The Paradox of the Phytoplankton, Part 2: Why else do we have so many species? (19 Comments)


A week or so ago, I wrote a blog post in praise of Hutchinson’s seminal 1961 paper “The Paradox of the Plankton,” while simultaneously but subtly singing praise of the “intermediate disturbance hypothesis.” As ecologist and blogger Jeremy Fox pointed out in the comments to that post, the idea of the “intermediate disturbance hypothesis” has been largely superseded by other mechanistic explanations. I’ll take a few moments to summarize Jeremy’s argument, provide a few comments of my own, and draw parallels to another longstanding tenant of ecological theory.

But first, I want to make it clear that I think Hutchinson’s paper is seminal not only for the idea it proposed (whether or not it has stood the test of time) but for presenting testable hypotheses and instigating the rise of modern ecology. Prior to the mid-20th century, ecology was largely the purview of the “natural philosopher” who was far more interested in observing and cataloging nature than in explaining it (obviously, there are notable exceptions to this statement, including Charles Darwin, Charles Elton, and others). It wasn’t until Joseph Connell started planting cages in the rocky intertidal in the late 1950s that the field migrated into the realm of the experimental ecologist, where it experienced rapid growth and attention, morphing into the multidisciplinary behemoth we know today. It is clear that Hutchinson’s original ideas were hugely influential on Connell and other ecologists working at the time, and for that he deserves some credit.

But as Jeremy points out in his post Zombie ideas in ecology, just because something is venerable doesn’t mean it’s correct, only that it’s harder to shake. Here are his arguments against the IDH, which invoke a lot of complicated math that I’m unable to convey, but hopefully I can get the gist of his ideas down:

  1. The idea: Intermediate disturbance reduces species’ densities and weakens the strength of competition, allowing coexistence. Too much disturbance leads to local extinction and too little disturbance allows competitively dominant species to take over. The rebuttal: Weaker interactions also leads to reduced threshold for competitive exclusion.
  2. The idea: Intermediate disturbance slows competitive exclusion, preventing an equilibrium state from being reached, and subsequently allowing all species to increase. The rebuttal: Disturbance prevents equilibrium, but also changes the long-term average mortality rate. This changes the difference in growth rates between competitively superior and inferior species, which may slow competitive exclusion but does not prevent it.
  3. The idea: The dominant competitor changes based on fluctuating environmental conditions, and thus over long time scales, no species ever remains dominant long enough to exclude others (Hutchinson’s hypothesis). The rebuttal: Environmental fluctuations change the relative fitness of species, but over long time periods, the species that is favored on average will come to dominate the assemblage. This point is a little more subtle and deserves closer attention. Fox argues that “a change in environmental conditions that creates an opportunity for one competitor necessarily creates the opposite of an opportunity for the previously favored competitor. [But] in order to persist in the long run, a species must be able to grow and compete sufficiently under all the conditions it will experience.” This is logical mathematically but ignores consideration of what relevant timescales might be for the system under investigation. Of course if the system is allowed to go on indefinitely, the best competitor on average will reign, but this approach ignores the fact the study systems are frequently of interest on much smaller timescales, where the IDH may be an appropriate explanation for the observed patterns (although here I am reticent to cherry pick examples that support this idea!). I also can’t help but feel timescales are necessarily limited because of other outside factors, such as recruitment (not to be confused with the colonization-competition trade-off, where disturbance clears patches that allow inferior competitors to recruit and reproduce before being excluded, and which Jeremy addresses in his recent TREE publication).

I actually agree with the majority of Jeremy’s points, and as an emerging ecologist, my job is to challenge the status quo (actually the job of all scientists!). It’s worth having a look at his post on the topic if you haven’t already, where he articulates his points far better than I, and reading his TREE publication. (Though I suppose I’m a little guilty of violating #7 on his list of “Rebuttals to my rebuttal” post.) His paper reminds me a lot of Don Strong’s 1992 paper criticizing trophic cascades, which generated a lot of debate on whether this too was a zombie idea in ecology (later meta-analyses showed, in fact, that trophic cascades were not “all wet” but this does not seem to be the case for IDH, see Mackey & Currie 2001). I’m curious to see what other young ecologists feel about this challenge to the IDH. Sound off in the comments.


Fox, J. 2012. The intermediate disturbance hypothesis should be abandoned. Trends in Ecology and Evolution 28(2): 86-92.

Mackey, R.L., and D.J. Currie. 2001. The diversity-disturbance relationship: is it generally strong and peaked? Ecology 82: 3479-3492.

