by simplifying them to a series of finite interconnected units (be it bricks, tetrahedra or any triangles: the elements) that have been given material properties appropriate for the structure (e.g. if it is a steel beam, the elements are given steel structural properties). It is known the method works incredibly well on man-made objects, and it is indeed the engineering tool used for everything from designing cars (and crashing them virtually) or planes, to bridges and buildings. Basically anything that an engineer might build, there is probably a finite element model out there somewhere.You may see where I am going with this then, the method works with varying degrees of success on biological structures for replicating strain magnitudes and orientations. Most recent work on mammals (monkeys, pigs) and reptiles (particularly alligators) manages to get very close replication of strain patterns across the models, but to date few studies have looked at birds. Birds are important as they have very mobile skulls (they have loads of extra little joints in the skull compared to most mammal and reptile skulls) are in a palaeontological context are important as the nearest living relatives to dinosaurs (being descended from them). Many studies have looked at how dinosaur skulls perform under feeding loads, but what does that really mean if we don't know how accurate models are on even their living relatives?

So building on the previous limited work that has looked at ostrich mandibles (Rayfield 2011), and finch beaks (Soons et al., 2012a,b,c), and in preparation for trying to understand ornithomimosaur (ostrich mimic dinosaurs) skull function, I started looking at validating an ostrich cranium (n.b. skull is cranium plus the jaws). We had some frozen ostrich skulls from an ostrich farm in the UK, and I used several in the course of the project, first as a practice dissection, then as a practice experiment, then one for the actual experiment/validation, and one more for material property testing. The one used for the validation was sent frozen to Hull/York Medical school for CT scanning prior to any work so we had a full digital copy, and could use it for making the computer models.

Labelled ostrich crania, showing the ‘average’ ten month old ostrich crania. From Cuff, 2014.

Myological reconstructions of an ostrich skull. A) M. depressor mandibulae, B) M. adductor mandibulae externus, C) M. adductor mandibulae posterior, D) M. pseodtemporalis profundus, E) M. pseudotemporalis superficialis, F) M. pterygoideus. From Cuff, 2014.

From the initial work, it was decided that the M. pseudotemporalis superficialis (See D in the above figure) was the best load to use. I dissected the muscles of the experimental specimen. From the dissection I was able to measure muscle mass, fibre lengths and angles and using these metrics you can estimate the force a muscle can produce. I actually measured higher potential force production by the muscle than we used, but this was to keep well within safety factor of the experimental set-up and the cranium whilst producing visible bending in the cranium. For the experiment, Jen Bright (now Sheffield) and I first had to apply a way of loading the cranium that would replicate a muscle. Previous work has either used the original muscle, or screwed some metal attachment to the skull. We tried something somewhere in between by screwing an artificial tendon (made of layers of fibreglass, resin and a carbon fibre loop) instead that would allow a flexible load application (a design that Colin Palmer, an engineer and now a part-time PhD at Bristol).

From Cuff et al., 2015. Artificial tendon. (A) Schematic of the artificial tendon construction showing the carbon fibre loop sandwiched between layers of fibreglass. (B) The artificial tendon screwed into place on the M. pseudotemporalis superficialis. Screws highlighted in black circles.

Once the tendon was attached, 13 strain gauges were applied to the dissected ostrich cranium, and cranium was then placed on the rig. For anyone who follows the field, they may have noticed this is the same one as seen in some of Jen Bright's earlier work on pigs (hence the affectionate name "pig rig", which now is the "ostretch")

From Cuff et al., 2015. Ex-vivo experimental set up. (A) Experimental testing of ostrich with gauges attached, under loading of the artificial tendons. (B) Schematic of experimental rig showing load and constraints.

From there we applied the loads, and using the gauges measured the strains. Unfortunately, and for reasons we do not know, gauge 6 was not functional during the experiment. Then came the fun computer model which was, to the best of our abilities, as identical to the experimental set-up. This involved first isolating the bone of the cranium (two types, the surface cortical bone, and the deeper honeycomb-esque trabecular bone), the beak, and sutures.

