Ideas, once they take root, are hard to kill. Thomas Henry Huxley famously referred to “the slaying of a beautiful hypothesis by an ugly fact” as “[t]he great tragedy of Science”. But like Hamlet, it’s a fictional tragedy—it doesn’t actually happen that way. Ideas, especially if they are widely believed, are intuitively appealing, and lack equally-intuitive replacements, tend to persist. And they persist not just in spite of a single inconvenient fact, but in spite of repeated theoretical refutations and whole piles of contrary facts. They are not truly alive—because they are not true—but neither are they dead. They are undead. They are zombie ideas.
Economist John Quiggin coined the phrase “zombie ideas“, but it isn’t just in economics where undead ideas walk among us. Ecology (and probably every field) has its own zombie ideas. In some cases they’ve survived decades of attacks from the theoretical and experimental equivalents of chainsaws and shotguns, only to return to feed on the brains of new generations of students. But this is 2011, and we have new weapons to deploy against the zombies. Weapons like blogging. Weapons whose effects can spread around the world via the internet like the bullets from a modern-day shotgun, hitting the zombies wherever they are found. Weapons I plan to use, starting right now.
The first ecological zombie in my sights: the intermediate disturbance hypothesis (IDH).
Broadly speaking, the IDH is the idea that intermediate frequencies and/or intensities of ‘disturbance’ or ‘environmental change’ maintain diversity by preventing competitive exclusion. The IDH was coined by Connell (1978) and given influential treatment by Huston (1979) and Grime (1979), among many others, but the idea goes back at least to Hutchinson (1941, 1961). The idea is now in ecology textbooks, such as the one I learned from, Begon, Harper & Townsend (2nd ed.). And refutations of the IDH have been around for a while, too. Mackey and Currie (2001) gave an empirical refutation, reviewing over 100 experimental tests of the effect of disturbance on diversity and finding that the predicted peak of diversity at intermediate disturbance levels hardly ever occurs (<20% of experiments). But more important are theoretical refutations, since a logically-invalid hypothesis literally can’t be supported (or rejected) by empirical evidence. Chesson and Huntly’s (1997) attack on the logic of the IDH and related ideas is one of my favorite papers of all time. Roxburgh et al. (2004) and Shea et al. (2004) are very good too, although they pitch their refutation as a ‘clarification’ of the IDH, a rhetorical strategy which certainly has its virtues but which also has the unfortunate drawback of letting readers think that there’s some kernel of truth in the core ideas which spawned the IDH. There’s not. In my view, zombies are beyond redemption, and trying to see the good in them while closing our eyes to the bad only exposes more people to the bad. Students especially often find it difficult to distinguish good ideas from superficially-similar bad ideas. Rude as it may sound, the only thing to do with zombie ideas is to kill them off, without mercy.
Here are the three zombie ideas at the core of the IDH:
1. Disturbance reduces species’ densities, thereby weakening or eliminating competition and preventing the competitive exclusion that occurs in undisturbed environments. But too much disturbance kills off all but the most disturbance-tolerant or quickest-recovering species, hence intermediate levels of disturbance support the highest diversity.
This is a seductively appealing idea (so maybe a better analogy than zombies would be the alien seductress in the movie Species). And it’s totally wrong. Yes, disturbances reduce species’ densities and thereby weaken competition. But as Chesson and Huntly (1997) point out, they also reduce the strength of competition needed for exclusion! Seriously, I cannot believe this zombie is so hard to kill. Anything that reduces your per-capita growth rate (disturbance, continuous sources of mortality, environmental ‘harshness’, etc.) also reduces the amount of growth that competition (or any other factor!) needs to subtract in order to push you into negative territory. Or, if you prefer to think in terms of abundances rather than growth rates (you shouldn’t, but in case you do), anything that reduces your abundance also reduces the number of individuals that competition (or any other factor) needs to subtract off in order to reduce your abundance to zero.
And if you’re the sort of person who only believes data, not math, well, I’m sorry for you, but fortunately for you the very nice paper by Violle et al. (2010) experimentally confirms theoretical refutations of this zombie idea.
