Here’s a specific example, from my own work, of how the avoidance of mathematical modeling led to a fundamental discovery that eluded modelers and experimentalist for decades.
At least, that’s how I see it when I’m not feeling humble. It’s about resource allocation in ants, not the grand unified theory, after all.
For context, for those newer to the site, consider this post as a coda to an ongoing series (and discussion of sorts with Dynamic Ecology) about approaches to designing a research program. I have advocated that exploration by tinkering with unexplained curiosities within natural systems often leads to the best discoveries as well as the most consequential research programs. This post from a few weeks ago provides a good summary of that series. Another precursor to this post is a discussion about the relationship between mathematical modeling, hypothesis development, and how much math you need to become a scientist. That is also a precursor to this post, though it is a “long read,” for those averse to verbiage.
The subject of this post — the scientific discovery — came out in a paper last year (go read it if you wish), which I wrote with Sarah Diamond and Rob Dunn. In short, we discovered a fundamental pattern that could have been obvious to everyone, if anybody just looked in that direction. This pattern explains many unanswered ideas, going back to theories that E.O Wilson developed in the 1970s, along with George Oster.
A twig nest of Pheidole sensitiva.
Photo: Benoit Guénard
Oster & Wilson set out to understand what regulates the varying levels of investment into the different members of ant colonies. Most inhabitants of ant colonies are functionally sterile, and in some species, there are multiple physical castes of sterile ants.
The genus Pheidole is the most species rich ant genus, and they’re found pretty much everywhere. All Pheidole (aside from a few exceptions) do something that isn’t found in many other lineages: they have two discrete sterile worker casts. They make big-headed soldiers and tinier minor workers, both of which do a variety of work for the colony. Some think that this dimorphic worker caste, and potentially the flexibility tied to its production, has enabled these ants to not only become ecologically successful but also to diversify.
Anyhow, Oster & Wilson made a number of predictions about the adapability of the ratio of soldiers to minor workers in Phediole colonies. One of their big testable predictions, or perhaps it could be seen as model to be falsified, is that the colonies actively adjust the ratio of soldiers to workers in response to environmental challenges.
It entirely makes sense. If a Pheidole colony is in an environment that requires more soliders, they would make more soldiers. Right? The problem is, despite a lot of looking carefully at Pheidole colonies, this wasn’t found. Finally in the mid ’90s it was found in the lab of Luc Passera, that P. pallidula colonies made more soldiers when they were exposed, without contact, to neighboring colonies. When I say it was found in the lab of Passera, I mean it happened physically in his lab. These were captive colonies.
A similar thing was found in the field in 2002, when I and Jeb Owen published a paper showing adaptive soldier production in another Pheidole species. (Also, my labmate Samantha Messier did the same thing before the Passera group, in a field experiment involving Nasutitermes termites and a machete.) Our studies were done in the field. In my experiment, when I put clumps of supplemental food in the field for months on end, the food was defended by soldiers, and in a short time colonies made more soldiers.
One thing I didn’t mention at the time, though, was that I didn’t find adaptive soldier production in a whole bunch of other species. However, I had less statistical power, and it was the most common species that showed this pattern. Maybe the less common ones did, but it was harder to detect.
If you were to ask around and dig into the literature, you’d see that it’s pretty clear that most species of Pheidole actually do not overtly shift their caste ratios when you mess around with their environment. Not every colony produces the same ratio, but a systemic environmental manipulation doesn’t cause an increase. Other than the two papers I just mentioned, I don’t think anybody else has found adaptive caste ratios in Pheidole. Others have looked, but it hasn’t emerged very clearly.
So, if most species just don’t ramp up and ramp down soldier production in response to the environment, what controls soldier production? For decades, there has been a consistent amount of work asking this question from behavioral, physiological and developmental angles. In the course of all of this excellent work (a lot of it being done by Diana Wheeler, Fred Nijhout, and their associates), we’ve made a lot of progress in understanding how colonies regulate their activity and how development is regulated through genetic, biochemical and physiological mechanisms.
