The Joy of x

Corina Tarnita and the Deep Mathematics of Social Insects

The mathematical biologist Corina Tarnita explains to host Steven Strogatz how quantitative modeling solved the mystery of fairy circles.

Corina Tarnita, professor of ecology and theoretical biology at Princeton University, brings the empirical power of mathematical modeling to the study of biological systems. She explains to host Steven Strogatz how that approach can illuminate the behaviors of social insects like termites — and how it solved the mystery of fairy circles in Namibia. This episode was produced by Dana Bialek. Read more at Production and original music by Story Mechanics.

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Steven Strogatz: I have ideas of where I want to go, but I’m sure we’ll take some detours and, and that will be fine. We have time, I mean do you have time, do you have —

Corina Tarnita: I do, yes, my husband is [LAUGHS] now with our daughter so —

Strogatz: Yeah, fantastic, congratulations on both aspects.

Tarnita: Thank you. [LAUGHS]

Strogatz: Because I think you were not even married when the last time we were together is that right?

Tarnita: No, but he’s… I don’t know if you’ve met him, his name is Rob Pringle. He’s actually a colleague in the department. We both started at Princeton at the same time — well, he started a bit earlier but, by just by a semester and things kind of worked out.

Strogatz: Wow. That’s fantastic.

Strogatz [narration]: From Quanta Magazine, this is “The Joy of x.” I’m Steve Strogatz. In this episode: Corina Tarnita.


Tarnita: And you know it’s just wonderful to be able… You get an idea in the middle of the night, you can tell your collaborator first thing in the morning.

Strogatz: [LAUGHS]

Tarnita: He doesn’t always appreciate that. Sometimes he just wants to be the husband in the morning, but… [LAUGHS]

Strogatz: Yeah, uh-huh. That’s funny. [LAUGHS]

Strogatz:: I’ve met Corina a couple times and I find that I really like to talk to her. First of all, she’s just a fantastic mathematician [MUSIC] so, so that in itself feels very simpatico. I just love to hear her on, on math, but she’s made this amazing transition from being an all-out high-power mathematician to now becoming an all-out high-power biologist.

She goes to Africa, she’s mucking around with termites, she’s getting her hands dirty. That’s not something you see very often and she, she is doing it. So she works with creatures that we normally think of as disgusting — termites. You know, we’re used to them as pests, but in her hands these termites in Africa are teaching her about the whole ecosystem with really big implications for things like climate change. So it’s just an unlikely pairing, you know: Of critters that we normally want to get rid of, they may help us save ourselves.

Tarnita: I grew up in Romania and I grew up on a farm, actually.

Strogatz: Really, uh-huh.

Tarnita: Yes, with my grandparents. My parents were very young, and they were trying to build their careers and I ended up spending 80 percent of the time for the first seven years of my life with my grandparents on this little farm being surrounded by animals and by nature.

Strogatz: Well, wow, so, so, but you say your parents were trying to make their careers. What were they trying to do?

Tarnita: My dad is an orthopedic surgeon and he was a resident when I was born, so really working day-in-and-day-out. And my mom — was finishing her bachelor’s in mechanical engineering and trying to get a position as an assistant professor at the, at the university. And she’s now a professor, a full professor in engineering and material science and such.

Strogatz: I see. And so I, I’ve read in some place or other that part of your interest in math as a girl had something to do with your mother’s influence.

Tarnita: I wouldn’t say that she made me love math.

Strogatz: Uh-huh.

Tarnita: Actually, we, we actually had quite tense interactions around math [LAUGHS] when I was little.

Strogatz: Oh really?

Tarnita: I was never in the mood [LAUGHS] for doing yet another equation.

Strogatz: Oh, so she was quite pushy about it.

Tarnita: Oh yeah, but she had this attitude that math is a language and the earlier you learn it the more comfortable you’ll feel with it.

Strogatz: Oh I see.

Tarnita: And so even though I wasn’t really into it, she was trying very hard to, you know, put some math into various interactions during the day. And when she was tutoring high school students for their college admission test, she always sat me down and gave me some equations as well.

Strogatz: Yeah.

Tarnita: And I had the greatest satisfaction when I would finish them before they finished theirs. So she always made it… I mean I think she, she built both the comfort with the math and my competitive side.

When I was 12, I started to go to math competitions and again you know she’d, she’d kind of push me and always tell me that I can do better. I mean, she was a typical parent who just kind of insists [CHUCKLES], persists and I remembered that really the moment that defined my, my, my love of math was when I was about 15 and I realized that my mom can’t solve the problems anymore. The problems that I was doing for the math Olympiads were quite a different flavor than the kinds of things that she was familiar with.

And she couldn’t help me anymore and she couldn’t push me anymore and she couldn’t tell — I, I knew that when I interacted with her she didn’t already have the answer. So I felt like, “Oh now I’m on own and I can really make a decision of whether I want to continue with this or not.” And it took me a few weeks, but I realized I actually loved doing this. This is who I am, it wasn’t just my mom.

Strogatz: Okay.

Tarnita: My mom just, you know, kind of nurtured something that was already there somehow.

Strogatz: So take me through your Harvard years. Did you end up majoring in math?

Tarnita: Yeah.

Strogatz: Uh-huh

Tarnita: I ended up majoring in math. It was really great, it was really fun. I mean, it is an amazing department and I had a wonderful mentor, Joe Harris. He’s an algebraic geometer and I ended up doing my senior year thesis with him.