February 6, 2013

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  • Good post, and thanks for the shout out! A few thoughts:

    I’d quibble with the claim that Hutchinson’s hypothesis is “testable”. It is, but only in the rather useless sense that *any* claim or prediction is testable. To pick a deliberately-silly example, if an oracle said that shoving potato chips up your nose makes you grow taller because shoving potato chips up your nose stimulates growth hormone production, well, that’s a testable prediction! You can in fact shove potato chips up your nose and see if you grow! But there wouldn’t be any *point* to testing that prediction, because it’s not well-grounded. It’s not derived as a logical consequence of checkable assumptions about the world. Hutchinson’s hypothesis isn’t silly, but is IS ungrounded. Hutchinson’s assumptions do NOT actually imply the prediction he thinks they imply. So his prediction is just as ungrounded as the oracle’s. Which means that, if you test Hutchinson’s prediction, the results of your test (whatever they might be) literally have NO implications for the truth or falsehood of Hutchinson’s assumptions. So testing Hutchinson’s “prediction” doesn’t actually teach you *anything*. Just as, if you shove potato chips up your nose and find that you don’t grow, you haven’t learned anything about growth hormone production–not even if or how it’s affected by shoving potato chips up your nose!

    Silly examples and zombie ideas aside, I think there’s an important larger point here. Ecologists of a certain stripe I think almost make a fetish of testing predictions. Testing predictions absolutely has its place (I do it all the time), but it’s far from sufficient, on its own, for doing good empirical science. For instance, testing assumptions often is just as useful. See this old post:

    Re: your concern about timescales and the relevance of theoretical long-run outcomes to the real world, I have follow-up posts that address that concern. Your concern is a common one, but it is misplaced.

    • Wow, that was fast! I’m not sure I agree with you that Hutchinson does not put forth testable predictions in the form of specific mechanistic explanations for the patterns he observed, although I suppose a more appropriate modus operandi would be to test the underlying mathematical model, which I agree he does not present (but then again, neither did many of his contemporaries. The field was just not there yet).

      The IDH is a topic I have only recently began to really think critically about after years of being fed the company line in introductory ecology classes, and this is largely as a consequence of reading your TREE paper. I suspect a lot of concerns and experiments have already been addressed by people who are much smarter than I, but I look forward to using this dialogue as a platform to continue to educate myself on this. I’m glad that this blog is serving out its purpose, in allowing graduate students (myself included) to dig into topics re: diversity that may not hugely influence our day-to-day actions, but are important foundational concepts in the field. So, that said, thanks for the links to your follow-up posts. They will make excellent reading over lunch!

      In regards to a fetish for testable hypotheses, your criticisms exactly mirror those I have against frequentist designs. Using an information theoretic or Bayesian approach, it is now possible to test multiple competing hypotheses simultaneously within a rigorous statistical framework. But for those proposing the models, addressing assumptions is also important. Given my background and research interests, I fall more into the former camp (testing predictions) than in constructing and evaluating theoretical models, hence my bias.

      • Re: testing Hutchinson, nope, sorry. With respect, you’re still not getting it. Let’s say you did an experiment along the lines you suggest (and people have in fact done such experiments). And let’s say you find that you do indeed get the most (or longest-lasting, or whatever) coexistence at intermediate frequencies of environmental change (which is a result people have in fact gotten). If you think that supports Hutchinson’s hypothesis, then I’m afraid you haven’t fully understood my blog posts and TREE paper.

        That someone as sharp and thoughtful as you is still wrestling with the possibility that a major idea from a famous guy might be not be testable (because not logically valid) is a sobering reminder to me of just how difficult it is to make the case I’m making in that TREE paper.

        Re: letting Hutchinson off the hook because he didn’t do the math, evolutionary biologists (specifically Sewell Wright) actually had already analyzed mathematical models precisely analogous to Hutchinson’s model, published their results in leading evolution journals, and come to the correct conclusions, before Hutchinson wrote. No, Hutchinson didn’t do the math–but he could have (or he could’ve read Wright’s math and recognized its relevance to ecology). And worse, in the decades since Hutchinson, lots of ecologists (before and after Peter Chesson, actually) have also done the math, and have published it in leading journals like Am Nat–and almost no one except for the most theoretically-minded empiricists has taken the least notice. The IDH is one of those ideas that’s so intuitively appealing, it’s basically immune to math. I’ve done the best I can to make the math intuitive, but frankly I’m not sure how successful I’ve been.

        p.s. Just to make sure I’m being clear, while having alternative hypotheses is great, and evaluating them in a Bayesian framework can be great, my point here doesn’t have anything to do with frequentist or Bayesian approaches to stats…

      • D’oh, you are right (naturally). I was trying to argue that Hutchinson at least presented a mechanistic explanation that could be tested experimentally, not whether the results of those tests could be used to infer the validity of what you have shown to be flawed mechanisms (which, as you argue, they cannot). This is the problem with trying to blog and do other productive stuff as well (and eat lunch!). I’ve taken out the silly lines in my previous post in an effort not to embarrass myself in perpetuity.