From Cuff et al., 2015. Digital reconstruction of the ostrich skull. Red triangles represent the constraints, black arrows show orientation and location of loads, red rectangles are membrane elements that mirror the strain gauges. Gauge 6 was non-functional so was not included in the model, but its location is marked. The blue lines are sutures, and the yellow material is the keratinous rhamphotheca. The trabecular bone is not visible. Gauges labelled with an asterisk (*) are sites where nanoindentation was performed. Direction from grid one is labelled as the white arrow from which strain orientation were measured.

And what the skull more or less looks like under loading to give an idea of the areas where strains will be highest (NB this is only to give an example, and is a skull, with only cortical bone, no beaks, and loaded with muscles).

From Cuff 2014. Ostrich cortical bone, and muscle model showing strain patterns.

As you can see from the two images showing the ostrich models, missing gauge 6 is a shame as it is in one of the high strain areas. It becomes important, when considering strain magnitudes (effectively change in shape, i.e. deformation) which don't particularly match:

From Cuff et al., 2015. Maximum and minimum principal strains for both ex-vivo experiments, and finite element models in microstrain. (A) Maximum, and (B) minimum principal strain for models with material properties from the literature; (C) Maximum, and (D) minimum principal strain for models with posthoc material properties; (E) Maximum, and (F) minimum principal strain for models with material properties from nanoindentation. Material properties for each model are listed in Table 1. Note that both experimental trials are shown.

This is particularly true for absolute magnitudes of maximum principal strain where gauge 7 far exceeds anything we could reasonably produce, but from here you can see the recurring theme for the other metrics we measured. Strain magnitudes, ratios (maximum: |minimum|) and strain orientations are similar in magnitudes in certain places, but don't match as well as we would expect in others. Generally the patterns are correct (where there are high or low strains), but that is the best we could achieve no matter what material properties we used (and included some novel ostrich property measurements).

These results are particularly interesting as similar methods have worked on mammals and alligators producing models that closely match those of the experiments. As for why the results are so far off in our models is unknown, and something that needs further investigating. It may come down to how we modelled the materials of the cranium, because joints in the skull are far more difficult to model than we have, because our new tendons were worse than before, or a myriad of other factors that I've not discussed here or in the paper. However, the data in the paper are all interesting and this is the first full attempted cranium validation of a bird ever. As a spin off issue from the paper, it showed me how difficult it is to publish negative results. Negative results are where the results of a study show no match between models and the experiments or in the case of medical science, where the medicine are no better than a placebo. However, these results are really poorly represented in publishing as they don't make sexy stories. This leads to the potential for replication of experiments that don't work repeatedly through time:

From: http://theupturnedmicroscope.com/comic/negative-data/

My paper went through a round of major corrections at one of the "traditional" journals, before being rejected when we put in more data showing the fact the model doesn't match. As such we sent it to PeerJ (a new open access more welcoming to all result types) who sent it through a round of major revisions, before accepting it. Most of the biggest problems stem from reviewers believing our results are wrong through some fault in the methodology and telling us to do more experiments (I accept some of the corrections were things that we needed to clarify, or tidy, or explain further). 1) This is problematic as the specimen quickly dries out during testing so would require a complete redoing of the entire thing which took me almost a year and 2) this perpetuates the not publishing negative results trend. If the method doesn't work, why shouldn't we tell people this doesn't work and not to try it again, or to come up with modifications that might improve it? I believe if our results had been very close with no issues it would have been published rapidly in the "traditional" journal and not taken 2.5 years. It is something I would love to test, but the ethics of sending papers out to review that are the same methods, but differing results is a bit dubious and would require some thoughts. If anyone has any idea or willingness to get involved on this, please let me know.

References
Cuff AR, 2014. Functional mechanics of ornithomimosaurs. Thesis. University of Bristol.

Cuff AR, Bright JA, Rayfield EJ. (2015) Validation experiments on finite element models of an ostrich (Struthio camelus) cranium. PeerJ 3:e1294 https://dx.doi.org/10.7717/peerj.1294

Rayfield EJ. 2011. Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models. Journal of Anatomy 218:47-58.

Soons J, Herrel A, Aerts P, Dirckx J. 2012a. Determination and validation of the elastic moduli of small and complex biological samples: bone and keratin in bird beaks. Journal of the Royal Society Interface 9:1381-1388.

Soons J, Herrel A, Genbrugge A, Adriaens D, Aerts P, Dirkx J. 2012b. Multi-layered bird beaks: a finite-element approach towards the role of keratin in stress dissipation. Journal of the Royal Society Interface 9:1787-1796.