And that was a great experience. And because we had such a great time working together I ended up wanting to do a Ph.D., and he really wanted me to stay at Harvard.

Strogatz: May, may I ask one little thing?

Tarnita: Oh sure.

Strogatz: It may be embarrassing, but I just, I, I have a recollection that you might have been chosen as the best thesis of the year or something at Harvard in the math department? Didn’t you get some kind of prize?

Tarnita: As an undergraduate. I was an undergraduate, yes, I got a prize and then as a Ph.D. student I had the, a prize for the best thesis, yeah.

Strogatz: Oh geez, now you’re really showing off. [LAUGHS]

Tarnita: Yes. [LAUGHS] Well, you set me up for that.

Strogatz: Well, I did, but I, no, but I thought I remembered that you were like this high- velocity undergraduate. You know, here you are, the best of the best, right? The Harvard Math Department attracts really outstanding undergraduate math students. Harvard was happy to take you to, to be a Ph.D. student, again maybe with Joe Harris, who is a really premier algebraic geometer, this is a very elite person and a nice person, a great mentor — has had a lot of great students over the years.

Tarnita: That’s the thing he was, he’s a really great mentor. He was a remarkable influence on me even though I ended up not doing math. So when I was 24 or 25 I had what I call my “quarter life crisis.”

Strogatz: Ah, okay yes.

Tarnita: I just, I just started to feel that even though I was perfectly set up to just love what I do, I wasn’t really in love with it anymore.

Strogatz: Huh. I’m, I’m impressed that you had this sense of your own self, that you were tuned into enough to your own feelings to feel and recognize what you were feeling. That even though, you know —

Tarnita: Well, it took — yeah.

Strogatz: I mean, by a lot of measures, everything should have been fine, but you somehow sensed it wasn’t fine for you.

Tarnita: Exactly. Yeah, I mean it, it, it threw me into a, it threw me for a loop for basically a year. I was really unhappy. I can’t say that I worked it out at the beginning. It took me a year to figure out what the problem was, why I wasn’t enjoying what I, what I had always enjoyed. And then because math was my identity — I, I, I love my work, in general I love my work and I love to love my work, that’s very important to me. So when that stopped being the case, I had the sense of “who am I then?”

Actually, Joe was instrumental there. I, I — he realized something was off. You know, I — he asked me, “What’s going on?” And I finally gathered the courage to tell him. [LAUGHS] And he said, “Oh you’re just burnt out. You know, you need a break. You just — look, just go to the math library and don’t touch any of the books about the math that you have already spent a lot of time thinking about. So no number theory, no algebraic geometry. Pick out some other math book and read that for a while and that will bring back the, the excitement and, and so on.”

And, and when I got to the math library, there were so many books, and all of them on the, on the outside looked the same. There was one colorful one and that was Martin Nowak’s book on Evolutionary Dynamics: Solving the Equations of Life[Editor’s note: The correct title is Evolutionary Dynamics: Exploring the Equations of Life.]

And I was amazed because I didn’t — I, I, I hadn’t taken any biology since high school. In high school I did not like biology. I, if I, if you made me memorize one more plant part, I was just going to drop out of school.

Strogatz: [LAUGHS]

Tarnita: So I thought, math and biology are as far from each other as you can possibly get. I mean, you know, maybe not as far as you can get with poetry let’s say, but one could make arguments. [LAUGHS] And so I was stunned that someone would bring math to biology.

Strogatz: Mm-hmm.

Tarnita: Because really, when I was memorizing all these plant parts, I thought, “There’s no method to this madness. There’s no system here, there’s not logic, you just memorize stuff.” And so when I saw that you can write … equations about biology, it, it was discovering a different kind of math, but it was also just seeing the world through a lens that I was comfortable with but, but seeing a part of the world that I felt very distant from, that somehow I hadn’t appreciated before. And now these, this, this lens of mathematics was giving me insight into this world of biology. It was just, it was really amazing. And I ended up going back to Joe and saying, “Boy, I read this book and I’m absolutely fascinated, and I would love to think a little bit more about this, but don’t know really how.”

He said, “Well, you know, Martin Nowak is a professor in this department. You should just go talk to him.”

Strogatz: [LAUGHS]

Tarnita: And so I did. And Martin gave me one project and I had a really great time working on it, because I was learning the ropes, but somehow it had really strong connections with math that I had already been thinking about. And I really enjoyed it.

But after about five months of working on it, I started to wonder, you know, “Will I ever be able to come up with my own questions in this field?” It’s one thing to solve problems that other people give you.

Strogatz: Sure.

Tarnita: But it’s a totally different thing to come up with your own questions and be able to define your, your own, you know, lines of research. And just as I was pondering that question, it naturally happened.

I, I realized that, you know, I had one question that emerged very naturally. I pursued it. It actually turned into one of my favorite papers. And then that was it, then I realized I can do this. And there was this, this energy that somehow had taken possession [LAUGHS] of me that this is it, that I can read about biology forever. I can read everything, and it will never seem boring to me.

Strogatz: What is it for you about biology? Can you say?

Tarnita: There’s, there’s something remarkable about the diversity of solutions that nature has found for these unbelievably complicated problems. That’s what I find fascinating. And the fact that there’s all of this diversity of solutions, that nature really comes up with these, with things that we struggle to figure out in so many different ways and, and to engineer all sorts of complicated solutions. And, and nature did it and does it every day. That I find absolutely remarkable and I could never get tired of, of like, of reading about that.