        Re: the math, this is something I think most graduate students struggle with. When a group of us read your TREE paper, we all had a really difficult time because none of us had any background in population modelling (beyond the obligatory slide or two in introductory ecology). I think this is more of a shortcoming of math being difficult for many people (including me!) than in your explanations. I did see on your website that you intended to make R code available. Did anything ever come of that? I think that would go a long way in hitting some of those points home.

        Finally, the comment re: statistics were in response to your post on testing predictions vs assumptions. Interesting stuff, but not really relevant to this topic. Just thought I would put it out there.

      • No, I never did put up R code to do the simulations in the TREE paper. I’ll try to get around to it. Playing around with simulations can help, but I’m afraid it’s not a substitute for understanding the math. If all you do is eyeball simulations, you end up making the sort of mistakes Huston (1979) did.

        Sorry to hear you still found the math in the TREE paper a struggle, but it’s really difficult to make it any simpler than that. Perhaps I’ll have another go at explaining this stuff on the blog at some point. Maybe throw in some worked numerical examples to go with the math that’s in the text boxes in the TREE paper.

        Explaining this stuff is hard. I’ve had people complain to me that the TREE paper and my blog posts have too much math, and then *also* complain that my arguments are just verbal arguments and aren’t backed by math! (really, that’s happened)

        I do sincerely appreciate that you and your fellow students are grappling with this. That’s really the only hope in the long run. Students are our future! 😉 (Now just try to retain those student-y habits of mind once you’re no longer students…)

  • Woosh, took care of that! Sorry about the dead post above. The submit button vanished when I wrote my comment.

    So, in the way I was introduced to plankton ecology (I work on very dead fossil plankton, long story), I was given a strong sense that a large reason for the co-existance of similar plankton was due to temporal dynamics; e.g. plankton species A dominated and bloomed in late May, while plankton species B dominated and bloomed in early July, each one (probably) physiologically adapted to the nutrients available during different seasons. Many plankton seem to be able to hibernate almost forever in sediments or at very low populations in the ocean, and thus can sit-out any interval they aren’t too well adapted for (for an extreme case in the paleo world, it has been argued that dinoflagellates survived the K-T mass extinction fairly well due to sitting in wait as resting cysts on the sea floor). So, the way I came to understand what I was being told, there’s maybe active selection for focusing on being active and reproductive during a particular season, and plankton are just turning time into an ecological gradient to adaptively subdivide.

    So, is this amorphous idea that I got a while back about ‘how plankton ecology’ works (I can’t attribute it to anyone, this isn’t my thing, man) just a re-telling of the Hutchinson IDH theory or is this something else? And how does Jeremy’s criticism of the third idea of IDH apply, if plankton can ‘sit out’ most of the year?

    Maybe my issue is I don’t see a clear line between the Hutchinson idea of IDH and being adaptations for different units of time. I mean, we could be silly and call diurnal cycles temporal disturbances, which allow for there to be both diurnal and nocturnal communities, by dint that one community is sleeping/hiding while the other one is out.

    • Hi Dave, glad to see a palaeoecologist enter the fray!

      Your reply is an interesting one but I’m afraid it’s mixing two ideas. You point out the very interesting way in which various species of phytoplankton have persisted through geologic time, largely as a consequence of their ability to sequester in sediments. This is a physiological/ontological adaptation to stress (or maybe competition? I’m not a phytoplankton guy). The IDH specifically invokes the relative susceptibilities of plankton to environmental factors in the context of their ability to compete with other plankton species. I’m afraid this is straying out of my area as well (even more so than the original post!) but there have been some early models by Connell and Slatyer that attempt to integrate competition and temporal fluctuations in abundance due to recruitment (which may touch on some of the temporal dynamics that you write about), which have undoubtedly been improved upon since then.

  • For the paleo folks who’ve chimed in, welcome!

    The short answer to your questions is that yes, it absolutely is possible for competing species to coexist stably due to environmental fluctuations. But the mechanisms by which that can happen emphatically do NOT include “sometimes one species dominates, sometimes the other one dominates, so therefore they coexist”. The “therefore they coexist” doesn’t follow. It’s not as simple as that. What you need is environmental fluctuations *combined with the right sorts of nonlinearities and/or nonadditivities*. The importance of those nonlinearities and nonadditivities is what Hutchinson missed, and most ecologists continue to miss. This isn’t a minor technicality, it’s a very important point, since without those nonlinearities and nonadditivities environmental fluctuations per se not only don’t give you coexistence, they don’t even *promote* coexistence! I have a series of blog posts explaining how nonlinearities and nonadditivities promote coexistence in fluctuating environments (I also explain this in the text boxes in the TREE paper Jon so kindly linked to). Here are the posts, which BTW use almost no math at all:

    • First, Jon, I’m not much of a paleoecologist! I leave that for my wife. I’m more an evolutionary paleobiologist, working with phylogenetic trees and plankton functional morphology.