Soons J, Lava P, Debruyne D, Dirckx J. 2012c. Full-field optical deformation measurement in biomechanics: digital speckle pattern interferometry and 3D digital image correlation applied to bird beaks. Journal of Mechanical Behavior Biomedical Materials 14:186-191.

Argentinian Fieldwork

So a few weeks after getting back from Argentina, and catching up on lots of work (including SVP preparation), I finally am getting around to writing about what we got up to out there.

Anjali Goswami, my UCL supervisor, has spent a long time searching for new field sites to add to the India fieldsite she has been working on for the last decade (or more). As such she has been looking for locations in Gondwana (the old southern continental land mass of Antarctica, South America, Australia, Africa and India), particularly sites that have never been searched for microfossils. Microfossils are the little fossils that are often overlooked when people are hunting for dinosaurs, but can be anything from dinosaurs teeth, down to any microscopic remains. Anjali however, is interested in the mammals, particularly with work from Thomas Halliday who finished his PhD at UCL (and continues as a postdoc) on Palaeocene mammals, suggesting that the placental mammals (what we are, compared to marsupials - e.g. kangaroos, and montoremes e.g. platypuses) originated just before the K-Pg mass extinction (the one that killed all the non-avian dinosaurs). As such the time just before and after the mass extinction are incredibly important in understanding mammalian evolution. Argentina is a well known locale for its dinosaurs. Patagonia in the south, is home to loads of different dinosaurs from large theropods, to some of the largest sauropods that ever lived. However, in the north of Argentina there are also dinosaurs, and some of the beds extend into neighbouring countries as well as covering the really important K-Pg boundary (although damned if we saw it). Enough of my rambling prelude though...

So we flew into Salta in NW Argentina, Anjali, Thomas and myself where we met our Argentinian collaborators, Agustín Scanferla and his friend and technician Javier Guillermo Ochoa. After a night in Salta acclimatising to the altitude (with the help of some wine and empanadas), we drove up to Parque Nacional Los Cordones (The National Park of the Cactuses/Cacti) where we would be based.

Wiggly road from the "lowlands" into the mountains.

The drive up was a long winding road, ascending from 2000m up to 3500m (see above). I sometimes have issues with being stuck in a car for long period of times, and with the altitude must say I was feeling a bit rough. It was on this drive I tried coca leaves for the first time. I know what you are thinking, yes it is what cocaine is made from, but chewing the leaves is a traditional remedy for altitude sickness. They taste just like tea (or at least to my uncultured non-tea drinking taste buds) and actually made me feel sicker, so I disposed of mine pretty promptly. Finally we stopped ascending and got to the national park, where you drive into it along the line of an old Incan road (now under tarmac).

The Incas could build straight roads!

The Argentinians have been very successful at developing little stopping points in the area that allow tourists to have a wander around and read some of the old myths about cactuses the Incans had (something to do with protecting a young eloping couple from angry parents).

Whilst Anjali isn't exactly tall, the cactus sure is!

Having had a quick drive down the road past where we were staying, we drove back as the sun was setting and the moon rising. It was also the first time we got to see the reason this area was a desert. Every night the clouds roll in but get stuck (more or less) at the edge of the basin creating the appearance of a wall of clouds.

Moon rise, sunset, and a wall of clouds arriving.

The accommodation was pretty basic, but can't complain too much as it had walls, hot water/shower and central heating. And occasionally electricity/wifi although that was all dependent on a very temperamental generator. I am thankful for it as we did see temperatures dropping below freezing most nights even if it was in the 20+C region most days.

The least flattering picture of Thomas I took in the field, but shows our adobe brick home, with a mud roof covered by tin held down by big stones.

Our first day out in the field we headed to a site previously described to us by a field geologist up the side of a mountain. Most of the morning was spent climbing up and down finding very little (we were one peak adrift of the site as we prospected). My best find until getting to the actual location was a stromatolite - layers of mud held in place by algal mats that build up over time.

Stromatolite in section. The layers showing how they build up are clear.

It is worth pointing out that the region is truly gorgeous in terms of scenery, with the rock layers fluctuating in colours from whites, to reds, to greys and purples. Truly an amazing place.