When I was working with Martin it became really interesting that he was very excited to finally have a pure mathematician in his group. He thought, “Now we can do all of this sophisticated math.” And I was going there thinking, “Now I can do all of this biology.” [LAUGHS]

And so inevitably at some point we started to, ah, disagree a little bit on the approaches, because I really wanted to delve more into the biology and, and, and, and Martin found that unexpected because he really thought I would just go crazy proving theorems in biology.

And, and, and certainly there’s a fascination with that. And, and, and one can do something along those lines, but that wasn’t what I wanted and it wasn’t really clear. I mean the first year or year-and-a-half of working with Martin I — there was just so much to learn and so much to learn from him and so much to read about biology. It really only became crystal clear when I started to work with E.O. Wilson, because hearing him talk about the ants and realizing how much… You know, that’s what, that’s what I wanted to do.


Strogatz: E. O. Wilson, also known as “Ed Wilson,” Edward Osborne Wilson, a great, great scientist who’s spent his career working on ants and ant societies.

Tarnita: He had an accident when he was a child and he lost vision in one of his eyes.

Strogatz: Uh-huh.

Tarnita: And he said that that made him focus away from the big things and onto the small things. And he discovered the tiny, tiny beings, and especially ants.

Strogatz: Oh. It’s really an ant as a member of a colony that’s kind of the amazing thing isn’t it?

Tarnita: Oh yeah.

Strogatz: What they do collectively?

Tarnita: Exactly. It’s their collective dynamics, it’s this superorganism that they become when they are all together. The, the ways in which they organize themselves within that colony and then interact with the rest of the world as not only individuals, but as part of this bigger whole.

Strogatz: Well, so, so that’s a theme that I think I detect in your work. It seems you’re fascinated with that idea of, like, the individual and a group.

Tarnita: Exactly right. I mean… I, I would say that what I work on is self-organization. And that just means how organisms without any external blueprint work by interacting with each other. They create something, some behavior emerges that is bigger than any one of the parts. The sum is bigger than the parts.

Strogatz: Mm-hmm.

Tarnita: And it’s this kind of self-organization that I try to understand — whether it’s from an evolutionary perspective or from an ecological perspective, whether it’s a really tiny scale of, of like tiny cells or ants or at the very big scale of, of ecosystems, but yeah that’s, that’s the general trend of my work.

Strogatz: How about if we talk about some of your recent work about the so-called “fairy circles” in Namibia? What are fairy circles? What would they look like if we were standing in one or — ? I, I don’t know really, never seen one in my life.

Tarnita: Well, from high up, you know, from an airplane or from a helicopter, they would look like the desert has a really bad case of chickenpox or had a really bad case of chickenpox and, and is now recovering. [LAUGHS]

Strogatz: Uh-huh.

Tarnita: Um, it, they’re just basically these tiny — they look like these tiny, little superficial craters. They’re not — they’re, they’re basically the — the vegetation in, in these very arid areas is just grass. And it’s kind of short grass and would more or less cover the whole thing completely, and it would look like a lawn.

But instead of looking like a lawn, it’s peppered with these big gaps. And the gaps are very irregularly distributed so they look like, you know, like a polka-dot dress, for example. It stretches from Angola to South Africa, so it really is a huge stretch of land. It spans countries.

Strogatz: Which is insane, right?

Tarnita: Ah, yes.

Strogatz: I mean, you don’t expect to see a regular polka-dot pattern in the middle of nowhere on earth just happening by itself.

Tarnita: Exactly, no you don’t. And you wonder, you know, what is it and, and people have their favorite explanations. And the reasons they’re called “fairy circles” is because one of the favorite explanations is that these were fairies that created this magical pattern somehow. I mean there are these wonderful types of explanations. “Oh, they are the breaths of the ancestors” or “Dragons that, you know, the dragons —somehow burned through the grass when dragons existed and, and this is what was left of it.

And when I started to work on this I actually had someone ask me, “Don’t you feel sad to come up with an explanation for something that’s somehow so magical?” And my immediate reaction — I mean, I was first a little startled by the question and then I, I, said, “You know, but the explanation that you’re — that we’re finding is far more magical.” The fact that you can find the culprit, you can find the actual thing that creates this amazing pattern on such a huge scale is, to me — that’s the, that’s the beauty of it.

Strogatz: Corina is so right. Scientific explanations are beautiful and often do seem like magic. So what is this magical, majestic creature that can create such a sweeping pattern across the African continent?

Tarnita: Okay, fairies, dragons… But we, we are revealing that it’s teeny, tiny termites, right? A termite is a few millimeters long, maybe a centimeter long depending on the species that you’re looking at, and it travels some significant distances compared to its size. You know, maybe it’ll go a few meters or a few tens of meters. But the fact that these tiny termites with their somewhat bigger ranges of movement can produce patterns at this enormous scale of hundreds of kilometers or hundreds of miles… That to me is, is, is really what makes nature amazing and ever appealing to me.


Strogatz: Turns out there are different types of termite mounds. Most are basically just big dirt mounts in the shape of haystack. They can get really tall and elaborate and they look sort of like a chimney or a cathedral.

There’s also termites that live more or less underground and then, in that case, the mounds are smaller and they’re covered in a lot of vegetation.

