Posted by: Jeremy Fox | March 22, 2012

Trying to save a zombie idea (UPDATED)

In a previous post I commented that it would be interesting to see whether the very nice paper by Adler et al. (2011) on diversity-productivity relationships in terrestrial grasslands would finally kill off the zombie idea that diversity generally is a humped function of productivity. I also suggested that this zombie might be more of an apparent zombie than a real one, because hardly anyone these days still believes in this zombie idea, it’s just that everyone thinks everyone else believes in it.

I was wrong on both counts (you’d think I of all people wouldn’t be so quick to see a zombie idea as dead or dying!) Writing in Science this week, Pan et al. and Fridley et al. criticize Adler et al., and the reply is here. Pan et al. claim that, properly analyzed, the Adler et al. data show a strongly linear diversity-productivity relationship, while Fridley et al. claim both that the data are “clearly deficient” as a test for a humped diversity-productivity relationship, and that they show a “clear” humped diversity-productivity relationship*.

In my view, the comments are a striking illustration of just how far even very good ecologists will go in an attempt to save a pet hypothesis in which they are heavily invested. I should emphasize in saying that that I don’t have a dog in this fight. The question of how plant diversity varies as a function of primary productivity is a purely empirical question. Addressing it properly requires careful study design to sample the full range of natural variation, control for confounding factors, etc. And personally I don’t care what the answer is. I just care that we get the right answer.

I think Adler et al. is the right answer, for grasslands. Pan et al. don’t, but as Adler et al. point out their comment basically amounts to cherry-picking data to obtain a linear relationship. Not consciously cherry-picking of course. But as a rule, in any large and complex dataset there is always some subset of data showing a relationship between variables different than that shown by the dataset as a whole, and you can always find some more-or-less-plausible post-hoc reason to pay special attention to that subset. As Grace et al. point out in their reply to Pan et al., Fridley et al. actually prefer to focus on a different subset of the data. That strongly suggests that both sets of commenters are, unconsciously, just looking for reasons to make the data show what they think the data ought to show.

As noted above, the Fridley et al. comment is, on it’s face, self-contradictory*. Fridley et al. also try to change the question, arguing that “productivity”, or any index of it, should be defined to include leaf litter, which would be contrary to the bulk of previous empirical and theoretical studies. They also argue that Adler et al. should have conducted various alternative analyses…that Adler et al. actually did conduct and presented in their paper. And finally, as Grace et al. show, what little “humpiness” there is in the Adler et al. data reflects the log-normal distribution of the data, so it looks slightly humped on an arithmetic scale.

I’m not an expert on this stuff (I’m not a plant guy), but I’m confident I know enough about it to come to an informed (not infallible, but informed) opinion. And in my view, the Adler et al. paper is totally unscathed. In grasslands, I think we now have the best data we can ever expect on the diversity-productivity relationship–collected at a large number of sites around the world, with good coverage of a big productivity range, sampled using a consistent protocol. And those data have been very carefully and thoroughly analyzed. The answer is clear: the diversity-productivity relationship is very weak and noisy, and it’s not humped. So we’d better learn to deal with it.

Even if you want to say that the humped diversity-productivity relationship is so well-established that we need extraordinary evidence to reject it, well, I disagree with your premise, plus Adler et al. is extraordinary evidence.

At the end of their comment, Fridley et al. conclude with some quite striking rhetoric. They claim that the hump-backed diversity-productivity relationship is a “cornerstone of plant ecology”, backed by “decades of careful mechanistic analysis”, and is “used by plant conservationists and restoration ecologists, as well as theoretical ecologists.” The first claim must surely be loose language on the part of Fridley et al., because taken at face value it’s patently false. Discarding the humped diversity-productivity hypothesis would not cause plant ecology to collapse the way a building would if you removed its cornerstone. If you think otherwise, your view of what “plant ecology” consists of is way too narrow. The vast bulk of research on plant physiological, population, and community ecology has nothing to do with the diversity-productivity relationship, humped or otherwise. I’m not sure what the second claim means, but I hope they’re not claiming that we’ve proven mechanistically that the diversity-productivity relationship has to be humped. There’s nothing in ecology like, say, the kinetic theory of gases that let’s us rigorously derive a diversity-productivity equivalent of the ideal gas law. And their other claims are irrelevant. If conservationists, restorationists, and theoreticians based their work on the assumption that the earth was flat, that wouldn’t make the earth flat (and yes, it is possible for many experts to be wrong about a matter of empirical fact). Worse, do you really want to argue that conservation and restoration practices, or theoretical modelers, should never adjust what they do in light of new data? Please don’t misunderstand me: the authors of the Fridley et al. comment include many very good, very smart ecologists (and Jason Fridley for one is a friend of this blog). I just find it striking that so many very good, very smart ecologists could be so reluctant to reconsider their position on what ought to be a straightforward empirical matter, and so willing to resort to what looks like quite poorly-supported rhetoric. Basically their rhetoric at the end amounts to saying “this zombie idea has been around for a long time–so therefore it can’t possibly be a zombie”.