2. Disturbances interrupt competitive exclusion by temporarily reducing all species to low density and weakening competition, thereby allowing all species to subsequently increase.
This is Huston’s (1979) version of the IDH, which he supported with some simulations of a Lotka-Volterra competition model with periodic, density-independent mortality events. Which just goes to show that mathematical models are ineffective weapons against zombies if you don’t fully understand your models. To his credit, Huston (1979) didn’t claim that disturbances in his model produces stable coexistence, but he did claim that they slow competitive exclusion. Which, again, is a really seductive idea (I’m starting to think I should have called these ‘alien seductress’ ideas…). I mean, you take a competition model which exhibits rapid competitive exclusion, you add disturbance, and you get much slower exclusion. Which means that disturbance slows exclusion, right? And if you look at the simulated time series, you see that all the competitors increase after each disturbance. Which means that disturbance slows competitive exclusion by interrupting it, right?
Wrong. Adding disturbances (here, density-independent mortality events) to a disturbance free model changes two features of the model, not one. Obviously, it prevents the model from reaching a deterministic equilibrium. But (apparently) less obviously, it changes the long-term average mortality rate. The correct ‘control treatment’ for Huston’s (1979) numerical ‘experiment’ is not his disturbance-free model. It’s a model with continuous mortality at the same long term-average rate as in the model with disturbance. And if you simulate the correctly-controlled experiment, you find that the fluctuations in Huston’s (1979) model are irrelevant to slowing competitive exclusion. What slows competitive exclusion is the increase in the long-term average mortality rate, which reduces the growth rates of all species, and so reduces the difference in growth rate between competitively superior and inferior species, thereby slowing the rate of exclusion. In Chesson’s (2000) terms, increased long-term average mortality rate in this model is an equalizing mechanism, but not a stabilizing mechanism. And fluctuations in mortality in this model are no mechanism at all—the visually-obvious short-term fluctuations they create in species’ abundances have precisely zero effect on the long-term outcome.
Our first two zombies illustrate a source of zombie strength which we’ll encounter again in a moment: failure to appreciate that long-term average dynamics are ultimately what matters. Disturbances matter if, and only if, they alter long-term average dynamics. They’re just noise otherwise. As Hutchinson (1961) wrote, “Mere failure to obtain equilibrium owing to external variation in the environment does not mean that the kinds of competition described mathematically in the theory of competitive exclusion are not occurring continuously in nature.”
Unfortunately, having fought off the two zombies discussed above, Hutchinson (1961) immediately (in the very next paragraph!) fell victim to a zombie idea of his own:
3. If, due to fluctuating environmental conditions, the identity of the dominant competitor changes on an intermediate timescale, no one species will ever have time to exclude the others and all will coexist. Overly-slow fluctuations will allow exclusion to take place before conditions change. Species will average across overly-fast fluctuations, and whichever species competes best on average under the full range of environmental conditions will exclude the others.
This is Hutchinson’s (1961) own favored solution to the ‘paradox of the plankton’, the apparent coexistence of dozens of species of planktonic algae in apparently-homogeneous lakes in which only a few resources and other factors could ever possibly be limiting.
When I teach my undergraduate ecology students about the consequences of environmental fluctuations, I start by showing them this zombie idea, and I read them some statements of it from Hutchinson (1961), and from ecology textbooks, just to make sure they’ve got it. And then once I’m sure they understand it and have got it down in their notes, I throw the textbooks against a wall and yell, “Now cross that out because it’s wrong!” I’m not kidding, I really do this. My hope is that by parading a zombie in front of them, and then executing it in dramatic fashion, I’ll immunize them against any future attacks.