One thing that I’ve always wondered about is, why do some species produce more soldiers than others? I’ve cracked open lots of twigs, and the numbers of soldiers are highly variable. And my experiments have shown that most species don’t obviously change their soldier production in response to environmental changes. There has been lots of great work to understand variation within a single species, but interspecific comparisons have been scant.
I can understand why there hasn’t been much comparative work. Measuring caste ratios of entire colonies can be hard. Find a Pheidole colony in the back yard and compare the number of soldiers and workers. See, not easy, huh? You’ve got to dig them up. Unless, of course, your backyard is a rainforest. In that case, you just pick up twigs. Over the years, I estimate that I and my students have picked up over 106 twigs over the years. Thousands of these have had Pheidole colonies inside. The rainforest is diverse, so I have data on many species. How do they compare?
Well, I learned that the caste ratios were different among species. Some species produced way more soldiers than others. Considering that we know so little about the natural history of these species, there wasn’t a great basis for comparing many of these species to one another. But one thing we could examine, quite easily, was body size. And, as it turned out, that was super-duper predictive of solider investment. Smaller species produced more soldiers than larger ones. When this pattern emerged on my laptop, it was one of those moments of elation that are very cool, but then you don’t have anybody with whom to share.
Then, I dug through the literature so see if the information that we had about caste ratios and body size shows the same pattern that I found in my rainforest. It turns out that the relationship is as identical as you can get. Our local scale pattern recapitulated Pheidole from around the world, and across the phylogeny.
Now, if you ask someone, what controls soldier production in Pheidole? You can say the answer is quite clearly body size. How and why does body size control this? There is some cool work that’s been done on this intraspecifically, that presumably is a mechanism that works more broadly.
How did my discovery of this generalized relationship come about from avoiding models? If you look at the work on soldier production, ever since Oster & Wilson published their monograph in the 1970s, there’s been a strong emphasis on modeling the mechanisms that trigger and regulate soldier production. Meanwhile, nobody before me bothered to step back to look at the big picture and ask, “how are species different and what is predictive of that?” If they did, then they would have found the caste ratio data in the literature as I had, and looked at the most obvious predictor: body size. Others were modeling solider production. I was merely trying to find a pattern.
I’m not claiming that the discovery of this pattern is earthshaking or that it explains mechanistically how colonies make more or fewer soldiers at the proximate level. The main take-home message from this paper is that many of the differences we find are driven by constraints rather than by adaptation, or that selection on body size is coupled with selection on soldier production. This leads to a lot of exciting thoughts about community structure, which we’re now working on.
This work by no means diminishes all of the careful experiments that others have done over the years on Pheidole. Though I’m not a developmental biologist nor as much of a behaviorist, I was able to find something that will be (or at least, I think should be) at the basis of future conversations about the evolution of caste ants.
This is why my choice is to keep asking “What is the pattern?” rather than attempting to model patterns.
Nice post Terry.
You pitched it by noting some ongoing discussions we’ve been having, so let me just note for the record that I don’t disagree with anything you said here and I certainly hope I’ve never implied otherwise. I do a lot of posts standing up for the value of mathematics in biology, and defending it against people who think it’s of little value, or who misunderstand why it’s valuable. But I certainly don’t think that all good biology is mathematical, or that the only way to discover anything is to first build a mathematical model to generate some testable hypothesis.
Believe it or not, my labmates and I actually have done work along these lines. Work that’s out ahead of existing theory, or disconnected from existing theory, that identifies new patterns that future theoreticians might want to explain. In grad school, my labmate Jill McGrady-Steed did one of the first biodiversity-ecosystem function experiments (McGrady-Steed et al. 1997 Nature). At the time, “theory” on this was hardly worthy of the name–people had a few arm-wavy verbal ideas, but that was it. I recall at the time that we all thought this was a strength of Jill’s experiment–it would be interesting no matter how it came out, because nobody really had any idea how such an experiment should be expected to come out. Jill also found some patterns in her data to do with the relationship between biodiversity and the variability in ecosystem function, which wasn’t something anyone at the time had even thought to look at. And in 2002 I used her data to ask some different questions, in the course of which I discovered that food webs tend to collapse to a roughly constant value of connectance, independent of their species richness. Which is really intriguing, because in comparative data from nature, food web connectance is indeed roughly constant, and more or less independent of species richness. Again, this is a pattern on which there’s basically no explanatory theory (though there really should be–c’mon theorists, get on it!). I often refer to these examples to push back against people who think that the microcosm systems in which I work are too simple to ever surprise us or teach us anything new.