One thing I learned in talking to Corina is that every mound has only one colony in it. And it’s really fascinating to learn what’s going on in there. The termites organize themselves in fantastic ways.

Tarnita: They, they just make these very organized societies where there’s many, many millions of individuals working together and coexisting in the same colony, and they have the same organization as the ants in the sense that they have a queen. Termites have a queen and king, but in principle only one or two individuals can reproduce, and the rest of the colony just works to raise those offspring and, and does all the other tasks that are important to the colony.

So there’s a not only a division of labor, they’re not only extremely organized, but they also have a division of reproduction. That’s what “eusociality” means: Only so many individuals reproduce.

Strogatz: Yeah and that’s, that’s just an amazing thought for us where all — we all, you know, imagine ourselves as capable of reproduction as human beings.

Tarnita: Right.

Strogatz: But imagine that, well, I don’t know… What would it be like if that — maybe some weird dystopian futuristic thing where only some of us could reproduce and the rest have to just be helpers?

Tarnita: That’s exactly right. In fact you know it’s a little bit like The Handmaid’s Tale, right? Just in the sense that the largest part of the society is sterile and can’t reproduce anymore and there’s this subset of some group of women that are still able to reproduce — everyone else is barren — and they are kind of held captive to help perpetuate the, you know, the society, the species.

Strogatz: Mm-hmm.

Tarnita: And in some sense, you know… We think about queens and king and queens in, in insect societies as — once you call it a “queen” it sounds like that’s the life you want to live, she’s the queen right? But in principle, she’s just held more or less captive. She can’t move, she doesn’t do anything else, all she does is eat.

Strogatz: That is so interesting. [LAUGHS]

Tarnita: Right, all she does is eat and lay eggs, right?

Strogatz: Yeah, wow. I had —

Tarnita: So it’s not — I don’t think it’s such a great life [LAUGHS] really.

Strogatz: No. It’s such an interesting point of view, how The Handmaid’s Tale can illuminate our understanding of these ant and termite societies. Like Mel Brooks said in one of his movies, “It’s good to be king,” but it’s not necessarily so good to be queen if, if your job is to just sit there and be fed by the workers and keep reproducing all your life.

Tarnita: Right. You basically never leave your little chamber or quarter ever, in ever. Ah, basically you start the colony in the beginning and then that’s it. The moment you have the first generation of workers that can help you, you’re just stuck to your royal chamber and everything else gets built around you into this enormous society, but all you do is basically lay eggs.

Strogatz: Wow.

Tarnita: So in some sense you’re kind of a prisoner, who’s just helping them reproduce.

Strogatz: If you were looking now at a much bigger scale, now — not just thinking about what’s going on in one termite mound — but we look at a, an arrangement of many termite mounds on the surface —or, or we look from above, say from a helicopter view —

Tarnita: Exactly, yeah.

Strogatz: That, there’s this amazingly regular arrangement of the termite mounds, so that they’re spaced sort of like, as if you were almost obsessive and you were trying to space them very evenly and regularly.

Tarnita: Exactly. First of all, they are competing for resources — food, let’s say. They organize themselves in, you know, by slowly moving and killing other colonies and fighting. There’s a lot of wars going on. In the end, no resources are being wasted.

Strogatz: Hmm.

Tarnita: And colonies are as far as they can possibly be from each other, so they don’t interfere with each other, but while at the same time not leaving any resources unused. And what happens is that because they are such amazing fighters and they really have these wars of attrition where they just, you know, go and, and completely kill another colony or engage in war until one of them is dead. Typically, a bigger colony with more termites is going to displace a smaller colony — it very easily, oh, just obliterates it.

Strogatz: Mm-hmm.

Tarnita: And so you can never have small colonies, they don’t last very long. They are easily found by bigger ones and killed. And so you end up with basically all… Eh, when you reach some form of equilibrium, all colonies have to have roughly similar sizes, otherwise the bigger one will win. And when —

Strogatz: So I can now see how this connects to your previous interest in game theory.

Tarnita: Right. [LAUGHS]

Strogatz: And, and also patterns that, you know — Math is often described as, as the “science of patterns.”

Tarnita: And also patterns, exactly.

Strogatz: So here you are seeing patterns made by these mindless bugs that are somehow very brilliant.

Tarnita: Exactly. I mean, obviously, they don’t see past, let’s say, past their neighbor, right? Even their neighbor… It’s doubtful that they would see the whole mound. They can run into each other, and at the borders there are going to be skirmishes and fights and so on, but they can’t see past that, right? And somehow without seeing past that, they can organize at these several orders of magnitude larger scales.

Whenever we need to build a building, right, a skyscraper for example, we need a blueprint, right? You have a big team of workers, they each know what to do and they all know the blue, the blueprint, right? Or at least they have various people who direct them because they know the blueprint. The termites are able to do something on an even bigger scale than that without any blueprint.

Strogatz: That’s amazing.

Tarnita: Right? That’s amazing.

Strogatz: Yeah, it is.

Tarnita: The fact that they can come up with a solution that we can’t come to. If you put together a hundred people and you don’t tell them anything, but you just tell them, “Now go build a skyscraper,” it’s unlikely [LAUGHS] we’ll see anything successful come out of that, right? And, and yet this is what termites do naturally as part of their daily existence.


Strogatz: After the break Corina reconciles two competing explanations for the “pepperoni landscape” and also she’ll take us into the best kind of love story.


