This post is inspired by an honest and good-humored comment by Robin Svensson on my post on zombie ideas in ecology. Robin, by his own admission, is a zombie—he stills sees value in classical theoretical ideas about the intermediate disturbance hypothesis (IDH) despite my attempt to blast these zombie ideas into oblivion. He also raises questions about the limitations of mathematical models as a tool for explaining nature.
I replied to Robin’s comment in that comment thread, and he’s since followed up with a further comment specifically related to the IDH which suggests to me that he is not totally in the grip of zombie ideas. But Robin’s initial comment inspired me to think more broadly about communication issues between empiricists and theoreticians in ecology. Put simply, empiricists and theoreticians in ecology (and in other fields) often seem to talk past one another, or just not “get” what the other is saying. Why is that?
One standard answer is that theoreticians often insist on searching for simple truths, while natural historians deny that there are any (e.g., Lawton 1995 Oikos). Lawton, quoting Mick Crawley, refers to the latter as the “WIWACS”, the World is Infinitely Wonderful And Complex School of ecology. Science journalist John Whitfield identified a similar divide in evolution. On the one side is the “lean and mean” school (many of them Englishmen or adoptive Englishmen, such as Fisher, Haldane, Hamilton, Maynard Smith, Price, Dawkins, and Grafen) who tend to emphasize the importance of natural selection above all else and who express simple ideas in the form of elegant mathematics (aside: Marek Kohn’s A Reason for Everything is a wonderful popular history of the leading figures of this school) On the other side is the “let a thousand flowers bloom” school, exemplified by Stephen J. Gould, who see the world’s evolutionary history as the net outcome of many complex and only partially-understandable factors acting on different levels at different timescales. (Interestingly, both schools can legitimately claim Darwin as their most important intellectual ancestor)
But while this divide is undoubtedly important, I’m not sure it’s the whole story, or perhaps even the main one. For instance, in his initial comment, Robin both defends the value (although not the complete correctness) of very simple classical ideas about the IDH, while also questioning the ability of any mathematical model to fully capture the polyglot complexity of nature. So on the one hand he’s valuing simplicity, but on the other hand he’s expressing a reluctance to simplify. Please understand that I’m not trying to pick on Robin here and I wouldn’t even say his views are necessarily contradictory (I’m sure a single blog comment isn’t a full and fair summary of his views). My point is simply that the views he expresses in his comment, which certainly aren’t unique to him, aren’t really well-summarized by calling him a member of WIWACS. And conversely, not all theoreticians always seek simplicity.
So what are some of the other reasons why empiricists and theoreticians so often seem to talk past one another or don’t quite “get” what the other is saying?
One reason is the ambiguity of words. Like many non-mathematicians, I suspect when Robin reads a theoretical paper he tends to skim over the math and just reads the words that summarize the math. Honestly, I often do the same. The trouble is that words are inherently less precise than math, so there’s always a loss of information when equations are converted to sentences. Further, in order to make their ideas understood, theoreticians (hopefully!) don’t invent new jargon every time they do a new bit of math. That would be not only off-putting to readers, but unhelpful, because the new jargon would then have to be explained in familiar terms the reader could understand. But unfortunately, there are only so many familiar terms in the world, and many of them have already accumulated various meanings (both denotations and connotations). So for instance, when Peter Chesson describes the storage effect as a model of “temporal niches”, and someone else describes Hutchinson (1961) as a model of “temporal niches”, neither description is incorrect. But using “temporal niches” to cover both Hutchinson’s logically-invalid model (in which fluctuations in environmental conditions actually have no effect whatsoever on coexistence) and Chesson’s logically-valid model, merely obscures the very important differences between them. If you have to use words people have already heard in other contexts, there’s a serious and probably unavoidable risk that you’re going to be misunderstood.
Another reason, which I find a little difficult to articulate and on which I may be way off base, is that I think theoreticians and empiricists sometimes misunderstand each other’s long-term goals. Let me try to get at this with a secondhand anecdote. Empiricists often complain that mathematical models are oversimplified descriptions of nature. In response, theoretician Hal Caswell (1988) relates going to a highly empirical poster session at an ecological conference and counting up all the explanatory variables used on each poster. The average was something like two, and no study considered more than a handful. From this, Hal concluded that empiricists “oversimplify” just as much as theoreticians, since in no case would anyone claim that the small number of explanatory variables studied were the only ones affecting the dependent variable of interest. At one level, Hal absolutely has a point, but Robin’s comments prompted to wonder if on a deeper level he’s kind of misunderstood what empiricists are trying to do. Empiricists aren’t stupid, and I’m sure they wouldn’t claim (because it typically would be a stupid claim) that in any one experiment they manipulate all the explanatory variables that matter. I doubt they’d even want to conduct such a manipulation even if it were possible (given billions of dollars, armies of field assistants, etc.). Rather, I think what many empiricists would (could?) say is that, over the course of many observations and experiments, aimed at addressing a variety of distinct and perhaps not even closely-related questions, they’re out to build up some kind of synthetic understanding of how their complex study system works and how various features of it all “fit together”. And I think they would further say that that understanding comprises something more than just the sum of the results of all those individual observations and experiments, even though it would be difficult or impossible to express that understanding in the form of a single mathematical model. So while empiricists aren’t necessarily uninterested in mathematical models, which might for instance help them predict the outcome of some particular experiment, they see existing models as just one small set of pieces in what will ultimately be some much larger edifice. Indeed, individual observations and experiments would just be small pieces in that edifice, too. In contrast, theoreticians often set out to understand the consequences of one particular phenomenon or process. In order to focus on that particular phenomenon or process, they often assume that everything else about the world is really simple. From a theoretician’s point of view, there’s no point in including arbitrary complexity in a model just for the sake of doing so—that would just get in the way of understanding the particular process or phenomenon of interest. If you’re a painter who wants to really learn how to paint flowers, you might isolate a vase of flowers in your studio and paint many studies of it, even though in the real world flowers (even vases of flowers) aren’t isolated from all other objects. Note that this isn’t the same thing as seeking simplicity per se–flowers themselves can be really complicated to paint, and analogously the consequences of a single process can be tremendously complex. Even when theoreticians do include complicating factors, there’s usually still one particular process or phenomenon that’s of primary interest (the flowers are still the focal point of the painting). And then when theoreticians figure out how a particular process or phenomenon works, they move on to a different one. The long-term goal is to accumulate an understanding of various distinct processes affecting various distinct things, not usually to build up an understanding of how a whole bunch of processes, all operating simultaneously and each of which affects various things, “fit together”. For instance, nobody ever tries to model the combined effects of all known coexistence mechanisms, even though in nature IDH-type mechanisms often co-occur with resource partitioning, competitive ability-predation resistance trade-offs, competition-colonization trade-offs, spatial niche differences, etc. And nobody would also try to include in their model the side effects of all those coexistence mechanisms on evolution, ecosystem function, etc.
