Skip to main content

Cope's Rule and rates of body size evolution

Extinct horses to scale illustrating differences in size: Left to right: Mesohippus, Neohipparion, Eohippus, Equus scotti and Hypohippus . (Heinrich Harder, 1914; Public Domain)

The evolution of body size has been the focus of countless studies, not only in palaeontology but also in evolutionary biology using data from extant animals (or neontology as palaeontologists would say). While some colleagues have argued recently that body size is not necessarily a good trait to study, nonetheless, it still stands that body size is an important factor of fundamental biological phenomena, including metabolism, physiology, biomechanics, and ecology. For instance, the largest source of variance in biomechanical performance measures like bite force is body size - a lion's bite force is an order or two higher in magnitude than that of a domestic cat just purely out of simple scaling. Similarly, prey size categories, such as large, medium/mixed and small, are highly affected by predator body size - obviously a tabby cannot kill an ox while a lion or a tiger can. Thus, body size is not only an important biological trait, but necessarily a fundamental physical trait.

Now that that's out of the way, I want to go on and discuss a bit about a very popular concept in the evolution of body size - Cope's Rule.

Cope's Rule - the observation that through evolutionary time, animal lineages tend to increase in body size - is a classic palaeontological hypothesis named after the American palaeontologist Edward Drinker Cope, that still holds relevance today (...although perhaps controversially).

For Cope's Rule to be observed in an evolving lineage of animals, successive descendant species must show a progressive increase in body size through geological or evolutionary time. Some palaeontologists have used a strict definition of Cope's Rule in that, the smallest descendants must be larger than the smallest ancestor, in order to satisfy Cope's Rule.

More broadly speaking, detecting Cope's Rule is about detecting a positive trend in body size evolution through time.

Traditionally, Cope's Rule has been studied using fossil sequences, where the occurrences of fossils in geological sequence is assumed to represent linear evolutionary change through time. Fossil equids (horses) are a great example of this where body size increase is seen in a clean sequential manner through geological time, with every younger fossil species evolving larger body size. More technically, quantitative palaeontologists have assigned fossil species to either an ancestor or descendant, and tested the overall direction of change in numerous ancestor-descendant pairs (e.g. John Alroy's seminal paper in Science; or Dave Hone's study in dinosaurs). Instead of assigning actual species as ancestors (because older fossil species don't necessarily equate to ancestors of younger fossil species), some authors have utilised reconstructed ancestors given a phylogenetic tree instead (e.g., Butler and Goswami, 2008; Churchill et al. 2015) - these studies tested for directionality in differences between ancestors and descendants across the entire tree, i.e. whether differences are significantly different from 0, and they found little to no evidence for directionality - changes are not significantly different from 0. However, this type of testing has a fundamental problem in that ancestors are reconstructed (under square-change parsimony), by minimising squared change across the entire tree, i.e. differences along branches are necessarily minimised to average at 0 by methodological design...

Obviously there are other studies on Cope's Rule out there, but my narrative here is that despite what some authors have claimed about the validity of Cope's Rule (e.g. little to no support as mentioned above), because of the ways that Cope's Rule has been tested in the literature, there is still scope for it to be true in at least some groups of animals.

And this is indeed the case.

Baker et al. (2015) found a positive trend in body size change through evolutionary time in mammals using phylogenetic comparative methods (a variable-rate model of body size evolution) on extant mammal body size data.

"Now, hang on," you might say. "How can you study trends when all the species are lined up at the present so that there is no time component to the data?".

A very good question.

Note that I used "evolutionary time" and not "absolute" or "geological" time.

Put another way, we can study temporal trends as a function of evolutionary time necessary for a trait to change along the branches under Brownian motion - or the total amount of evolutionary change. What this means is that if body size were to evolve at a constant rate, how much time we would need, for let's say an elephant, to attain the size that it did from the last common ancestor of all mammals. This kind of time will not necessarily line up with absolute geological time - some species might have undergone accelerated evolution some time in its evolutionary history while others may have undergone substantial slowdowns. Now, this is where the variable-rate model comes in. This type of model can allow different rates across clades and branches on the phylogenetic tree and effectively will stretch or compress relevant branches so that trait change will essentially fit Brownian motion.

If Cope's Rule were true, we would expect there to be a positive trend in body size change with evolutionary time - in other words, species with shorter overall evolutionary time (from root to tip) would have changed little (or remain relatively small) while those that have attained larger sizes would have longer overall evolutionary time. To put it in another way, yet again, there should be a positive correlation (regression) between body size and evolutionary time. This is exactly what Baker et al. (2015) found using a phylogenetic regression of log body size on evolutionary time (path length; sum of rates from root to tip), which correctly accounts for phylogenetic non-independence in the data and bivariate relationship. They also fitted separate slopes for the different mammalian orders.

