Katie Koelle delivered the opening talk in the Ignite session on “theory vs. empiricism” at the ESA meeting.* I thought she raised several interesting issues that weren’t really touched on in the rest of the session. I was struck by one remark in particular: that theory in ecology is dying, or at least going out of fashion, and is being replaced by modeling.
Theory here means trying to discover or derive general principles or laws–the fundamental simplicity underlying and unifying the apparent polyglot complexity of nature. Think of evolution by natural selection, the laws of thermodynamics, general relativity, MaxEnt, and statistical “attractors” like the central limit theorem and extreme value theory.
In contrast, modeling here means building a mathematical description of some specific system, in order to explain or predict some aspect of that system. The model need not include every detail about that specific system, but it is tailored to that system. So there’s no hope or expectation that it will explain or predict any other system (though importantly, there could still be commonalities or analogies with other systems). Think of global climate change models, or models of various cycling species, or Meg’s award winning work on host-parasite dynamics in Daphnia.**
Hopefully it goes without saying that both theory and models are hugely valuable in science (indeed, both John and Tony note this in the links above). But there’s much more that can be said about the distinction (and I do think it’s a real distinction, or at least two ends of a continuum). Here are my thoughts (strap in, there’s a lot of them!):
- I think Katia and Karen are right that modeling is the hot thing right now in ecology, while theory’s not, except for a small number of theories that are hot because it’s possible to treat them like models in the sense that you can fit them to data (e.g., MaxEnt). I think John Harte gets at one big reason why in the interview linked to above: advances in software and computing power mean that it’s now easier than ever to do simulate complicated, analytically-intractable models, and to fit those models to data using computationally-intensive statistical approaches. Water flows downhill, following the path of least resistance, and so does science. If X becomes easier to do than it used to be, people are going to do more of X. Which is a good thing, at least up to a point. I mean, if there was something we wanted to do more of, but couldn’t because it wasn’t technically feasible, then surely we ought to do more of it once it becomes technically feasible! The danger, of course, is that people start doing X just because it’s easy (never mind if it’s the right thing to do), or because it’s what everyone else is doing (a bandwagon). There’s a thin line between hammering nails because you’ve just been given a hammer, and thinking everything is a nail because you’ve just been given a hammer (or thinking that, because you’ve just been given a hammer, the only thing worth doing is hammering nails). There’s an analogy here to adaptive evolution. The direction in which a population evolves under natural selection depends both on the direction of selection, and on the genetic variance-covariance matrix. The “direction of selection” in science is what we’d do if we were unconstrained by technology, time, money, or effort. The “genetic variance-covariance matrix” is the constraints that define the paths of least resistance, and the intractable dead ends. The art of doing science well is figuring out the optimal “direction of evolution”, balancing what we’d like to do and what’s easiest to do.
- I think the trend away from theory and towards modeling in ecology is a long-term trend. See for instance this essay from the early ’90s from Jim Brown, arguing for the continuing value of theory (well, maybe; more on that in a second), and the response from Peter Kareiva, arguing that ecologists need to get away from general theories and move towards system-specific modeling. I think Kareiva’s point of view is winning. As evidence for this, recall that in recent decades, the most cited papers in ecology have not been theory papers, in contrast to earlier decades.
- That Kareiva essay gets at another reason why I think modeling is ascendant over theory in ecology: theory often is hard to test. It’s not merely that lots of different theories tend to predict the same patterns, so that those patterns don’t really provide a severe test of any of the theories, although that’s often part of it. It’s also that, because theories aren’t system-specific, they’re often hard to link to data from any specific system (and all data come from some specific system or systems). How do you tell the difference between a theory that “captures the essence” of what’s going on but yet doesn’t match the data well because it omits “inessential” details, and a theory that’s just wrong? The link between theory and data (as opposed to model and data) often involves a lot of hand-waving. And while I do think there’s such a thing as good hand-waving, so that “good hand wavers” are better at testing theory than bad hand wavers, I admit I can’t really characterize “good hand waving” except to say that I think I know it when I see it.
- If the previous two bullets are right, then that means ecologists are getting over Robert MacArthur. That is, they’re getting away from doing the sort of theory MacArthur did, and trying to test theory in the way that MacArthur did (e.g., by looking for a fuzzy match between qualitative theoretical predictions and noisy observational data). On balance, and with no disrespect at all to MacArthur (a giant who helped invent ecology as a professional science), I think that’s progress. But I’m not sure. Maybe it’s progress in some respects, but retrogression in other respects, with the net result being difficult or impossible to calculate? Brian for one seems to have mixed feelings. On the one hand, he has called for mathematical descriptions of nature to start “earning their keep” more than they have (e.g., by making bold, quantitative predictions that are testable with data). Which would seem to be a call for more models and less theory. But on the other hand, he’s also lamented that ecologists seem to be running out of big theoretical ideas. And Morgan Ernest has expressed mixed feelings about how we’re becoming more rigorous but less creative, better at answering questions but less good at identifying questions worth answering.
