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1 month ago
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Warning: long, rather strange post; but stick around; there’s art.
If you’ve been reading Scientist Sees Squirrel for a while, you’ll know that I enjoy finding interesting connections between seemingly unrelated things. I may have jumped the shark, because today I want to tell you about how I connected my research on the evolution of biodiversity to depictions of lions in late Medieval and early modern art. No, really.
Let’s start with biodiversity. One conspicuous and near-universal property of life on Earth is that some groups are much more diverse than others. Among mammals, for example, there are rather few cats (we’ll start with cats, since we’re heading for St. Jerome’s lions); there are rather more antelopes; and there are a metric crap-ton* of mice. Among animals as a whole, there are far more insects than anything else; among insects, there are a handful of scorpionflies and several metric crap-tons of beetles.** The pattern shows up in evolutionary trees (which summarize the history of diversification in a group of related species) as a property called imbalance: if you look at the two lineages that descend from any ancestral “node” (branch point), they rarely lead to equal-size groups. That is, evolutionary trees are far more likely to look like the tree on the right than the tree on the left.
The most influential paper I ever published did something important (almost completely by accident): it established how much imbalance we should see in evolutionary trees, if that arose just by luck – that is, if all lineages had equal underlying speciation rates, with some growing more diverse than others simply by chance. You might expect that if all lineages have equal speciation rates, their descendants ought to be of roughly equal diversity (the resulting evolutionary trees not very imbalanced, like the tree above left). But that turns out to be a thing about which intuition is spectacularly wrong, because there’s a positive feedback process at work.
Let’s oversimplify (a lot!) and imagine that the first two mammal species to evolve were a cat and a mouse. Coding the cat red and the mouse black, their very simple evolutionary tree would look like this:
Now let’s imagine how this tree might evolve, assuming that every lineage (every species of cat or mouse) has the same speciation rate. The first interesting event is when one of the two lineages speciates (splits into two descendant species). It’s equally likely to be either (because we’re assuming equal speciation rates), but let’s say it’s the mouse. Now we have this evolutionary tree for our 3 mammal species (one cat, two mice):
The next speciation event could involve any of the three species, but it’s twice as likely to involve a mouse (because there are two) than a cat (only one). If it does, then we have this new evolutionary tree:
Now the next speciation event is even more likely to involve a mouse – and so on. The early chance event (that the first speciation event involved a mouse) snowballs, and even though there’s no underlying difference in speciation rates, we get a quite imbalanced evolutionary tree. (Had the first speciation event happened to involve the cat, we’d likely get a tree imbalanced in exactly the opposite way).
I wanted to quantify this – to figure out exactly how imbalanced evolutionary trees should be, under the equal-speciation-rates model. That’s because nobody really believes that model is true! Instead, we’re sure that some lineages are more successful, evolutionarily, than others – surely beetles (and mice) are doing something right? But you can’t be sure of that unless the evolutionary trees containing them are more imbalanced than they should be under the equal-speciation-rates model. So how imbalanced is that? I got some important mathematical help on that point from a population geneticist, Warren Ewens, who pointed out to me that the mathematics underlying the model had been worked out. That’s because diversification with equal speciation rates is a Pólya urn process.
What on earth, you might ask, is a Pólya urn process? Well, imagine that you had an urn, and inside the urn were one red ball and one black ball.*** You draw one ball (no peeking!), and then replace it along with an extra ball of the same colour. So, if you draw a black ball (a mouse), you put two black balls back; now your next draw is from an urn with two black balls and one red one, so it’s more likely to be a black ball. And so on – and Pólya worked out the expected contents of the urn (how many red balls, how many black ones) after a given number of draw-and-replacement cycles. Which means he worked out, for the equal-speciation-rate model, the expected number of cat and mouse species after a give number of mammal species have evolved! And I could use that to show that real evolutionary trees are more imbalanced than they should be under the equal-speciation rates model; and therefore, that we’re right: some lineages really are more successful (mice) than others (cats).
Speaking of cats, what the heck is up with St. Jerome’s lions?**** I’ve made two trips to Europe (Italy, Switzerland, and Austria) in the last year, and both times I binged on art galleries. From roughly the 1200s to 1600s, European art was pretty heavy on depictions of saints and other Christian religious scenes, and St. Jerome crops up a lot. St. Jerome was an early theologian (4th to 5th centuries) who worked at biblical translation (he made the first translation of the Old Testament into Latin directly from Hebrew). More importantly to my weird obsession with paintings of him, during his time living as a recluse in the Syrian desert St. Jerome is said to have tamed a lion by removing a thorn from his paw. (If you remember this from childhood as a story about Androcles, as I do, that’s a 2nd-century Roman story that may well have been borrowed for St. Jerome). Here he is, in the act:
Anyway, painters representing St. Jerome very often included a lion as an identifier (there are a lot of saints, and viewers have to be able to tell them apart). But the lions, generally, are weird.
