Of Sea-Urchins and Computer Models

I’m sure no-one would accuse my posts on Extinct of being populist, or relying on cheap or attention-grabbing novelty. But, part of our job here is drawing attention to philosophy of paleontology, and sometimes, that demands vulgar click-bait. Hence today’s post. It’s about sea-urchins. And what computers can tell us about sea-urchins. Sell-out, I know.

Sea Urchins, Credit: Paul Nicklen, National Geographict

Sea Urchins, Credit: Paul Nicklen, National Geographict

Those spiky red thingies are sea urchins. They live on the seabed, slowly creeping along eating algae and whatever else they can get. They used to be called ‘sea hedgehogs’, which is a good name. They plausibly play an important role in North America’s kelp forests—they’re part of a classic ecosystem involving key-stone predators. The Sea-urchins eat kelp, and sea-otters eat sea-urchins. When sea-otter numbers plummeted due to increased Orca predation in the 1990s, so too did the kelp forests: as predation pressure relaxed on urchins, their numbers shot up, and they left areas of ‘urchin barren’ in the kelp forest (which is weirdly terrifying when captured on time lapse video).

Sea Otter performing its proper trophic function. (credit)

Sea Otter performing its proper trophic function. (credit)

But we’re not here primarily interested in sea-urchin conservation ecology (here’s a nice discussion though), we’re interested in the evolutionary history of sea-urchins. Sea-urchins, sand-dollars, brittle-stars and starfish are the echinoderms—and there’s an evolutionary mystery about them. Extant echinoderms are pretty alien, I’ll admit, and very interesting (if you want to learn more, preferably with bountiful photos and breathless use of caps and punctuation, look no further!)

Brittle-star doing its best tiny-Cthulu impression... (credit)

Brittle-star doing its best tiny-Cthulu impression... (credit)

But extinct echinoderms are a different matter entirely. Echinoderms arose in the late Ordovician (say, 450 million years ago) and seemed to be going along nicely until the close of the Palaeozoic (say, 250 million years ago) when… Something Happened. Basically, a whole bunch went extinct and only a few—the ancestors of today’s sea-urchins—squeezed through. What’s the mystery then? Well, check out the pre-Palaeozoic echinoderms:

Pre-Palaeozoic Echinoderm body plans (from Smith, Zamora & Alvaro 2013)

Pre-Palaeozoic Echinoderm body plans (from Smith, Zamora & Alvaro 2013)

They are incredibly varied, right? They are what a palaeontologist would call highly disparate. That is, there are many different kinds of body plans represented in the group. Compare them to us pathetic vertebrates with our boring bilateral symmetry and 4 limbs: where our body-plans are basically variations on the same simple template, ancient echinoderms take on a wild variety of body-plans. But then, once we enter the Palaeozoic, echinoderm disparity plunges. Sand dollars and sea urchins are basically roundish things, starfish and their kin have different numbers of arms I suppose, but are nowhere near as varied as their ancestors.

So, what happened: why have contemporary echinoderms settled into a conservative old age, when the youthful echinoderms of ancient time were so much fun?

One way paleobiologists have approached this question concerns the critters’ developmental systems. Sea-Urchins are made of a hard, spiny shell or ‘test’. The test consists of a set of plates. Your basic sea-urchin grows via addition: new plates are grown individually during development. But that’s not the only way of doing it. They could instead grow via accretion: the body could grow, and then the plates could divide. Your fingers and toes developed via this latter method: your hands starting out a bit like paddles before the digits were divided. Unless you are a newt, of course: some grow their digits via addition (if you are a newt, please write in!). Anyway, the thought is that the ancient echinoderms developed differently from contemporary ones. If development by addition is less flexible than development by accretion, then it would constrain the possible forms echinoderms could evolve into (to use the language of evolutionary-developmental biologists, one method of development has higher evolvability). Or perhaps there are less extreme changes to echinoderm development which could explain the disparity in disparity (sorry, couldn’t resist).

But how would we test these kinds of ideas? The lineages we’re interested in went extinct over 250 million years ago. We can’t experiment on them, we can’t watch them develop—it’s very hard to infer a developmental process from an adult fossil, and fossils mid-development are vanishingly rare. So: to the computers!

Back in 2009, Louis Zachos built a model for growing sea-urchins. Basically, you set growth rate, plate size, and maximal plate size, and it will generate a sea-urchiny shape. Check it:

A virtual sea-urchin test constructed using Zachos' model (from Zachos & Sprinkle 2011)

A virtual sea-urchin test constructed using Zachos' model (from Zachos & Sprinkle 2011)

For extant sea-urchins, we know that they develop by addition, and—obviously—what they look like, so we’ve got a pretty good reason to think that Zachos captured the basic dynamics of extant echinoderm development. Ok, so how can this help us understand ancient echinoderm development?