Strogatz: So you and your colleagues actually proposed something that was a paper published in Nature just two years ago now, 2017, that was, you know, I think, a really interesting result about multiscale patterns.

Tarnita: Right. So when I moved to Princeton and wasn’t entirely sure exactly what I was to going to work on — and everyone who starts their lab will, might, might, you know, this might resonate with them, might sympathize with the idea of, “Oh, now I’m starting and what is going, what’s going to be my new thing, my thing?” right? And as I was developing different directions, one of my collaborators, Rob Pringle, brought up this question, right? “How do these…” You know, we see these termite mounds being very irregular in Kenya. They were not the fairy circles, we weren’t thinking about the fairy circles at all at the time. And he said, “We know now that the fact that they are organized like that, it really boosts the productivity of the system. So they help the whole system be more productive. You have, on termite mounds, you have more of everything. On these particular termite mounds that allow vegetation to grow on them you have taller grasses, you have better trees, you have more spiders. Spiders make more babies, everyone seems to be happy on termite mounds.”

Strogatz: That’s nice, yeah.

Tarnita: And wonderfully, and so each one of the termite mounds is like a hotspot of productivity. And the reason that that’s, that that happens is that termites — people might not know this, but termites are really great degraders of cellulose, of basically — of, of stuff that nothing else can degrade. [LAUGHS] So they can digest dead plant material and release the nutrients in a form that that can be taken off by plants again.

And they do that on their termite mound and when they do that, if there are plants growing on the termite mound or near the termite mound, those nutrients seep into the soil and the plants grow really well. And also because they — because of how they engineer the soil and all the tunneling that they do, water infiltrates quite differently on termite mounds. And so plants all of a sudden are in this really fertile region where they have a lot more nutrients and better access to water, and they just get a boost. And because plants are doing so well, everything else that’s on plants also does well and, and, and so forth.

Strogatz: Hmm.

Tarnita: And so each one of the termite mounds became like a hotspot of productivity. But what Rob and his collaborators had shown a few years before we started to talk about this question was that because they were organized in this polka-dot pattern, they, the, the, the sum of the productivity, like the overall productivity that they, that they produce in the system was higher than if they had been organized in any other pattern.

Strogatz: Oh, I see, right. So if you had just imagined, like, sort of like… If I put pennies on the tabletop, if I just put pennies at random and think of each penny as this productive — meaning biologically productive, good for all the stuff growing there — if I, if I arrange them just sort of higgily piggily haphazardly, it wouldn’t be nearly as good as if you sort of packed them together in that hexagonal… You know, like, if you pack all the pennies together as neatly as you possibly could that’s, that’s close to the pattern that you actually observed in nature.

Tarnita: Exactly, exactly. And, and it’s also if you want to think about it like, you know, let’s say markets in a, in a really big city. Imagine you live in New York City, what would you prefer? Would you prefer an enormous market somewhere, somewhere located in the city or would you like to have many mini-markets that are well stocked but smaller, but every, you know, every few blocks, right?

Strogatz: Of course, right. That’s the beautiful thing in New York. There’s a guy selling fruit on practically every corner.

Tarnita: Exactly.

Strogatz: You can go out and get fresh cherries or whatever you want and you only have to walk one block.

Tarnita: Exactly. Because if you had to take the subway to buy cherries, you probably would never end up eating cherries anymore, right? If you had to travel quite so far to, to do your shopping.

Strogatz: Mm-hmm.

Tarnita: So it’s the same, right? They’re just, they’re, they’re distributed evenly enough that at any point in the landscape, any… anyone at any point in the landscape is kind of close to one of these spots of productivity.

But, but what they hadn’t figured out is why would this happen? What exactly produces this pattern? Is there an underlying template that was geological somehow in nature? Or are the termites themselves doing something to create the pattern?

And so basically my strategy is that I never say no to a question that involves social insects. If you pose to me a question about social insects, I will embrace it because I know I will learn something amazing from that. That’s what I learned from E.O. Wilson and the ants.

Strogatz: Okay.

Tarnita: So I immediately just embraced this. I thought, “Okay let’s, let’s think about it.” And, and so in that system we realized that this competition for resources is what is driving the, the self-organization of the mounds. That you don’t really need to see very far away, all you know is that you want to be far away from your neighbors because they will fight with you for those resources. And if you are seeing neighbors who are smaller than you are, you’ll kill them.

Strogatz: Uh-huh.

Tarnita: So that strategy is enough to produce this basically hexagonal pattern, we call it. It’s, it’s like, if you were to draw the edges of the territories, if you were thinking about the territory of such a mound, that’s the territory in which the termites go out to forage for their resources. If you drew such edges around them, they would look like a honeycomb. They would at the, the landscape scale, they would create this honeycomb pattern.

Strogatz: Mm-hmm.

Tarnita: And so the idea is that this pattern of having six neighbors, all of them of, of equal sizes and, and equally spaced from you, is the optimal way of arranging yourself to use up resources.

And that was one, that was one thing that we, we figured out. But at the time there was a, a bigger question and the question was: You know, people had been working on patterns in ecology for a while and spot-like patterns, these things that you see form the sky and they look like a pepperoni pizza, either the pepperoni are either dirt or they are vegetation, but basically it’s, it’s the same, the same organization of the, of the pepperonis…

Strogatz: So let’s get to the bottom of this. How did the savannah get its spots?