Varying the relative timescales of environmental fluctuation and competitive exclusion is not sufficient, on its own, to affect long-term average competitive outcomes. Here’s the right way to think about it. Imagine a constant environment, in which species A is favored over species B (i.e. has a higher per-capita growth rate). Species A of course will exclude B in the long run. Now imagine that the environment fluctuates, but that it mostly favors species A; it only favors species B quite rarely (say, 1% of the time). Now, without worrying about the frequency with which the environment changes and assuming all else is equal, tell me: which species do you think will win? If you’re like the undergrads I teach, you immediately said “Species A—it’ll just take a little longer”, which is absolutely right (well done!) Now imagine that the environment favors species A 51% of the time, and species B 49% of the time. Which species do you think will win? That’s right, species A still wins, it just takes a really long time. Finally, imagine that the environment favors each species exactly 50% of the time. Which species wins? The answer, of course, is neither, at least in a deterministic world (if there’s demographic stochasticity, one species or the other will eventually drift to extinction, just as with neutral genetic drift in evolutionary biology). Notice that we never said one word about the timescale on which the environment fluctuates. Because all that matters is which species is favored on average. Indeed, constant conditions that slightly favor species A would lead to exactly the same long-term outcome as fluctuating conditions that favor species A slightly more often than species B.
I think part of the reason ecologists succumb to Hutchinson’s zombie idea is that they focus on the opportunities created by fluctuating conditions. Competition is wiping some species out, we think, so we need some mechanism that gives those species an opportunity to grow. And yes, fluctuating conditions that temporarily favor one species over another do create an opportunity for that favored species to grow. But when conditions change, that creates an opportunity for a different species—which means a lack of opportunity (or better, the opposite of an opportunity) for the previously-favored species. You can’t have your cake and eat it too. You have to take the bad with the good. What fluctuating conditions giveth, fluctuating conditions taketh away.
So much for our third zombie. Let me put down my shotgun and talk about the implications of this battle.
It’s important to recognize that the above refutations are not empirical; they’re logical. The zombie ideas refuted above literally cannot be correct. If you argue that “All men are mortal, and Socrates is a man, therefore Socrates likes ice cream,” your argument is incorrect (more precisely, ‘invalid’), and no amount of data showing how much Socrates likes ice cream can make your argument correct. Analogously, there certainly are environments in which competition is weak. But the consequences of this are not correctly described by the zombie ideas discussed above. And there certainly are systems where diversity peaks at intermediate disturbance. But the reasons for this are those discussed by Chesson and Huntly (1997), Pacala and Rees (1998), Roxburgh et al. (2004), Shea et al. (2004), and Miller et al. (2011), not the zombie ideas discussed above.
Broadly speaking, disturbances and fluctuating conditions matter because, and only because, of nonlinearities and nonadditivity. In a linear, additive world, all that matters is long-term average conditions, because the effects of good times and bad times cancel out in the long run. But in a nonlinear, nonadditive world, the effects of good times and bad times no longer cancel out in the long run. For instance, temporal fluctuations in the identity of the dominant competitor can promote coexistence—if species have some way to take full advantage of the good times and then ‘store up’ those advantages while somehow avoiding or minimizing the damage of the bad times. That idea is what Peter Chesson calls the ‘storage effect’; it turns out that ‘storage’ is a form of nonadditivity.
I’ll conclude with a few zombie-fighting lessons, distilled from the above, which you can use to protect yourself not just against the IDH zombies, but against any other zombies which might try to eat your brain (I’ll be slaying some of them in future posts).
1. Don’t trust your intuitions without doing the math. Your intuitions about ecology, unaided by mathematics, are mostly worthless. Don’t feel insulted; mine are too. So are everyone’s. Ecological systems are complex, dynamic, and characterized by feedbacks rather than ‘one-way’ causality; verbal intuitions about such systems are notoriously unreliable. The people who originally developed the IDH are some of the smartest and (deservedly) most influential ecologists of all time; this post is not a criticism of them personally. The IDH is not a dumb idea. If it was, it never would’ve ended up in all the textbooks. But just because it wasn’t dumb doesn’t mean it’s not totally wrong. Mathematics (by which I don’t mean primarily mean numerical simulations, I mean analytical techniques like algebra) is a tool which makes us smarter. It forces us to precisely and explicitly define all our assumptions, and to logically work out all their consequences. Words are ambiguous, and logical reasoning of any complexity is immensely difficult. If your verbal hypothesis really is logically valid, you should be able to express it in mathematical form. Probably, you’ll discover that your idea doesn’t work precisely the way you thought it did, or at all. Which means that the math has shaken up your intuitions, and hopefully helped to replace them with better intuitions. And no amount of data is a substitute for doing the math, because data doesn’t interpret itself, you interpret it. Connell (1978) took his inspiration for the IDH from his tremendous empirical knowledge of tropical forests and coral reefs—and it didn’t protect him from the zombies.