The vertical rock beds, showing the different colour layers. Somewhere over there is fossils.

We spent the early afternoon at the site and found many fossils, but were unable to extract much due to the hardness of the rock (and not wanting to climb a generator 1.5km horizontally before 1km vertically). As such we collected some scree from the exposure to test how it will prepare under acid digestion.

From left to right Agustín, Javier, Anjali, Thomas. Up the hill (mountain) on day one.

The next day we did a major prospect and found nothing. This was to set the trend for the trip as we alternated days of no fossils and fossils for most of the first week. Just the occasional trace fossils. The Palaeocene seemed strangely devoid of macro fossils, but this is likely due to the environment of the basin which was forming as the Andes started to rise. It wasn't until the 3rd day we came across fossils in a location we didn't know about with Thomas finding a mammal tooth, and me being competitive climbed up a silly slope in the area and found a vertebrae and some other small bone of a mammal whilst the rest had taken a break. There were also a few teeth in amongst some of the small conglomerates (old river channels with rocks/pebbles instead of just sand).

Mammal vertebra in-situ

Over the duration of the trip it would become a recurring theme that it felt like the landscape didn't want you there. Many of the locations were giant sandstones with no fossils, and were covered in bucket loads of cactuses and thorny bushes. If you weren't careful you could easily sit on them as some cactuses were tiny (as Thomas and I can attest).

Spines, spines, and red rocks

If that wasn't bad enough, we realised we were in cougar/mountain lion territory with sittings of footprints, followed by Javier finding a panther hairball (as indicated by the size of it). Whilst in another place, location way up a mountain, I came across a lovely little cave filled with bones (I assume guanaco), so promptly made a hasty retreat from the area.

Puma hairball

Puma cave

I am going to blame that and the crazy amount of time climbing up and down mountains (and so watching your footing rather than looking for rocks) for our lack of finds as much as the locations. This can be attested to by poor Thomas who, whilst following Agustín up a hill (who successfully, and unintentionally, destroyed all the footholds by climbing up) slid down about 5m of hill before he managed to stop himself falling much further.

However, after much failing in one region to find anything, we spent some time in the Cretaceous where I found my first bits of Argentinian dinosaur bones. The first bits were scrappy, but due to the same bed being exposed for some way, I found much more as I followed it along, including a small vertebra.

My first Argentinian bits of dinosaur bone.

On the walk back to the car that day, I was trying to find my way to a GPS point on the top of the hill and apparently forgot that we were in the southern hemisphere so went the wrong way. In my typical lucky/persistent way I happen to stumble across a bunch of bones eroding out of a single location including some unusual shaped ones. Probably bits of girdle from a sauropod, but unfortunately they weren't very extensive, and the bits of rib and long bone were no better. However it was a start!

Chunk of dinosaur bone

The next day we were in a new location, once again expecting no fossils, as we were still alternating days on and off for fossils and we'd found dinosaurs the day before. After an adventurous drive we stopped at the intersection of hills and badlands. Thomas and I went up one hill, Anjali another, and Agustín and Javier into the badlands. Having climbed one hill, Thomas and I were on our way back when I spotted an eroded slab with a fossil on it. We believe it's a tooth, but still none the wiser until it gets prepped.

View from the top of the hill. Note the clouds rolling in.

However, whilst smacking more rocks to see what else we could find we heard Agustín and Javier shout in excitement. They said they'd found a skull. After some discussion, we believe it is indeed a skull, but heaven knows what. It is only the back of the skull if it is, and with the bone almost matching the colour of the rock extracting it was difficult for Javier. We spent another day and a bit there, searching the badlands and finding no more, but up on the hill some more fish bits, including a bit of skull (and maybe a mammal tooth...), as well as finding lots of locations for future exploration. We built/rebuilt the road so we could drive in and get the specimen out. It also turns out that it hand't rained in over a year, but between our 2 days of visiting the location, it did rain!

My nerdy photo of a fossil fish scale, with lichen growing on it, taken with an iPhone through a hand lens.

The final day in the area, we returned to the area where I'd found dinosaur bones to do a thorough exploration. Everyone found some more small bits of dinosaurs, but typically I waited until the last hour as we were returning to the car to stumble across a large bonebed full bones of all sizes (although to be determined if they are just bits of big dinosaur bones or actually small bones), plus a few teeth. There is even an almost complete dinosaur rib that dives into the hill, but that was left there for now. Almost certainly part of a sauropod, but we did find a theropod tooth.