UPDATE: Commentary from one of the co-authors of Adler et al. here.

*Grace et al. also note that Fridley et al.’s comment is self-contradictory. I agree with that characterization.


  1. The cosigners on the Fridley comment are certainly some big names in the subfield, but I was going to mention that if we could use the number of people making the statements as an indicator of the weight of belief, the original authors hold a slight majority. Maybe this was the ‘last stand’ of the hump-shaped diversity-productivity model (and now I’m imagining Peter Adler and James Grace as Wyatt Earp and Doc Holliday…).

    Then again, I don’t know what it means when 1/3 of the original coauthors neglect to add their names to a response comment; did they just not reply in time, or did they intentionally not want their names on the response?

    • I actually don’t think measuring “weight of belief” is the way to go at all. But then, I would say that. But if you insist on looking for ways independent of the data to judge who’s right here, I don’t know that I’d look at number of signatures. I’d be more inclined to look at things like citation patterns–does one side mostly cite themselves for instance? I’d also look at things like which side has published more, and more prominently, on the topic. *Not* to determine who has more “expertise”, but to determine who’s invested a lot in a certain position that they’re therefore more likely to dig in and defend. Some of the authors of Fridley et al. are indeed big names–but they’re big names who’ve built their careers on the hump-backed diversity-productivity claim.

      That some of the original coauthors didn’t sign the reply almost certainly just indicates that they were too busy or didn’t care enough to bother, and trusted their colleagues to handle it. I’m sure it doesn’t mean that they don’t actually believe in the reply. But if you’re really interested, I know some of the authors of the reply and could ask them…

      As to whether this was the last stand of the hump-backed diversity-productivity claim, I don’t think zombie ideas really have last stands. They just fade away, as their proponents retire. Which takes a loooonnnnngggggg time, because the proponents of any idea will have students and close colleagues who will tend to become proponents themselves, who will have their own students and close colleagues…only when the “R0” of the zombies is <1 can we say that the zombie outbreak is starting to fade. Not sure if we're there yet for this zombie.

      • Right, to determine which side is closer to the truth we need to consider the vested interests of both sides and whether or not they make their arguments with clear, empirical statements. That part is pretty settled for me (I agree that “the diversity-productivity relationship is very weak and noisy, and it’s not humped”).

        I know very little about invasion analysis but this seems like a good application of it (or at least a good opportunity for me to learn some about it). If the R0 of one trait/idea is greater than the other, would it matter if the R0 of the other is less than 1? Would the new idea still ‘win’ even if the zombie idea was still around?

      • Nice try, but I’m not going to teach you invasion analysis. 😉

      • If the R0 of one trait/idea is greater than the other, would it matter if the R0 of the other is less than 1? Would the new idea still ‘win’ even if the zombie idea was still around?

        Depending on the particular parameter values, we might get coexistence between zomA’s and zomB’s

      • Mike: If I understand correctly, you’re asking about the “relative fitness” of alternative ideas rather than the absolute fitness of a single idea. If we’re thinking of relative fitness, then the idea with the highest relative fitness will win in the sense that it will replace the alternatives and “sweep to fixation” in the “population” of ideas. With the caveat that, if the absolute fitness of every competing idea is less than 1, the winning idea itself will eventually die out (e.g., everybody stops caring about the diversity-productivity relationship, and so nobody any longer has any ideas about the form of the relationship).