2. Just because a famous ecologist, or lots of ecologists, or a textbook, says something doesn’t make it true. The IDH probably would never have achieved the penetrance it has if it hadn’t been developed by some of the most famous ecologists of the last 70 years. That led some ecologists to try to test the IDH. After all, if the G. E. Hutchinson or the Joe Connell proposes a hypothesis, the rest of us sit up and take notice. That led other ecologists to attempt further tests; once a topic becomes ‘hot’ lots of people pile in just because it’s ‘hot’. And once that body of work reached a critical mass, it had to go into the textbooks, which are written and updated to reflect the current state of the field. None of which changes the fact that the IDH doesn’t stand up to logical scrutiny. Remember my earlier post on the importance of contrarian ecology? Well, the penetrance of the IDH is what happens when too few contrarians arrive too late to save us from the zombies.
3. You have to be careful about how you teach ‘classic’ ideas. I teach Hutchinson (1961) because, in order for students to appreciate what’s right about modern ideas like the storage effect, they have to appreciate what’s wrong with classic ideas like Hutchinson’s. I do not teach Hutchinson (1961) as an idea that was ‘further developed’ or ‘clarified’ by subsequent workers, because that just encourages students to gloss over challenging, non-intuitive ‘details’ like nonlinearities and nonadditivities and just focus on seductively simple, apparently easy-to-understand claims. Frankly, I’d prefer not to teach Hutchinson (1961) and other ‘classic’ IDH ideas at all, but because these zombie ideas still walk among us, I’m worried my students will be viewed by others as ignorant if they haven’t at least heard of these ideas.
p.s. Interestingly, evolutionary biologists never fell for the IDH, at least not nearly to the same extent ecologists did. Their textbooks, such as Graham Bell’s Selection: The Mechanism of Evolution, contrast ‘opportunities in space’ with ‘obligations in time’. The idea is that spatial variation in relative fitness (equivalent to what ecologists would call spatial variation in the relative competitive abilities of different species) is a powerful force for maintaining genetic diversity. That’s because each genotype can just live in those locations where it’s fittest and never need experience locations where it’s relatively unfit. But on its own, temporal variation in relative fitness can’t maintain genetic diversity, because different genotypes have no choice but to experience the bad times (the times when they are relatively unfit) as well as the good times. It’s not as if you can use a time machine to avoid experiencing conditions that don’t suit you. In a temporally varying environment, the winning genotype is the one with the highest geometric mean fitness in the long run (which by the way is mathematically equivalent to having the highest arithmetic mean relative fitness (Grafen 1999); natural selection doesn’t work any differently in a temporally-varying environment than in an unchanging one). And although evolutionary biologists tend not to use the same jargon as ecologists, they’re well aware of the nonlinearities and nonadditivities that you have to combine with temporal fluctuations in relative fitness in order for such fluctuations to stably maintain genetic diversity.
I suspect the reason evolutionary biologists never fell for the IDH is that the first evolutionary biologists to consider the effects of temporal fluctuations in relative fitness, and of temporal fluctuations in population size, were mathematical theoreticians like Sewell Wright (1948). Because evolutionary biologists started out with the right, mathematically-derived answer, they were vaccinated against the verbal zombie ideas that later took root in ecology.
It’s interesting that evolutionary papers like Wright (1948) predate Hutchinson (1961). I assume Hutchinson, and the other IDH advocates who followed him, were unaware of Wright’s work, or else didn’t realize that it pre-refuted them. I’d suggest that this is an argument for the virtue of reading widely—except that I wouldn’t want evolutionary biologists to start reading zombie ecological ideas! Just as with variable environments, the variability of what you read doesn’t matter unless you have some way to store up the effects of the good material while minimizing the damage of the bad material.