Tarnita: There was an explanation for such patterns that involved also a phenomenon of self-organization, but that was driven by the plants.

Strogatz: Uh-huh.

Tarnita: And that work was very much inspired by work that Alan Turing had done in the, in the early ’50s to try to understand how patterns form on animal coats, right?

Strogatz: So, right, so we here we have to just pause to let that sink in, because this is a cameo appearance now from one of the great minds of all times really, but certainly of the 20th century, Alan Turing. Who people think of as, you know, one of the creators of computer science, the, the hero of the movie Imitation Game, if you saw that with Benedict Cumberbatch as Turing, helping to break the Nazi Enigma code.

Tarnita: I did.

Strogatz: Right.

Tarnita: Right.

Strogatz: So, we got Alan Turing, who right at the end of his life started thinking about biology in a very serious way with his paper about pattern formation, morphogenesis in biology.

Tarnita: Right.

Strogatz: And so this is what you’re talking about that, that Turing had a model that would predict these hex— what, like hexagonal spot patterns under certain circumstances?

Tarnita: Exactly.

Strogatz: But you say it’s the vegetation that were responsible.

Tarnita: Exactly.

Strogatz: What do you mean about the vegetation being responsible?

Tarnita: So, so Turing really wanted to understand how animal coats get their patterns and this pepperoni pizza pattern is basically like a leopard spot pattern.

Strogatz: Mm-hmm.

Tarnita: Um, and so Turing made a model that had to do with chemistry and, and morphogenesis and tried to understand how such patterns can develop. Ecologists in the ’90s and, and — when they became aware of these very large-scale patterns of vegetation, I mean ’70s, ’80s, ’90s — started to embrace the same model to try to explain how such patterns might arise in ecology or, you know, just out there in nature.

And the main idea behind those models is that vegetation can also self-organize. And what does that mean? So plants actually interact with each other. When we think of plants, we think of something very static, but that’s not true, they’re very interesting and they have a lot of really weird and unusual behaviors. They’re, they’re statically so, but they can communicate with each other, they can compete with each other, they can do all sorts of things for each other. And so, two very simple types of interactions are facilitation and competition.

So if you think about a tree and you’re in the desert and you’re a grass, it’s very good for you to be close to that tree, because you’re shaded, let’s say from the very, you know, unforgiving sun that would destroy a really tiny plant. So being in the shade of another plant, it’s a good thing.

Strogatz: Okay, so you’ve been facilitated by that tree.

Tarnita: So you’ve been facilitated. Another thing is that if you’re, if you’re — again, think of some place that’s really barren. If a plant is in a, is, is somewhere — has somehow managed to establish itself in that really barren area, then its roots are going to maintain moisture at the surface at just the right level for other plants to be able to establish, so other plants can grow nearby. So that’s another example of facilitation.

Strogatz: Uh-huh.

Tarnita: But also of course, plants also compete. I mean, in the same way they compete for water and they compete for nutrients and — it’s this interplay between the facilitation and the competition. It, it’s good to be close to another plant, but once that group of plants becomes really big and strong, they’re very competitive in getting the water from the environment and other plants nearby can’t have access to the water anymore. And so you establish this area where no other plants can grow.

And then when you’re far away from this successful clump, you maybe can establish as a new plant and so on and so forth. So there, there’s going to be a region where plants do well together and because those plants do well together, immediately near that there’s going to be a region where other plants can’t do well.

Strogatz: Mm-hmm.

Tarnita: And so this kind of interaction that happens at these different scales can lead to pattern formation, where you had green and then barren and then green and then barren and then green and then barren and then repeats itself. And, and so that’s one way of creating such spots of vegetation.

Strogatz: Mm-hmm, mm-hmm.

Tarnita: So when I started to think about this and I saw those spots I could have sworn that those were the result of such models of these Turing-type models. But then when Rob told me that there’s a termite mound under each one of those spots, I thought that the coincidence is a little bit too much, um, and I wanted to understand —

Strogatz: [LAUGHS] Wait, so right under the mound, you mean it’s just — that it’s a known fact that under spot there happens to be a termite [LAUGHS] mound under there.

Tarnita: And exactly one, right, exactly one.

Strogatz: And just one, okay.

Tarnita: So this was a little bit too much, right? So it’s, yeah, I mean, then you can ask the question, “Okay, well maybe it’s a little bit hard to believe that the vegetation spots have grown to that one size that is exactly the size of a termite mound.” To me it was, it made more sense to think that, “Oh, it’s probably the termites that are doing something and then their activity is driving the pattern in the plants.” And we see them as spots of vegetation, but we actually aren’t seeing the real actors. The real actors are underground and they’re the termites.

I thought that both explanations made a lot of sense in the sense that the mechanisms that go into these two different kinds of models could in principle both arise. So yes, there’s going to be facilitation and competition between plants and, yes, termites are going to compete for resources.

So then I asked myself, “What would happen if you had all of these mechanisms play out in the same system, but possibly on very different scales?” So maybe the termites fight with each other, you know, at a 30-meter distance, but plants only facilitate each other on a few centimeters and maybe compete with each other on half-a-meter-to-a-meter distances, right? So there could be very different distances on which these mechanisms play out.

Strogatz: Mm-hmm.

Tarnita: And I thought, “What if I made a model that, that threw all of these mechanisms together, what would I see?”