In 2011 Zachos teamed up with James Sprinkle to explore just this question, leading to perhaps the greatest double-name to grace a publication (seriously, why isn’t there a cartoon called ‘Zachos & Sprinkle’, which features two echinoderm scientists having zany adventures, and hopefully time-travelling?). They wanted to see what would happen if they pushed the model beyond the developmental sequences seen in living sea-urchins. Specifically, they targeted the ‘ocular plate rule’: basically, in living echinoderms plates are inserted at two locations during development. By increasing the number of insertion points, suddenly a bunch of new geometries were generated. Some of which were quite similar to extinct echinoderms:

On the left, fossil of stem-group echinoderm, on the right, model with 6 insertion points (from Zachos & Sprinkle 2011)

On the left, fossil of stem-group echinoderm, on the right, model with 6 insertion points (from Zachos & Sprinkle 2011)

So, we don’t need to posit dramatic differences in echinoderm development to explain what changed across the Palaeozoic border—simply that the ocular plate rule was relaxed in the old days. As Zachos & Sprinkle put it (presumably during a lull in their loony-tune adventures through time and space),

Paleozoic echinoids appear odd because of their range of morphological disparity characterized by the number of plate columns (15 to over 150) but the same model for growth of individual plates can be applied to both modern and Paleozoic echinoids (Zachos & Sprinkle, 91).

Well so what? It seems to me that this study has given us pretty good reason to think that the difference between extant and extinct echinoderms is that the former, and not the latter, obey the ocular plate rule. And that’s kind of remarkable, considering that on the face of it this result is not based on the usual things we associate with evidence: there’s no new theory here, or any literal experiments, or any new empirical data. Zachos & Sprinkle basically played with a very simple computer model. And yet, the results seem to be reasonably treated in terms of old-fashioned hypotheses testing.

When philosophers have thought about modelling, the idea that a model might actively decide between hypotheses is not often considered. Some models—like climate simulations—are definitely used to make things that are a bit like predictions, but these are very different beasts to Zachos’ little computer program. They are highly complex, highly sophisticated, and, frankly, break my brain. (Wendy Parker’s work is the place to go for discussion of this kind of thing). But Zachos’ model just generates geometric shapes given inputs: it’s a very simple idealized system. Philosophical discussion of these kinds of idealizations have tended to follow three lines (I’m here following Michael Weisberg). First, sometimes simplified models are basically heuristics—they’re a just-good-enough stepping stone to better models or theories. Second, some models are ‘minimal models’: they seek to capture the basic dynamics of a system, and thus hopefully explain various aspects of that system. Third, they are used in combination with other models which themselves idealize in various ways: models must tradeoff between (say) how accurate they are, and how tractable they are, and so using different models which navigate the trade-offs in different ways can make up for this.

But Zachos & Sprinkle don’t seem to be doing this – at least not obviously – instead, they’re using the model as something like a critical test. It more-or-less decides between two hypotheses—it decides in favour of ancient and modern echinoderm’s having similar development, as opposed to radically different ones.

How can a computer study decide between hypotheses regarding the developmental systems of animals which lived 250 million years ago?

I’m inclined to take the study at face value: under certain conditions, computer models can produce evidence for or against hypotheses. But we can easily problematize this answer. Let’s do it using the ‘Law of likelihood’, which is supposed to tell us when some observation counts as evidence for one hypothesis over another. It goes as follows:

Some observation O is evidence for one hypothesis H1 over another H2 just when P(O|H1) > P(O|H2).

In English? An observation is evidence for a hypothesis when we should expect to see that observation, given that hypothesis (well, at least expect it moreso than the competitor hypothesis). Imagine that we’ve been collecting data on sea-urchin populations in a North American kelp forest. We notice that the sea-urchins have been declining in number. Let’s take that as our observation. We know that there is an inverse relation between sea-urchin and sea-otter populations. So, if otter populations have decreased, we should expect urchin populations to have decreased. In virtue of this, observing decreased urchin populations give us reason to think that otter populations have as well (certainly in comparison with hypotheses involving otter populations increasing!).

So far so good. But: notice that there’s a causal connection between sea urchins and sea otters which underwrites our expectations. Because otters eat urchins, and because we’ve seen it happen before, we should expect a drop in otter number to be accompanied by an increase in urchin number. And, crucially, we have reason to think that if urchin number were different, so too would otter number. But what connection is there between how Zachos & Sprinkle’s computers behave and the developmental systems of long dead echinoderms? How their computer behaved depends upon its hardware, software, and how it was programmed. Not how echinoderms developed in the deep, deep past. The two just don’t seem connected, so: how could observing one grant us any expectations about the other?

I have an answer to this puzzle (it’s basically a chapter of my book), and I’m not the first to think about how models help us uncover the past (Derek discusses it, and with T. rex, in case you think echinoderms are too crowd-pleasing – and Alison Wylie has been thinking about how they’re used in archaeology), but I think I’ll leave you with the puzzle:

On the one hand, it certainly feels like Zachos and Sprinkle’s study has given us evidence about the past. But on the other hand, it’s unclear how a computer study could do so, because observing a computer doesn’t seem to be connected with the past target in the right way to count as evidence. So, is the study playing such a role, and if so – how? If not, then what is going wrong?