Re: the pattern you found indicating a body size “constraint” on worker production, can you elaborate? I ask because there are lots of features of organisms that are correlated with body size for adaptive reasons. It’s adaptive for large organisms to be one way, and adaptive for small organisms to be a different way. Even things like the metabolic rate-body size allometry can be explained as ultimately arising from adaptation (if the West, Brown, Enquist story is right), rather than as a “constraint” in a Gouldian “this has nothing whatsoever to do with adaptation” sense. Sorry if this is an ignorant question to which the appropriate answer is “quit being lazy and go read my paper.” ;-)
p.s. You call your post a “coda” to our ongoing conversation. But I’m afraid that conversation isn’t over yet–I have two more posts in the pipeline on math in biology! One a plug for an old paper of Bill Wimsatt’s on all the ways in which false models are useful, and one on how my UG students reacted to EO Wilson’s editorial. Sorry about that! ;-)
Well, what’s science without math? There’ll be more of this ongoing conversation, of course. When editing, I realized I had to cut back on, “this idea came from this link, and that one from that one…” and I’m now in frantic getting-ready-for-field-season-even-though-there-is-so-much-left-to-do mode, so I’m into shifting gears.
Oh, I haven’t seen anywhere that I don’t agree with you. Our stuff comes from different perspectives but I think there’s mutual appreciation to go around. You’re making my case that stepping back to find the fundamental nature of relationship is something we need to do more! Not that I’m getting arguments against it, but few want to do what gets called “descriptive work.” The key is to choose something interesting and novel to describe rather than just filling in little holes.
More about the constraint: At this point, we actually don’t yet know whether this emerged from adaptation. (I do need to catch up on the latest take on the metabolic scaling story – it’s adaptive?) All we know is that the investment into soldiers is predicted by body size. The phylogeny suggests that it does respond to selection rather than merely reflect inefficiencies, and the existence of the allometry might be adaptive in terms of the competitive environment. I (Actually, I do have all of the community level data to test this, to see if community structure and body size shift together along with changes in the environment. I think that’s the case. But, that’s an analysis that I won’t have time to do until the fall, or later, unless a collaborator steps in. That’s one of those manuscripts that is 98% done. Well, maybe 90% done.)
Theory is built on trying to explain patterns. Sometimes the theory in explaining known patterns also provides predictions for interesting or important patterns not yet measured (or even thought of). Other times many theories are developed for a limited set of patterns, and people spend a decade unsuccessfully trying to use these limited patterns to differentiate among the theories of the underlying mechanism, when what was really needed were more patterns.
I guess the goal of theory should be to help you make educated guesses about the important things to measure but oftentimes it can be a distraction in that people will spend a long time using limited data to try to confirm or reject theories.
I find this super interesting! Thank you for pointing me to the paper! Sorry you didn’t have anyone to share it with, I would’ve flipped out = ). Can I ask a few questions?
So clearly you collected a ton of colonies of all of these species to get the per-species regression. Was there any association within-species between colony size and worker size? I don’t know much about Pheidole – are there minims? In Solenopsis invicta (which is continuously polymorphic), workers tend to get larger on average and the total variation in worker size increases as a colony gets older (and worker number increases).
What happens if you regress minor size versus major size among all the species? You said that they’re strongly autocorrelated, but what’s the slope of that line?
And this last question is unrelated, but maybe you’ve seen it in the literature somewhere: what’s the size distribution of Pheidole larvae? Is it typically normal/unimodal, or is it bimodal, with a population of larvae destined to become majors and a population destined to become minors? I feel like the threshold shifting model sort-of implies a unimodal distribution, where the threshold is just getting moved further and further left on the curve.
And P. harrisonfordi – was it the most charismatic of your microfauna?
Buck, you should sign up for the SWRS ant course this summer!