Strogatz: Mmm, nice.

Tarnita: And, and, um, the prediction was that I should see two different kinds of patterns, one at a larger scale and one at a smaller scale. And the one at a larger scale it, it made a lot of sense, it — they, they were the termites, because they really are much more broad in how far they can travel. But then it, it, it suggested that we should find this much smaller scale pattern also very much like a pepperoni, you know, pizza but at, at this much smaller scale, the scale of centimeters or tens of centimeters.

Strogatz: Which would be manifested — how would it be visible, what would it look like? It’s, it’s grass clumps or something or what?

Tarnita: It’s grass, it’s exactly that. It’s grass clumps where every clump would be, yeah, you know, maybe, let’s say 20 centimeters, 25 centimeters, so maybe 10 inches in diameter and then the distance between them would be something of a similar scale.

Strogatz: Okay, uh-huh.

Tarnita: And so again, this was still in Kenya and I had been going to Kenya for a while by that time. And it really seemed to me like, “Boy I, I think I’m wrong, but how can I be wrong?” So, so it was just this moment of, like, well, if there’s going to be such a pattern, why haven’t I ever noticed it?”

Strogatz: [LAUGHS]

Tarnita: I walk around amongst these termite mounds, you know, on a daily basis when I’m there and I spend months there at a time. And so what happened was, you know, we went into the field and I with, with my collaborator, and we started to look. And we’re like, “It’s, it’s not here.” So clearly [LAUGHS] something is wrong about the model.

Until we drove and we found an area — so, so this is, this is just to, just to back up a little bit. This is the savannah, so it’s like, it’s kind of like the prairie: You get tall grasses that are dry in, in when — they, they can grow quite tall. And it’s very hard to see anything on the ground, because these tall grasses obscure any kind of soil, you just see a sea of grass basically.

Strogatz: Uh-huh.

Tarnita: And we, by driving around and, and — and kept thinking, you know, “Why can’t we see these patterns?” We got to an area where someone was doing research on the effects of fire, so they had just burnt an area. And a, a very controlled burn. And that got rid of all of this dry, dry grass and what you had was just the clumps of green grass that were very much at the bottom. It also got rid of all the litter, so it exposed all the bare ground and all of a sudden there it was: exactly the pattern that the models had predicted.

Strogatz: Whoa. [LAUGHS] This is fantastic. So you’re saying that the math led you to this prediction.

Tarnita: Right.

Strogatz: That was actually sort of under your nose except not, because it was obscured by these taller grasses.

Tarnita: Exactly.

Strogatz: And then once they were, they happened to be burnt down by this controlled burn there they were… The math got it right.

Tarnita: Exactly. And we just, we got lucky, right? If that person hadn’t started their fire research project, you know, we maybe, we’d never, maybe we would have just said, “You know, well, clearly the, the model is off. We have to think about it some more.”

Strogatz: [LAUGHS]

Tarnita: And so this led us to discover these two patterns at different scales and that led to some very, you know, useful predictions and interesting predictions about the interplay of these different patterns and, and feedbacks between them and what role that might have for the survival of that ecosystem in the face of various stressors. For example stressors that are associated with climate change like, like decreased precipitation.

That’s now we started to think about these multiscale patterns. And as we were thinking about this system that had nothing to do with the fairy circles, we, we got into the literature a bit more and we found this example of the fairy circles. And we realized that it was a pretty controversial topic, where people had been arguing for a long time about what exactly causes them and there are many different kinds of explanations — again, from the kind of quirky ones with fairies and dragons and whatnot to, you know, very reasonable scientific explanations.

And the two major ones that were under heated debate at the moment, at that moment were: Is it vegetation that has self-organized and is creating these barren patches or are there termites underneath?

And we thought, “Well, surely this is, this, this multiscale pattern formation that we are starting to develop might be the one thing that will help us move a little bit from this stalemate.”


Strogatz: What Corina is saying is that there are actually two patterns, but most people were so mesmerized by the large-scale pattern, the fairy circles, that they kind of ignored or overlooked the small-scale pattern, the, the tiny one that Corina and her team uncovered. Once they observed that there was more than one pattern, they could make better sense of the ecological forces that were driving them.

Tarnita: And, and that’s the beauty of it. That now that we know that there are two patterns in that system, no one explanation can provide both patterns. You need —

Strogatz: I see.

Tarnita: — multiple things going on.

Strogatz: A natural question, though, is, you know… You and I both as math people love explaining patterns for their own sake, but there is still this larger question of, “What’s the…” You know, is there some bigger significance to the work that you’ve done?

Tarnita: Right. So why do we care?

Strogatz: Yeah.

Tarnita: Interestingly, the, the Turing model that I mentioned that was employed to try to explain what’s going on also made a prediction that in, in dry systems, as the precipitation declines, as you have less and less precipitation, what you’d expect is that you start to lose your vegetation, right? Less water, things are going to start doing poorly until you have nothing.

Strogatz: Sure.

Tarnita: In the end you should get to desert.

Strogatz: Yeah.

Tarnita: But the prediction of the model is that, to get to desert, you don’t go there just by having a lawn of vegetation that quickly … that, that’s slowly kind of become smaller and smaller and smaller, but rather you go through a series of patterns. The first thing you start to see are gaps in your otherwise beautiful lawn, just gaps of dirt.

Strogatz: Uh-huh.