        To get stable coexistence of competing ideas, their relative fitnesses would have to be frequency-dependent for some reason. It’s hard to see why that would be the case.

  2. Aaron, as you guessed, the reason not every original author signed is that many did not respond in time. Science requires authors to fill out quite a few forms, and the deadlines on the Comments/Replies are tight. No one asked to have their name removed.

  3. […] is itself a zombie idea. That’s a question I’ve asked myself about another zombie. But I was wrong. And in this case, well, sorry Nate, I sincerely wish you were right, […]

  4. […] Nick Gotelli who know a lot about statistics. Because famous ecologists never make mistakes. Nope, never.* Also interesting to see the same commenter imply that, by publishing his criticisms in a blog […]

  5. There are some serious flaws in the Adler et al. study, most notably the fact that 91 % of samples were taken from sites of low or extremely low biomass production (4000 g m-2) in wetland communities. Some of these points are addressed in Grime’s new book (of which I’m joint author), and I’ve included a quote below. Perhaps the main point is that many ecologists do use the humped-back curve as a general rule of thumb simply because herbaceous vegetation that produces large amounts of biomass is usually strongly dominated by only one or two species (and has low species richness), and diversity is favoured by factors such as mowing, grazing or fire that do not allow these potential dominants to dominate and produce a relatively large amount of biomass. That’s why dry calcareous meadows and pastures can host 40 or 50 species per square metre, but a wetland might have 3 or 4 (or even just one). Because moderate disturbance is so important for the creation of local species richness (and thus species-rich habitats such as meadows), this is key to conservation and management plans and this view of biodiversity is actually recognised by legislation, at least here in Europe (in the form of the particular habitats that are covered by the Habitats Directive). So, the humped-back curve is relevant and of great practical importance to conservationists – I’m one of a new generation that sees this model as important, and far from a “zombie idea”. Here’s the quote from Grime & Pierce (2012):

    “Recently a large-scale survey of herbaceous vegetation (Adler et al., 2011) has claimed to falsify the humped-back model, describing diversity/biomass relationships as ‘weak and variable’. However, the majority (91 %) of sampling points in this study exhibited biomasses of less than 500 g m-2, and the maximum biomass sampled was only 1534 g m-2. Adler’s co-authors (Grace et al., 2007) previously recorded biomasses exceeding 4000 g m-2 in a number of species-poor wetland communities. Despite the gaps in their dataset and oddities in their main analysis, Adler et al. state that they actually found a statistically significant humped-back curve at the global scale, but were able to make it non-significant by omitting, without explanation, a wetland community and nine sites that they deemed particularly anthropogenic. This exclusion of high biomass/low diversity sites and the strong emphasis on communities of low biomass indicate that the ‘Nutrient Network collaborative experiment’, from which the study emerged, was not designed as an objective test of the humped-back model over the full productivity range. Ironically, in their main analysis maximum biodiversities of ~40 species m-2 were evident at biomasses of 400-500 g m-2, with much lower diversities at productivity extremes, broadly agreeing with the view of the humped-back curve as an upper limit to diversity peaking at ~500 g m-2 (as in Fig. 5.8). We predict that completion of Adler et al.’s publicly available dataset will yield a humped-back maximum potential biodiversity curve.”

    • When I submitted that post, a whole chunk of text was apparently omitted between “91 % of samples were taken from sites of low or extremely low biomass production” and “(4000 g m-2) in wetland communities.” The 91% of samples in low and extremely low productivity sites in the Adler et al. study were below 500 g m-2, with nothing measured in the 1600 – 4000 g m-2 range, and I then went on to make the point that the study obviously had not been originally designed to investigate the full productivity range, and that wetland sites of high productivity but low diversity were specifically excluded, as explained (or, actually, not explained but at least stated) in the Adler et al. paper. Note that it was John Grace and Eric Seabloom (amongst other Adler et al. coauthors) that measured low diversity in wetlands of >4000 g m-2 biomass (published in Ecology Letters10, 680-689), so their defence of Adler et al. is particularly baffling.

      • Again, thank you for your comments Simon. Again, we’ll have to agree to disagree.

    • Thank you for your comment Simon. As the post makes clear, you and I will have to agree to disagree on this.