Baker et al. (2015) actually didn't just stop there, they further went on to reconstruct ancestors given their body size on rates regression model. This means that the reconstructed ancestors will not only be informed of phylogenetic relations but will have been accounted for the positive trend through evolutionary time as well. What this resulted in, is an ancestral body size estimate for all mammals that match that predicted from the fossil record. You can see this in their Fig 3, where the model reconstructed ancestor of all mammals overlap with the fossil estimate while a Brownian motion estimate (e.g. ML, REML, or square-change parsimony) is way off. This demonstrates that it is indeed possible to study macro-evolutionary trends through time using extant data alone - contrary to the recent trend emphasising the importance (or even necessity) of incorporating fossil data into comparative studies - albeit given that you use an appropriate method and model. Though, as a palaeontologist, I won't go so far as to say that we don't need fossils. They are important, but there are ways of getting the same answers without them.

As a disclaimer of sorts, I guess you can call me biased towards variable-rate models since I am currently working within the group that developed the program (BayesTraits). However, I do genuinely believe that such models are powerful tools (if used with careful thought) to infer the underlying evolutionary processes and to reconstruct the evolutionary history of a phylogenetic group that ultimately led to the current biodiversity.

Finally, in this blog post, I hope I'd demonstrated that: A) there is still scope for Cope's Rule in some groups (but maybe not as a universal law); and B) that inferred rates of evolution can be powerful indicators of evolutionary time that fits well with what we know from the fossil record. As George Gaylord Simpson said, "[rates of evolution] is the fundamental observational problem in evolution" (Simpson 1944).

Comments

Popular posts from this blog

R for beginners and intermediate users 3: plotting with colours

For my third post on my R tutorials for beginners and intermediate users, I shall finally touch on the subject matter that prompted me to start these tutorials - plotting with group structures in colour.

If you are familiar with R, then you may have noticed that assigning group structure is not all that straightforward. You can have a dataset that may have a column specifically for group structure such as this:

B0 B1 B2 Family
Acrocanthosaurus 0.308 -0.00329 3.28E-05 Allosauroidea
Allosaurus 0.302 -0.00285 2.04E-05 Allosauroidea
Archaeopteryx 0.142 -0.000871 2.98E-06 Aves
Bambiraptor 0.182 -0.00161 1.10E-05 Dromaeosauridae
Baryonychid 0.189 -0.00238 2.20E-05 Basal_Tetanurae
Carcharodontosaurus 0.369 -0.00502 5.82E-05 Allosauroidea
Carnotaurus 0.312 -0.00324 2.94E-05 Neoceratosauria
Ceratosaurus 0.377 -0.00522 6.07E-05 Neoceratosauria
Citipati 0.278 -0.00119 5.08E-06 Oviraptorosauria
Coelophysi…

The difference between Lion and Tiger skulls

A quick divergence from my usual dinosaurs, and I shall talk about big cats today. This is because to my greatest delight, I had discovered today a wonderful book. It is called The Felid√¶ of Rancho La Brea (Merriam and Stock 1932, Carnegie Institution of Washington publication, no. 422). As the title suggests it goes into details of felids from the Rancho La Brea, in particular Smilodon californicus (probably synonymous with S. fatalis), but also the American Cave Lion, Panthera atrox. The book is full of detailed descriptions, numerous measurements and beautiful figures. However, what really got me excited was, in their description and comparative anatomy of P. atrox, Merriam and Stock (1932) provide identification criteria for the Lion and Tiger, a translation of the one devised by the French palaeontologist Marcelin Boule in 1906. I have forever been looking for a set of rules for identifying lions and tigers and ultimately had to come up with a set of my own with a lot of help fro…

Top 10 scientifically important theropod dinosaurs of all time (off the top of my head)

I thought I'd do a fun post for once. And since list based articles are the norm for fun on the internet, I thought I'd do one on dinosaurs, but given that I know most about theropods, I've decided to restrict my list to theropods (...maybe in a future post, I'll do other clades).

My ranking is based mostly on scientific importance so it may not reflect awesomeness, and it is obviously subjective as to how I rank importance to science. For instance, interesting discoveries or unique palaeobiology are ranked relatively low compared to wealth of information and data or completely revolutionising our understanding of the evolution of theropods.

So here are my top 10 scientifically important theropod dinosaurs of all time (off the top of my head)

10. Megalosaurus

Being the first dinosaur to be named, Megalosaurus automatically deserves a spot on this list, but given the fragmentary nature of known fossil specimens, and being mostly useless as a meaningful source for biologi…