I mean, look at those lions! They’re terrible. When I started noticing them – and noticing them over and over again – I reasoned that after all, it was rather unlikely that a 15th or 16th century painter working in northern Italy would have actually seen a lion. There were lions in Medieval Europe, mind you; they were prestige specimens, kept in royal or private menageries (the English king Henry III, for example, acquired three in 1235; they wound up in the Tower of London, back when it was a nice place, not a prison for Guy Fawkes or Anne Boleyn). But they wouldn’t have been particularly easy for an artist to visit; and I figured that was all it was: artists taking wild guesses at what a lion actually might look like. But it’s not just that the lions are terrible; they’re all terrible in roughly the same way, with flattened faces, high foreheads, and human-like eyes. And that’s harder to explain from painterly ignorance.
Now, you’re probably way ahead of me here; you have a guess as to why all St. Jerome’s lions are terrible in the same way. But the penny didn’t drop for me until I was looking at an embarrassing (for an entomologist) eight-legged bee in this still life by Hendrick Schoock:
Why did Schoock paint a bee with eight legs instead of six? Well, he wasn’t painting a bee from life; he was copying an older painting (as the gallery signage explained), and there was a shadow in the original that Schoock misinterpreted as an extra pair of legs! This kind of copying was routine (especially for young painters studying in a master’s studio, but not only for them). And had another painter copied Schoock’s bee, the copy would have had eight legs too. And that, I realized, is a Pólya urn process!
Told you there’d be a connection. The mathematics underlying the diversification of species can also explain why St. Jerome’s lions are so weird. Artists weren’t painting lions from life.***** Instead (I hypothesize), they’d paint lions by working from older paintings (or other illustrations). Imagine two early paintings: one competent lion (the one on the left, by Matthias Stomer, isn’t too bad), and one incompetent one:
That’s a Pólya urn with one red ball and one black one. If an artist happens to copy the bad lion, there are now three lion paintings, and two of them are bad (we’ve drawn a black ball and replaced it with two black balls). It’s now more likely that the next artist will copy one of the bad lions than the good one; and as more copies of the bad lion get made, the likelihood of even more bad copies gets higher. The result: just a couple of poor painterly decisions can cascade to give us the corpus of terrible (all in the same way******) St. Jerome’s lions we see today. And if Pólya urns underlie St. Jerome’s lions, perhaps they underlie a lot of other cultural conventions: dwarves and elves and orcs in fantasy fiction, for example.
It just pleases me that a simple bit of math can underly such very different phenomena, so I can see two of my little obsessions (one scientific, one art-history) connected. I did warn you: this post has been a long strange trip. I hope you’ve enjoyed the ride.
© Stephen Heard August 27, 2024
UPDATE: Courtesy of Jeremy Fox, here’s someone else wondering “Why Medieval Artists Drew Such Goofy Looking Lions“. I’ll let you decide if they got any further than I did. Also via Jeremy, a really fascinating look at a similar question: “Why do babies in medieval paintings look like ugly old men“? And now I bet you’ve spent all the time you should budget today on these issues.
Images: St. Jerome, “St. Jerome Extracting the Thorn”, workshop of Rogier van der Weyden, 1450; Detroit Institute of Arts, Detroit, via Wikimedia.org. Incompetent lions, details from “Saint Jerome and the Lion”, Albrecht Dürer. ca. 1500-1500, Barnes Foundation, Philadelphia; “St. Jerome and the Lion”, workshop of Rogier van der Weyden, 1450, Detroit Institute of Arts, Detroit; “Madonna and Child with St. John the Baptist and St. Jerome”, Callisto Piazza, 1526, Pinacoteca di Brera, Milan, Italy; “Vision of St. Jerome, Guido Cagnacci, ca. 1660, Kunsthistoriche Museum, Vienna, Austria; and “Scenes from the Life of St Jerome”, Sano di Pietro, 1444, Louvre, Paris, France. (More) competent lion: “Saint Jerome”, by Matthias Stomer, ca. 1630-40; Galleria Sabauda, Turin, Italy, contrasted with “Madonna and Child with St. John the Baptist and St. Jerome”, Callisto Piazza, 1526, Pinacoteca di Brera, Milan, Italy. Still life with eight-legged bee: “Vase with Flowers, Insects, and Two Snails”, by Hendrick Schoock, ca. 1670-79; Galleria Sabauda, Turin, Italy. Cowardly lion © MGM Studios. Photos by me except as specified; line drawings by me but animal silhouettes via Phylopic.org