- As Tony Ives notes in the interview linked to above, being a modeler as opposed to a theoretician doesn’t mean just becoming a mathematical stamp collector and giving up on the search for generalities. Because there often are analogies and similarities between apparently-different systems. One way to model a specific system is to recognize the ways in which that system is analogous to other systems. See this old post for further discussion, and this excellent piece for a discussion in a related context.
- It’s tempting to think that the divide between theory and models might have cultural roots, much as the divide between theory and empiricism ultimately is cultural. Perhaps it reflects a cultural divide among mathematicians between theory builders and problem solvers.*** Maybe theoreticians in ecology are really mathematicians or physicists at heart, while modelers are biologists or engineers at heart. Maybe theoreticians care about simplicity and elegance, while modelers revel in complexity. Maybe theoreticians care about fundamental questions while modelers care about practical applications. But I’m not sure. For instance, in that interview linked to above, theoretician John Harte talks about the value of theory (as opposed to models) for conservation, and for getting policy makers to take ecologists seriously. He also talks about how important it is to him to do field work and to get out in nature. Conversely, Ben Bolker is a modeler rather than a theoretician, but in describing his own motivations he talks about loving the ideas of physics and mathematics and being only loosely anchored in the natural history of particular systems. So I’m not sure that the divide here is a cultural one; it might be more of a personal, different-strokes-for-different-folks thing. And in any case I hope it’s not cultural, since cultural divides are pretty intractable and tend to give rise to mutual misunderstanding and incomprehension.
- That linked piece from the previous bullet on the two cultures of mathematicians suggests that there are areas of mathematics where you need theory to get anywhere, and others where you need modeling to get anywhere. That’s a fascinating suggestion to me–do you think the same is true in ecology? For instance, to use John Harte and Tony Ives as examples again, maybe you need theory to make headway in macroecology, as John Harte has been doing in his MaxEnt work? While maybe you need modeling to make headway on population dynamics, as Tony Ives has been doing?
- The difference between theories and models isn’t always clear. For instance, is the “metabolic theory of ecology” a theory? I’m honestly not sure. The core of it–West et al. 1997–looks like a model to me. For instance, it’s got a pretty large number of parameters, and it’s got different simplifying assumptions tailored to circulatory systems that have, or lack, pulsatile flow. Ecologists refer to the “theory” of island biogeography–but isn’t that really just a very simplified model of colonization and extinction on islands? The same way the Lotka-Volterra predator-prey “model” is a very simplified model of predator-prey dynamics? Maybe theory and models are more like two ends of a continuum? The more simplifying assumptions you make, and the less tailored your assumptions are to any particular system, the closer you are to the theory end of the continuum?
- One can talk about subtypes of theory and models too. For instance, Levins (1966) famously suggested a three-way trade-off between realism, precision, and generality in modeling. Models that sacrifice generality for precision and realism are what I’m calling “models”. While models that sacrifice precision for realism and generality, and models that sacrifice realism for precision and generality, are different subtypes of what I’m calling “theory”.
- Some applications of mathematics in ecology kind of fall outside the theory-model dichotomy (or theory-model continuum). I’m thinking for instance of partitions like the Price equation, or Peter Chesson’s approach to coexistence theory. They aren’t models or theories themselves. Rather, they tell you something about the properties that any model or theory will have (e.g., any model or theory of stable coexistence will operate via equalizing mechanisms and stabilizing mechanisms).
- I’m curious how aware empirically-oriented ecologists are of the theory-model distinction. And how their awareness of it, or lack thereof, affects their attitudes towards mathematical approaches generally.
- As a grad student, I got into microcosms because that seemed like a system in which theories were models, or at least close to being models. That is, the drastic simplifying assumptions of the theories in which I was interested (“community modules”, as Bob Holt calls them) were closer to being met in microcosms than in most other systems. So that theories could be tested in a rigorous way, much as system-specific models are tested. But I’ve found myself increasingly getting away from that, and wanting to build models for microcosms. And more broadly, I’ve found myself becoming more excited about the Tony Ives approach of using models tightly linked to data to solve system-specific puzzles. I think that many of the most impressive successes in ecology over the last couple of decades have come from that approach. Even if you’re interested in general theories (and I still am), increasingly I feel like bringing data to bear on those theories is best done by bringing data to bear on models that incorporate theoretical ideas.
- After I wrote this post, I was alerted to a new paper on theory in ecology that covers much of the same ground. It’s very interesting, looks like good fodder for a future post.
*On behalf of Karen Abbott, who couldn’t make it. UPDATE: Marm Kilpatrick and Kevin Gross also contributed a lot to the intro talk.
**Yes, I know others have defined “theory” and “model” differently. Which is why I defined my own usage for purposes of this post.