A third reason why theoreticians and empiricists sometimes fail to “get” each other is that, paradoxically, it’s precisely because empiricists are so sensitive to all the wonderful details of the ecology of their study systems that they sometimes latch onto quite simple verbal ideas and hypotheses, such as classical versions of the IDH. It’s a bit like someone clinging to a life raft in a vast ocean. If you know that all models are wrong, or at least incomplete, (as indeed they are), and you’re daunted by the vast range of models out there, then maybe you feel that you might as well just stick with the simplest wrong model. Like climbing into the closest life raft, or clinging to the nearest bit of floating debris, rather than swimming around trying to locate a seaworthy boat you know doesn’t exist.
So how can the divide be bridged? It’s pretty pointless to just call for theoreticians to explain themselves better—they mostly already try to explain themselves as best they can—or for empiricists to learn more math—they already spend all their time learning and doing other things they need to learn and do. But I have a couple of suggestions.
One (and this is really a wish more than a suggestion) is that empiricists do need to realize that some false models are just uselessly false. That life raft you think you’re clinging to? It’s actually a great white shark, and you would be better off swimming away and looking for something else to cling to, or just trying to float without clinging to anything, because the risk of drowning is preferable to the certainty of being eaten. (okay, I think I’ve now officially broken the whole life raft metaphor…) If I predict that intermediate levels of disturbance prevent competitive exclusion “because that’s the way the Flying Spaghetti Monster wants it”, finding that intermediate levels of disturbance sometimes prevent competitive exclusion is not evidence for the Flying Spaghetti Monster. Just because a prediction is testable does not mean it’s useful to test it.
Second, if you line up various alternative theoretical models rather than just testing the predictions of a single theoretical model against some statistical null, and if you make sure your tests are stringent ones, I think you’ll start to develop better judgment as to when a model is worth taking seriously, and when it should be regarded skeptically. For instance, many very different models predict that diversity will, or might, peak at intermediate levels of disturbance. So to distinguish those alternative models, or even develop evidence for or against any one of them, you can’t just test their predictions about the disturbance-diversity relationship. Testing alternative models also forces you to pay close attention to the distinctions between them, rather than glossing over those distinctions (e.g., mistakenly thinking of all “temporal niche” models as basically the same). And don’t just limit yourself to testing weak predictions. Predicting that one variable has a humped relationship with another variable (e.g., diversity peaks at intermediate disturbance) is a weak qualitative prediction, which will often turn out “correct” just by dumb luck. That is, the model (sometimes) gives you the right answer for the wrong reasons. A stopped clock is right twice a day, but that doesn’t mean it’s a good clock, even only for two brief moments per day. If I think that flipped coins always come up heads, I’ll call half of all coin flips correctly, but that doesn’t mean I have even a halfway-decent model in my head of how coin flips work.
Third, I recommend that empiricists read theoretical papers that directly address their concerns about mathematical models, and that share their larger goals. For instance, if you worry that all models omit real-world biological complexities, you should read stuff like Dave Tilman’s 1990 book chapter in Perspectives on Plant Competition. Here, David adds various realistic biological complexities into his famous, extremely simple theoretical models of resource competition and asks how these complexities affect the model predictions (in this case, the answer is “they don’t”). If your larger goal is to figure out the joint consequences of a bunch of interacting processes, read stuff like the wonderful work of theoretician Tony Ives and colleagues (Ives et al. 2008). They showed how the dramatic but irregular fluctuations in the abundance of an Icelandic midge can be explained by a very empirically-detailed population model When I asked Tony how he’d developed the model, he said that he basically just sat down with his colleagues, who’d been studying these midges and their environment for many years, and they told him everything they knew about the biology of the midge and its environment. Tony just converted all that biology into math. And it turns out that that biology does explain the dynamics, but for reasons that have to do with stochastic switching between alternative attractors and so couldn’t possibly have been fathomed without doing the math. There’s a world of theory out there, developed for a variety of purposes, and not all theoreticians are always seeking to simplify at all costs. Seek out the ones whose “style” and goals match your own.
p.s. While the above discussion was inspired by Robin’s comments, my intent is not to put any words into Robin’s mouth—he can speak for himself, obviously. Robin’s comment inspired me to think about this stuff more broadly, and the point is not to attribute to him any specific views on all this.