On October 11th, Simon Levin visited the University of Washington to give a seminar on “The Challenge of Sustainability and the Promise of Mathematics.” Interviewing Dr. Levin had been on our minds since we launched Diverse Introspectives, and we were further motivated when his name was put forward in response to a call for suggested interviews on twitter. Halley Froehlich and I jumped at the opportunity to talk with him, and are fortunate to have secured some of his limited time so that we could share his thoughts with you.
Dr. Levin is the George M. Moffett Professor of Biology at Princeton University. He holds many distinctions, probably most famously as having received the MacArthur Award and producing the highly influential lecture/paper on the “Problem of Pattern and Scale in Ecology.” Trained as a mathematician, he brings a unique perspective to ecology, one that is well expressed in a quote from Darwin that Vinicius recently shared:
“…at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.”
Many thanks to Dr. Levin for sharing his extra sense with us!
- Can you share with us a paper or papers that were particularly influential to you when you were a graduate student or early career scientist?
Well, in a sense, I was never actually at that point in my career, because I got my PhD in mathematics. I became involved in biology through my post-doctoral work, and more so when I became faculty. I was actually initially more influenced by books than papers. I started out by reading Slobodkin’s Growth and Regulation of Animal Populations, Evelyn Hutchinson’s several writings but especially The Ecological Theater and the Evolutionary Play, and Dick Levins’ book, Evolution in Changing Environments. The most influential papers were ones I came to only after I was done reading these books, but I would say a paper I keep coming back to is Hutchinson’s Paradox of the Plankton, about how species can coexist. Another highly influential paper for me was by Skellam (1951), which was one of the first papers that tried to incorporate space into ecology.
- How did you come to ecology and what motivated you?
So, as most people are when starting grad school I was pretty young and didn’t know exactly what I wanted to do. I went to graduate school in mathematics because it was the thing I did best, and I thought it couldn’t hurt to learn the methods no matter what I was going to do; but even then I began to direct myself toward applying mathematics to understand problems in the world. I thought I could make the biggest impact in biology because it was just expanding and because I was interested in the environment from a young age, when I spent a lot of time in the outdoors. I accepted a position at Cornell as an assistant professor of mathematics; and just by chance Cornell had one of the strongest ecology programs in the country, so it was very easy for me to begin sitting in on ecology lectures and courses and talking to colleagues. So I started working in the late sixties on highly theoretical ecological problems.
One of the first things I worked on was inspired by the sorts of questions that Hutchinson had raised: how do species partition the environment and how do species coexist? Early on I was thinking about competitive exclusion, but then I realized that the usual theories did not take into account the role of space and how species subdivide the environment or the role of predation. Both of those things led me very quickly to Bob Paine’s work here at the University of Washington, where I came in 1973 to do sabbatical work with Paine bringing the ecological theories down to earth by doing empirical work. We began a collaboration that is still going on. Over the years I’ve gotten closer and closer to the empirical side and closer and closer to things relevant to policy.
- It’s been over 20 years, since your MacArthur lecture and the publication of “The problem of pattern and scale in ecology”, which has become one of the most influential papers in ecology of all times. What do you think we have learnt in this past 20yrs and what are the main challenges for the next years in order to understand the problem of pattern and scale? -Vinicius Bastazini
Thanks, that’s a good question. There are lots of issues and directions that come, for me, from that paper. It’s now sort of taken for granted by people that they have to be concerned about the problem of scale, that is, that the scale at which they are studying the problem is not the only scale to think about–that the systems that they’re studying are made up of lots of entities that are interacting at a much smaller scale, and in turn the interactions at the scale they are interested in are probably giving rise to patterns at a higher scale. The real challenge, I think, is how do we understand the dynamics of large systems in terms of the interactions and dynamics of components that make them up? How much detail is necessary and what details can and should we ignore? The point is not just that models become easier when you ignore details; but if you don’t ignore that detail you get the wrong answer- you are over-parameterizing the model.
Emergence has become a huge issue in many different fields where things happen at the macroscopic scale that are the consequences of large numbers of interactions at the smaller scales. The same thing happens with the stock market. Lots of individual investors collectively influence the stock markets to rise and fall or crash or not. Having all the parts doesn’t mean you know how the system is put together, how things operate. There have been huge advances mathematically and computationally in this. It’s hard to think of a problem in science, especially in biology, that doesn’t have this feature of having to understand how an organism works in terms of all the cells, or how a collective works in terms of all the individuals. So this scaling problem I think is one of the key issues and I think we’ve made a lot of advances on that.