Tarnita: Those gaps get bigger. As they get bigger, they start to form like a mazelike pattern. As the, as, as things do even more poorly, as you have less and less precipitation, those labyrinthine, you know, mazelike patterns break apart and you start to see these spots of vegetation. So the model predicted that you’re going to lose the vegetation in the system in a very predictable manner.

Strogatz: I see, so there’s a progression of catastrophe.

Tarnita: Exactly. And that if that’s the case, and it’s always the same progression, then by looking at the pattern you should be able to tell how healthy your ecosystem is.

Strogatz: Oh.

Tarnita: If it has gaps of vegetation, then it’s not so bad. But if it has spots of vegetation then you should probably direct resources to that area because that system is in danger of collapse. It turns out that the spots are the most dangerous ones in those models. It’s basically the last pattern you see before you go catastrophically to desert.


Strogatz: You get this feeling that there’s all these quiet mechanisms that we’re not aware of happening that are structuring the landscape and structuring life in this ecosystem. And, and where math comes into that is that we can write equations for all of those interactions. And, and the push-and-pull between them for the plants, for the termites, for everybody out there, in a way that if you just tried to understand what was happening by pure, you know, verbal reasoning, just by words, you wouldn’t see all the implications. The math is, is the infrastructure for drawing out the surprising implications of what happens in these ecosystems when the plants and the termites are doing their thing.

Tarnita: In our case, we had the spots of vegetation but they were created by termite mounds underlying those spots. And then there were the smaller spots of vegetation in between these big spots. So which spots predict what? And so when we made that model that was coupling these different mechanisms, the prediction was that actually if the big spots of vegetation that you see are created by termite mounds and not just by vegetation self-organizing, then that system is actually very healthy.

Strogatz: Hmm.

Tarnita: So it’s the exact same spots, they look like spots of vegetation. Everything looks like the pepperoni pizza. But if the big spots of vegetation are driven entirely by plants interacting with each other, facilitation/competition then that’s a system that’s in danger of collapse to desert. If those same spots are in fact driven by termites and they look like spots of vegetation only because the plants do so well on the termite mounds, then that system is actually very healthy.

Strogatz: Hmm.

Tarnita: So this was interesting because you know you could have the exact same pattern and yet unless you know exactly what’s underlying that pattern, you won’t know how to use the pattern as an indicator for anything else.

Strogatz: Huh, so it’s very interesting that, that, that just too superficial an understanding will not give you these kinds of insights. It’s, it’s not just the patterns, but the — the patterns have meaning that, that comes only from this deeper understanding.

Tarnita: Right, and, and I think, you know, it’s one of these moments of, of really reconsidering. I mean it’s very tempting now to use, you know, big datasets and global datasets and, and satellite imagery and, and do a lot very remotely, right? Do a lot of analysis because of course it’s, it’s really — we have access to this kind of information and, and it’s really important to, to use it, but at the same time, this kind of example — you know, multiple mechanisms leading to the same pattern with very different consequences for the system as a whole — really shows you how important it is to still go back on the ground, revisit those systems, be the naturalist that, you know, that Ed Wilson would want everyone to be and, you know, understand the biology of the actual system that you’re thinking about. And, and only then can you, can you begin to understand, you know, how everything is connected.


StrogatzAt, at the end of our conversation, I was thinking back about what Corina had said about E.O. Wilson, how he was so enamored of his ants. And it kind of got me thinking about how all of us in science have our own favorite creatures, our favorite equations. There are just those little somethings that are so special to us, because they often illustrate much bigger principles.

Tarnita: You know it’s like when, when you fall in love, especially when you fall in love for the first time. You want to talk about that person all the time.

Strogatz: [LAUGHS] Yes, you do. [LAUGHS]

Tarnita: You just never tire of saying how amazing they are and how many different things they can do, right?

Strogatz: Yeah.

Tarnita: It’s, it’s not so much that you clinically understand a lot about that person and you can describe it as if you were their therapist, right? No, it’s, it’s, it’s you love to talk about that person, right? That’s how it felt to me to listen to Ed Wilson.

Strogatz: [LAUGHS] It’s so true. I see.

Tarnita: And, and I wanted to feel like that. Like not just, not just that, “Oh, it’s amazing that I understand so many things about the biology and now I can tell other people about it.” It’s, it’s that I feel that I, I can barely contain my enthusiasm in telling you about these patterns and, and how these tiny, tiny insects create these patterns. And so that’s, to me, that’s the feeling I wanted to have and, and I, I, I think I have it, yeah.

Strogatz: It sure sounds like you have it. [LAUGHS]

Tarnita: Right. [LAUGHS]

Strogatz: Well, that is, that’s beautiful, that’s great.


Thank you very much, Corina for telling us all about that.

Tarnita: Sure, my pleasure.

Next time on “The Joy of x,” John Urschel solves a puzzle, how to play for the NFL and be a mathematician.


“The Joy of x” is a podcast project of Quanta Magazine. We’re produced by Story Mechanics. Our producers are Dana Bialek and Camille Petersen. Our music is composed by Yuri Weber and Charles Michelet. Ellen Horne is our executive producer. From Quanta Magazine, our editorial advisors are Thomas Lin and John Rennie. Our sound engineers are Charles Michelet, and at the Cornell University Broadcast Studio, Glen Palmer and Bertrand Odom-Reed, though I know him as Bert. I’m Steve Strogatz. Thanks for listening.


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