Pheidole are dimorphic (a few are trimorphic). Discrete soldiers and workers, with little intraspecific variation in size in each caste. I didn’t measure body size with respect to colony size, but others have and have found little association.
The slope of that line is, I think, around 1. There is appreciable variance, though. Both are predictive of soldier ratio, but the relationship is tighter for minors. It would be interesting to find out what sorts out how some species have much bigger soldiers than others. That’s been out of my scope, so far.
Larval size at the last instar varies, of course. The physio work by Wheeler and others have shown that the body size of larvae (and hormonal titers) at a threshold moment determines whether the larva will follow the route to a minor or a major. What I found is that this threshold shifts down with body size, more or less. Andy Yang has a great paper on this in Current Biology, with lots of figures of distributions.
The harrisonfordi thing actually bugged me. I had to redraw the figure in review, because before Wilson, it was ruida. I hate changing figures once I get them pretty.
That’s funny about harrisonfordi. Yeah, actually I did the calacademy ant course in Uganda this past summer; I’m a 4th year undergrad, starting a PhD this fall. I’m headed to Rockefeller University, very possibly to work with Daniel Kronauer.
The question about the distribution of brood sizes was because it might provide further evidence (or not) for the threshold shifting idea. I’m not sure if this is right, but my thinking is that if the the brood are more or less unimodally distributed in size (within a given colony), then it’s easy to see how you could shift the threshold between workers & soldiers up, and end up with larger minors and soldiers and fewer soldiers overall, so it fits the hypothesis.
But if it’s a bimodal distribution, that might imply that the ants are underfeeding a subset of the larve so that they become minors, and overfeeding a different population so that they become soldiers. I feel like that must be the case at least some of the time, because some species have such massive soldiers, it’s hard to imagine they’re just the outliers of an otherwise minor-destined population. Does that make sense? If a bimodal distribution is the case (some or all of the time), it seems like moving the threshold might not necessarily change the average worker size or the proportion of soldiers very much; if the ants are capable of “choosing” whether a larvae is fed to become a soldier or minor (which I think would be implied by a bimodal distribution), why doesn’t selection just drive them to the ideal ratio in each species, destroying the pattern you’ve seen? I agree with your interpretation – I think there must be some sort of constraint that preserves the trend.
Larval body sizes start out distributed unimodally; then those above the threshold size, soldiers differentiate. The relative position of the threshold drops with body size, intraspecifically according to Yang, and throughout the genus according to this paper. It’ll be interesting to see if any outliers are found.
Got it. Thanks for the information!
Hello, and a pleasure to find your blog. I enjoyed this post, and it is fitting as I literally JUST put down EOWs new book ‘letters to a young scientist’. Anyways, I’d like to respectfully disagree a bit, and mostly semantically. This is NOT avoidance of modeling. It is just doing a modeling of a different sort. I recently (started and) wrote a blog post about just this issue, specifically in communication between mathematical and experimental biologists – which can be read here: http://cancerconnector.blogspot.com/2013/04/whose-model-is-it-anyways.html
Where I talk about how we are really ALL modelers! Our models just look different. Where the data collecting scientist (think Tycho Brahe) spends his/her time dreaming about where to look and what to look for, the pattern former (your role here – think Johannes Kepler) seeks the big picture patterns and the ‘modeler’ in your terminology (Isaac Newton in the analogy I’ve been using) puts together the more rigorous connections. There is no rigorous theory without patterns to connect, and there are no patterns without data. We are all on the same team. And, it’s a lot of fun whichever role you play.
Anyways, great post, just wanted to argue the semantics :)
\end{rant}
For full disclosure, I’m a phd student in mathematical biology.
-Jake
Jake, well, when you’re a hammer, everything looks like a nail.
Yeah, we’re all on the team. I myself, in this one study, didn’t do the modeling. But if you read the paper itself, it’s interpreted in light of the preexisting model. It’d be interesting if you made comments on the PLoS ONE site for the paper, which has been seen more than this post to be sure.
If you’re preparing more for writing up about the EO Wilson bit, be sure to read my take on it, as well as Dynamic Ecology (also in the link):
http://smallpondscience.com/2013/04/08/tribalism-in-the-sciences-empiricists-vs-theoreticians/