That evening, after a bit of a rush due to my find, we left our field station, and headed down to the south to a town called Cafayate (although one of the things I learnt is that Argentinians, at least those from Buenos Aires, pronounce the y like a sh sound) where we stayed in a hotel for the night. We then headed to a previously published ancient lake full of fish and frogs. So we sat and split lots of slabs of rock. We found a few partial frogs, before Thomas found something that might be the biggest tadpoles at the site. Whilst packing up were were working to sort the good from bad (ie the keepers vs those we were leaving), and there was a nice pelvis on one rock I was keen to extract. I hit the rock and one of the layers popped apart, exposing a beautiful frog fossil, preserved down to the individual bones in the phalanges in the hand and foot. It was probably the find I loved most, despite always loving dinosaurs more than amphibians,

The fossil frog, part and counter part. The left specimen has the head facing down. Big man thumbs for scale?

Myself looking very proud of my frog

With that being the last find of the trip, that rounds up our reconnaissance of the area having found some new areas with fossils, seen lots of new areas to recon, and set the ground work for what will be a hopefully incredibly productive location for Anjali and her field crews for many more years (and grant money is already being applied for so there can be a return).


If you are still reading, I did a things I've learnt from the field in my last blog on the matter, which I will add some new things to here:

1. Altitude is hard. Don't get tired because getting your breath back is far harder than taking it easier the whole time.
2. Coca leaves taste like tea. Basically you chew leaves, get a buzz, don't feel altitude, and in my case feel sick. Everyone has a different experience though.
3. Walking sticks can be useful. Everyone else used them and raved about them. I however, did not, and this links to point 4.
4. Walking sticks have downsides... Climbing steep slopes with them becomes a pain unless you are Agustín and climb like a mountain goat. How I envy him. I am very much a scrambler requiring 2 hands as well to climb things.
5. Pumas are everywhere but remain hidden. Same goes for snakes.
6. People look ridiculous wrapping fossils whilst wearing gloves.
7. Argentina does good steak, wine and cheese (as if people didn't already know).
8. Despite this I still lose weight in the field even after getting fit for the altitude first,
9. The scenery in Argentina is the most spectacular anywhere I've ever been. I'd go back just for that!
10. I remain lucky (or have some crazy 6th sense) at finding fossils. Long may it last as it means I get taken to go hunting for more!

Big cat: small cat

So it’s been a while since my last post, but this one comes as an exciting advancement in my scientific career (and a day late for my birthday). My first postdoc paper was accepted and has now been published:

Cuff et al., 2015.Big cat, small cat: Reconstructing body size evolution in living and extinct Felidae. Journal of Evolutionary Biology. doi: 10.1111/jeb.12671.

This post isn’t to say how amazing the work is, more a way of me distilling and simplifying the information so that my family, non-scientific (or at least phylogenetics based) friends and interested others may be able to understand what I have published on (see last post). If you are interested in a copy and do not have access to it online (we unfortunately could not justify the £2000 for open access), and can't wait a year, please do email me and I can get you a copy.

The postdoctorate I am working on is part of a larger project trying to understand how all living cat (felid) species vary particularly with respect to their muscles, bones and scaling with body size. In modern species this size range is from 1ish kilos in the black-footed cat and rusty spotted cat, to 3-4kgs in domestic cats, to the largest male lions and tigers pushing 300kgs.

Body mass ranges of living felids.

If we look back in time there were even bigger cat species, with some of the sabre toothed cats (belonging to the Machiarodontidae) and largest cave lions pushing 4-500kgs. Despite work being done on other groups’ evolutionary history (e.g. dogs – Valkenburgh et al., 2004) no-one had yet looked at it in felids, and this is where this paper comes in.

Body mass range of living and extinct felids.