A topic that keeps arising every ten years or so with a different perspective is what is called a critical transition. Now it’s become a hot topic- that is, when systems that are operating in one realm are about to suddenly undergo a transition into another realm. A tipping point is another term for it. So is the stock market about to crash? Is a lake about to go from oligotrophic to eutrophic? Is an ensemble of birds about to split apart? Are there tipping points in the global circulation patterns? I’m interested especially in the tipping points of social and economic systems in terms of attitudes toward things like climate change and smoking and gender equality. All of these issues are related in terms of representing problems of pattern and scale.
Another related issue that came out of my work here at UW is the whole notion of patch dynamics. The literature now on metapopulations is exploding. For us it was in terms of the dynamics of the patches in the systems at Cape Flattery and Tatoosh Island. We weren’t the first to characterize systems in terms of patch dynamics, but insufficient attention had been paid for example to A.S. Watt’s paper on pattern and process. But now much of conservation biology is largely built on patch dynamics.
- What is an example you can think of where analytical approaches have aided in conservation management? Where different scales have been linked via mathematics to provide an effective ecological solution?
The simplest answer is reserve design. We can conserve or set aside a certain amount of land or a certain amount of the ocean into a reserve, but how do we choose where to do that? Formally this fits very nicely into a standard framework in operations research and fields of that sort. We assign each parcel of land a certain value, and then maximize the value subject to some constraint. The problem with that formulation is that these parcels of land are not independent on each other. So if we remove one parcel of land then the parcel next to it changes in value. But despite this limitation,reserve design clearly represents one application.
The other and probably more classical application where analytical tools, despite their failings, have had a tremendous positive impact is in fisheries. There have been very sound analytical foundations that have become more sophisticated with structured models of populations and things of that sort.
- What did you mean when you said “if you adopt an ecosystem services perspective”?
Ecosystem services are something I’m really interested in. I just taught a mini-course on it with the juniors at Princeton. It raises some issues that have ethical and pragmatic dimensions. When I taught the course there were three sections. The first was: Is it ethically okay to filter all decisions about conservation through the human perspective? Then, if we are filtering through the human perspective, is it OK to monetize services, and if so, how do we quantify them? A lot of people confound the first and the second issues, but they are different things.
So let me take those one at a time.
There are those who argue that it’s arrogant for us to filter everything through a human perspective, that animal species have their own right to exist and that we shouldn’t just assign specific importance to them and try to go the ecosystem services route. My answer to them, though they are generally not satisfied, is that there are two problems with that perspective. One is that if you took that perspective and said species are important in and of themselves, then it sometimes is argued that all species are equally important. But species are to some extent an arbitrary filter that humans have put on the system anyway. It’s not that there isn’t any interbreeding between species or that they don’t change over time.
Peter Kareiva and I edited a book together, actually in honor of Bob Paine, called The Importance of Species, where we asked the question: Are some species more important than others? And my conclusion is that some species have to be more important than others. But then how do you judge which species are more important? What about nitrogen fixers, like rhizobia? Without them, the nitrogen cycle would collapse, which raises the question of whether other species could replace them. But you’ve allowed then the point that certain species fulfill desirable roles for society, without which the whole ecosystem would collapse.
The other half of my argument is that even to say that all species are important is imposing a human ethical system–we’ve already put this through a human filter. So, that having been said, I come to the conclusion that it’s OK to put things through a human filter, but one has to understand in a broad sense that we don’t just need the species that we use for food and fiber and fuel and pharmaceuticals; we also need the species that help to preserve the ecosystem and to mediate climate and also the species that we put special aesthetic or ethical value on. I have no problem with saying that some species, just on ethical grounds, are more important to humans than others. I come to the logical conclusion that you have to put it through a human filter.
Then the next step is that you can give lip service to things like ethical values but that isn’t done in practice. An argument is that too much emphasis is placed on commercially important species. That’s a real problem. There are really two choices: (1) you can try to put a monetary value on everything, but there are some pragmatic problems with doing that. There is the problem that people don’t like to put a value on certain things that should have ethical importance, like human life. (2) A second alternative is to give tradeoff curves. You can say: “I don’t know how much you value the beauty of nature versus an agricultural field and I’m not going to put a monetary value on nature but I’ll give you a curve that shows that when the amount of agriculture goes up the amount of protected area goes down.” Then leave society with that information to decide via whatever democratic process. But it’s tough to do.
There are certain things you know how to put a value on because they are traded commodities. But how do you put a value on a national park? So there are a lot of pragmatic issues associated with taking this on, and these come up not just with ecosystem services but any economic decision. We have to find a way to wrestle with them. I come down to that the ecosystem services perspective is a valid one to use, that the methods are deeply flawed and we need to do better, but to some extent we are logically forced to do something similar.
- How do you or how should we put a value on biodiversity?