      Reading your linked posts, Jeremy, and your comment, Dave A, I see now how the plankton system is involving non-additive and non-linear effects. Seeing the range of ways species could modify their temporal response to environmental change, as an evolutionary biologist, I wonder why i haven’t seen more comparative work looking at the range of such strategies developed in various groups of organisms.

  • p.s. lest I come off as somehow personally criticizing Hutchinson here, let me emphasize that I mean to do nothing of the sort. GE Hutchinson was a great ecologist and deserves to be remembered and respected as one. That doesn’t mean he didn’t make a serious mistake that set ecological research on the wrong track. Everybody makes mistakes, including serious ones. I’m certainly no exception (even Einstein was famously wrong about quantum mechanics). Science is hard. Ecology is hard. But if we hesitate to call serious mistakes for what they are just because they were made by famous people whom we respect and admire, those mistakes will simply persist.

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  • Hi Giuliano,

    Sorry you feel that way. But with respect, it’s you who called me the Pope, not me! I have never set myself up as an authority figure. I have never told anyone what or how to think. I’ve told people what I think, and why–which is no different than what anyone else does. I have *never* ordered people to think as I do! I make my arguments, and people are perfectly free to agree or not. Do you think I have the power to “excommunicate” anyone from ecology, or from the internet? Do you think I have the power to prevent anyone from expressing their own views? Heck, do you even think I have the power to make anyone read my blog?

    As for whether or not I ever change my mind, I’d like to think that I change it when I’m given good reasons for doing so, and not otherwise. For instance, I once did a post about how people shouldn’t live tweet talks that was basically totally off base. Commenters pointed this out, and I subsequently updated the post to say that I’d changed my mind:

    Or see here for a post in which I expressed skepticism about structural equation modeling, and then stopped being skeptical because commenters addressed my concerns:

    But I’ve never claimed to be perfect. If there specific cases where you think I have willfully ignored opposing views or contrary evidence, or where I’ve simply insisted that people accept my views without offering evidence and arguments for my views, please point them out.

    As for my frequency of commenting, I’m not going to apologize for commenting on the posts of others. It’s actually not something I do that much, except on my own blog. For instance, I’ve commented only on a couple of the posts on this blog. My comments do not prevent anyone else from commenting. If you think my comments are unproductive for whatever reason, you should complain to the blog owner and ask to have me blocked.

  • I urge you all to take a look at Tron Thingstad’s theoretical papers on the ‘Kill the Winner’ hypothesis. It makes some pretty accurate predictions on predation-mediated coexistence under single-nutrient limitation (the crux of Hutchinson’s paradox!). I suspect these papers have gone unnoticed by many ecologists due to their marine microbial bent.

    • Yes, I’ve seen some of this work. “Kill the winner” is basically one way, among many others, of getting negative frequency dependence, and thus stable coexistence, into a dynamical system that would otherwise lack it.

  • I wanted to give a slightly different view that will (hopefully) resolve some issues for people by combining a few ideas posted here. For the paleo guy, as Jeremy suggested, temporal fluctuations in the environment can indeed promote coexistence. And as Jeremy said, this only occurs when there is a certain nonlinearity in the growth rates of species (the way in which they respond to environmental variation). The way Dave described the change in “superior” species given different environmental conditions sounds a lot like Hutchinson’s idea. There is an important missing point here.

    When the nutrients in the lake are good for species A, they are not so for the other species and vice versa. And when the environments are good for a species, it does very well (plankton blooms and what not). But, when the environment isn’t so great for that plankton species, it doesn’t suffer nearly as much as it does well in good years. This is that nonlinearity that Jeremy is talking about, and a point that Hutchinson missed. While it seems like a minor point, it is important because it allows species to have a positive long-term growth rate from low density. And that simply means it won’t go extinct. And if neither species goes extinct, then they coexist. What I described is exactly the storage effect with its three components: species specific responses to the environment (lake conditions good for species A aren’t so good for the others), buffered population growth (plankton don’t go extinct if they get the environments they don’t do well in), and covariance between environment and competition. I have assumed here that this covariance works in a way that promotes coexistence, but this is mostly a technical point that distracts from the central idea.

    You see, without this nonlinearity that Jeremy describes, you miss out on real way in which the environment interacts with competition to promote coexistence. It doesn’t simply happen by one species being dominant during one time, and another during a different time.

    First time poster. I look forward to hearing what you think of this explanation!

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