So the first step in trying to understand the evolution of body mass in the felids, is getting a family tree (phylogeny) of all living and extinct species. There are some great phylogenies of modern taxa (e.g. Johnson et al., 2006), but the problem with these trees based on genetic material is that very few contain fossil taxa (there are some exceptions including cave lions and the American lion, for which some DNA has been preserved. The challenge then became tracking down an extensive phylogeny for both modern and extinct taxa. The best available at present is that from Piras et al., (2013) which has a very thorough sampling of modern and fossil taxa. From this phylogeny it should be stated here that we used a variety of permutations that affect particularly the fossil ages: first occurrence (when the first fossil appeared, or at least the oldest estimate for the fossil is), mid (midpoint between first and last), last occurrence (when the species died out or oldest estimate for a fossil), as well as looking at only the modern clade of felids (both including and excluding fossil taxa).I will caveat here that a few modern species have moved relations compared to the genetic information (particularly those of the Panthera genus – lions, tigers leopards etc.). There are also some newer fossils belonging to the Panthera genus that were not included (e.g. P. blythaea: Tseng et al., 2014). However, I am hopeful that even when a new, bigger Felidae phylogeny is made, the results will hold true. We’ve also included all of our materials and methods in the supplementary information so it should be easy enough to replicate.

The next step was finding a database of felid body masses. For most of the living taxa there is a lot of data known on the body masses (or at least a range for male and female). These were used to calculate an average for each species (nearly all of my data came from a coauthor’s previous paper – Randau et al., 2013). For the remaining species where the data wasn’t readily available, estimates for body mass were taken from their describing papers, or from an average calculated from skull length (condylobasalar length – from snout to vertebral attachment) using an equation calculated from living species.

Now we have the data for family tree, and for each of their masses. The next step was to remove all of the species from the tree for which we didn’t have body masses. When this tree pruning was done, the next step was to assess the amount of phylogenetic signal in the data - the amount the shape of the tree, and the position of the species on the tree affect the data. In simplest terms, you’d expect the most closely related species to have masses more similar to each other than species that are less closely related. In our data it turns out there is a lot of phylogenetic signal allowing us to carry out the next tests, testing mode of evolution that family was undergoing. When I say mode of evolution, I really mean the way body mass evolves. Initially we tested for Brownian motion, white, trend, OU and early burst.

Brownian motion is a random walk pattern. Imagine flipping a coin, heads you increase in body mass, tails you decrease. Over time you could have all heads, all tails, but more likely a relatively even mix of both the longer the length of time studied. A white model has no change at all through the tree. A trend model is best described as a Brownian motion pattern where there is a directional pattern (e.g. selection that meant only heads were flipped if going back to our coin analogy). There are some famous models e.g. Cope’s “rule” which suggests there is an increase in body mass through lineages in time (not going to discuss the joys of Cope’s rule here as that would be as long as this post is too). OU (Orstein-Uhlenbeck) models are similar to trend models initially, so there is a selection pressure encouraging animals to evolve in a particular direction (e.g. all heads), however once they reach an optimal position they stay there (i.e. there is stabilising pressure so that masses stop increasing or decreasing from the optimum). This is often best described in an adaptive landscape (I am changing analogies here), where fitness of an animal is described as a hill (or island depending on preference), if you are at the bottom, you want to get to the top where you are more optimally adapted for the environment. But once at the top (or above sea level), it’s disadvantageous for the species to leave this hilltop/island, so they stay there. Early burst is the final model, where there is a rapid evolutionary pulse near the origin of the group where all major morphospaces (hills/islands) are occupied, with then some further expanding (into the small islands) of the range across the rest of the group’s history. The Cambrian explosion often is cited as a good example of this.

The test for which model all of these is best is called the Akaikes information criterion (AIC). A more recent version corrects for finite sample sizes (as we do not have infinite numbers of samples) and is perhaps understandably known as the corrected Akaikes information criterion (AICc). This method compares the probability that a model fits the data and then gives a likelihood of any model being best (normally displayed as a percentage as in our results). From this there was the suggestion that an OU model best described the data for the first occurrence phylogeny, and Brownian models best explained the mid-, last and modern occurrences. However, with the AICc we could only test single OU optimum models, and this is where SURFACE and bayou come in. Both of these packages are plug-ins for R (which is rapidly becoming the go-to stats program online) independently developed and tested. Both of these packages allow for testing of multiple OU optima (e.g. a big size and small size) and whether there is convergence between them.