Well first of all I’m not sure that I would focus on biodiversity as the thing that you are trying to protect. But why do I think biodiversity is important? Well I would tend to put values on particular species and then aggregate that to get some value of biodiversity. But it’s true that biodiversity in and of itself has some value in addition to the value implicit in the individual species. There is this sort of mutual fund aspect of it, the insurance aspect of it. For example, we know that nature is a great source of pharmaceuticals. We don’t know what they are going to be, but we know that preserving a large amount of biodiversity gives us more to choose from. How you put a value on that is uncertain.
A fundamental question that comes up in any field, is the tradeoff between exploration and exploitation; this is a fundamental debate you’ll find between Republicans and Democrats and I won’t make any political statements here but it comes down to: How much do you discount the future? How much importance do you put on the fact that you’ve got a solution to today’s problems against the insurance aspects of knowing you are going to need new solutions and to explore things in the future? How much do you set aside for the future?
So that’s one aspect of it, and the other you can view in terms of experimental work that’s been done at places like Cedar Creek (by Dave Tilman) on the relationship between biodiversity and stability. There is a lot of debate surrounding this, but a lot of it is semantic. When MacArthur’s paper first came out about stability what he really meant was resilience. That means that a system wasn’t at a fixed equilibrium but that it was continuing to operate over some range of behaviors.
The paradox is that more diverse systems tend to bounce around more but because they bounce around more they have more opportunities to explore and more ways to compensate for changes. So Dave Tilman’s system shows that the more diversity within the system, the more the individual species bounce around but the more stable the ensemble average. Biodiversity is important insurance.
I think that’s a value that goes back to the emergent properties we talked about before. One has to place a value on biodiversity beyond the sum of the values of the individual species for the insurance aspect. I don’t think that we know how to do that in terms of how much you need to set aside for insurance.
This is an issue in evolutionary biology too, which is that we have mutations and recombination and you might think of these as errors; but it’s a way to explore adaptations to new environments, so there is second-order selection on mutation rates. Salmon populations generally stick to certain streams, but they are subject to something called “straying” and I think that’s been selected for as a way that when environments change, or local populations are destroyed, some individuals are able to explore new opportunities. That’s what we call adaptability.
Any kind of regulatory system has to be adaptive. So in conservation biology we need to think about the adaptive capacity of systems and biodiversity is one way to do that. If you have a system with three species that are performing the same function and you say OK, well we can spare that species we’ve got the other two, and then you spare another one, but now you’ve lost all of your backup system. The precautionary principle applies.
- What is the best way for empirical scientists to engage theory and theoreticians? – Phil Levin/Twitter
Well Phil is a good example; he’s done a good job of that. I think that you can do a good job if you avoid doing things like what Ed Wilson recently said. He said you don’t need to learn math, that there will be times when you need math but you can always find a mathematician off the shelf to do it. And I think that’s just wrong. I think the best ways that partnerships happen is when the biologist learns something from the mathematician and the mathematician learns something from the biologist, the problems become really joint problems, and you don’t know whose ownership it is.
I think people bring certain skills to the table and the only way these things really work well is when there is a mutualism when both of them learn enough about the other’s way of thinking. I’ve been trying to do that for the last 20 years in a different sphere by working with economists. So I’ve learned a lot of economics and it’s fun to learn but it also helps me to get into their way of thinking. These can’t be one way streets. I respect E.O. Wilson, but I think his advice is just wrong.
- Speaking as a student, why do think many biology students shy away from higher level math? What advice would you give these students to have them overcome their quantitative trepidations?
Well there are two possibilities. The first is to choose something else. Go into English or something. The other is to do it whether or not you are afraid. You know, I don’t want to do gels, I don’t even want to do computer programming any more. I have to learn enough to understand what’s needed and what can be done and understand who can do it. But in an increasingly multidisciplinary world the real challenge for people is to find out how to do collaborations.
Students of biology, if they really hate the math and don’t think it’s useful that’s one thing and they really should go into another field. But if they know that an analytical perspective would be helpful but they don’t feel capable or they don’t want to make the investment of time–the real trick is to learn how to choose collaborators and how to work with them. The second half of that is to do it as a real partnership with mutual respect. I’ve been lucky with that, but you really have to be careful about how you choose your collaborators and it’s not easy to teach.
But the answer to the biologists who don’t want to learn mathematics is the opposite of what E.O. Wilson said. It is the case that you need to find people that can fill your gaps. On that I agree with him, but in order to do that you have to learn a little bit about mathematics, about what the subject can do, about the newest computer languages and what can be done with the computer and what the strengths and weaknesses are so you can choose appropriate collaborators. That’s really the art for biologists trying to choose a mathematician to work with, but really for anyone looking for people to fill their gaps.
November 12, 2013