Using these programs, SURFACE recovered 2 optima for modern felids, with the Panthera lineages and Puma evolving to convergent large body masses, and the rest of the felids staying at smaller sizes. bayou did not recover any pattern different to that of Brownian motion. The first occurrence data was probably the most entertaining as far as things I’ve ever written into results with SURFACE finding a range of optima, including two ridiculous ones: a large body mass (near the size of Juipiter); and a small body mass (close to carbon atom size). These are obviously not real optima, although they are entertaining to consider, and the crazy scale is most likely associated with: 1) the optima being evolved towards have not been reached; 2) the strength of the selection across the tree (i.e. how quickly things walk or run up their hills) varies across the tree. Because bayou runs many simulations (I ran 1,000,000 per model) multiple selection strengths could be tested, and the results found again two optima, a small one and a larger one. The mean and last occurrence data, both found two convergent optima supporting a large and small body masses in SURFACE, but this is only also recovered for the last occurrence data in bayou.

From Cuff et al., 2015. Phylogeny of all extant and extinct felid taxa using last occurrence dates (modified from Piras et al., 2013) showing the results from ‘SURFACE’ and ‘bayou’. (a) ‘SURFACE’ and ‘bayou’ phylogenies with shifts shown. ‘SURFACE’ shifts shown on the branches (red and blue), whereas ‘bayou’ rates are shown on the nodes with the colours representing increases and decreases, and the size of the circles showing the probability. (b) Phenogram showing distribution of taxa body masses against their phylogeny for posterior probabilities >0.2 (Table S4). Convergence shows the puma/cheetah lineage mostly being in the large body mass optima, whereas the clouded leopard species converge into the small body mass optima.

What does this all mean? Well there is some data for Smilodon from the La Brea tar pits suggesting they do attain larger body masses through evolutionary time. So despite using average masses (which would hide this signal), there is reason to believe that the last occurrence results are most realistic and best match what we see in the modern world. If this is the case, felids evolve two body mass optima, with large body forms and small body forms. The exact value for these optima varies depending on the method used, but generally they are divided somewhere around 5kg and >25kg ranges. The upper body mass limit fits with previous biomechanical and ecological data showing that large felids (>25kgs) have to take prey as large or larger than themselves in general to maintain their energy levels, whilst smaller species tend to take small prey. From this it may also be able to extend our understanding to some of the extinct species and what their ecologies were. Our results differed from what has been found in canids (dogs, foxes, wolves etc.) where there seems to be a trend towards continued larger body sizes (i.e. Cope’s rule), except in the foxes which show smaller sizes (Van Valkenburgh et al., 2004; Finarelli, 2007). It should still be mentioned that despite canids evolving increases in body size, the largest (at 70kgs in wolves), do not match even the largest living felids, let alone the incredible size (500kg) found in some of the extinct species.

References

Cuff et al., 2015.Big cat, small cat: Reconstructing body size evolution in living and extinct Felidae. Journal of Evolutionary Biology. doi: 10.1111/jeb.12671.

Finarelli, J.A. & Goswami, A., 2013. Potential pitfalls of reconstructing deep time evolutionary history with only extant data, a case study using the canidae (Mammalia, Carnivora). Evolution 67, 3678-3685. doi:10.1111/evo.12222

Johnson, W.E., Eizirik, E., Pecon-Slatter, J., Murphy, W.J., Antunes, A., Teeling E., et al., 2006. The late Miocene radiation of modern Felidae: a genetic assessment. Science 311:73-77

Piras, P., Maiorino, L., Teresi, L., Meloro, C., Lucci, F., Kotsakis, T., et al., 2013. Bite of the cats: Relationships between functional integration and mechanical performance as revealed by mandible geometry. Syst. Biol. 62: 879-900

Randau, M., Carbone, C. & Turvey, S.T. 2013. Canine evolution in sabretoothed carnivores: natural selection or sexual selection? PLoS ONE 8: e72868

Tseng, Z.J., Wang, X., Slater, G.J., Takeuchi, G.T., Li, Q. & Liu, J. et al. 2014. Himalayan fossils of the oldest known pantherine establish ancient origin of big cats. P Roy Soc B-Biol Sci 281 (1774): 20132686.

Van Valkenburgh, B., Wang, X. & Damuth, J. 2004. Cope’s Rule, hypercarnivory and extinction in North American canids. Science 306: 101-104.