      • Oh come on Jeremy, that’s the kind of cop-out reply someone gives when they can’t find a snappy come back. What is your opinion about the fact that if I measure biomass production in a single species stand of Fallopia japonica I get high values, but if I measure biomass production in high diversity meadows (and note that the word meadow means that it has been mown – i.e. subject to disturbance) or pasture (i.e. subject to grazing disturbance) I will find moderate biomass and somewhat higher levels of richness than just the one species (40 – 50 spp. m-2). (Note that this is not a hypothetical question – I have, amongst other things, measured this in a recent paper submitted to Annals of Botany). That’s not my opinion, that’s what you find in the field – high biomass in single species stands or vegetation dominated by small numbers of species, with high diversity in habitats of moderate disturbance, usually imposed by mowing, grazing or fire. So if you want to agree to disagree, you’re effectively telling me that meadows are low-biodiversity habitats, and that conservationists should concentrate on saving the Fallopia. Is that your final answer?

      • Um, no, it’s not a cop out. I make decisions all the time about what’s worth my time to write about, and what’s worth my time not to. My views are stated in the post, and because I don’t see how your comment adds anything new to the issues discussed in the post and in the linked letters, I chose not to reply to you further. Now that you’ve goaded me, I may perhaps reply in more detail if the mood strikes me and I can find the time, but no promises.

        Not sure what you mean by snappy come-backs. I suggest that you may wish to read through the archives, where you’ll find that I frequently reply to commenters at great length, including commenters who disagree with me. Yes, my writing is often strongly worded, and my humor is often snarky. But I think you will find that I never use rhetoric or humor as a substitute for substantive argument.

        In the meantime, since you appear keen to re-argue the issues raised in the post, I assume you will be commenting at length on every one of them, and that your arguments will go beyond, rather than simply repeat, those raised in the post and in the linked letters?

  6. Jeremy, I certainly mean no offence and don’t mean to goad, but I would argue that you are relying on rhetoric to defend your view, or at least to avoid answering. My original reply to Adler et al. was published in Science, as part of the Fridley et al. comment. My other comments on the biodiversity/productivity issue are published by Wiley-Blackwell alongside Phil Grime, and are based on field data (humped-back curves are common amongst plant, coral and bacterial communities). I am not re-arguing issues raised in your blog – it is you that are commenting on at least some of the work that I have published in peer-reviewed publications. I realize that a blog is meant as a platform for opinion, but a blog linked to Oikos should at least consider the arguments before rejecting them out of hand. When I ask your opinion on the comments I made, it’s because I would seriously like to hear your view on the higher diversities evident at moderate disturbance intensities – not what models or argument suggest we should see, but what we actually do see when we compare the species richness of communities at different sites and over a wide range of biomass production (rather than within sites or communities, which can muddy the interpretation of meta-analyses). No goading, no hard feelings, no agreeing to disagree – what do you think about the fact that ecologists such as myself regularly observe and measure situations that are in broad agreement with the humped-back diversity/productivity curve and the intermediate disturbance hypothesis?

    • Thank you for the clarification Simon, I appreciate it.

      Re: the intermediate disturbance hypothesis, it depends exactly what you mean. If you simply mean the purely empirical claim that, in some systems (probably a minority), diversity peaks at intermediate frequencies or intensities of disturbance, I agree (although if that’s all you mean, I question whether we need a special name for such a limited, narrow claim). If you mean still purely-empirical but stronger claim that diversity usually or always peaks at intermediate disturbance, and that if it appears not to do so it’s likely because of other confounding variables, I disagree; I don’t think that’s a correct reading of the empirical evidence. If you mean the causal claim that diversity peaks at intermediate disturbance, or should be expected to do so, for any of the three reasons discussed in my first zombie ideas post, I disagree. Those mechanisms, while intuitively appealing, are logically flawed and can’t actually hold in any system. There are mechanisms that can cause diversity to peak at intermediate disturbance, but they are either based on nonlinearities and nonadditivities in the sense of Chesson, or else are (in the case of certain models of competition-colonization trade-offs) not actually nonequilibrium mechanisms at all. And those same mechanisms can, if the parameter values are tweaked, also cause diversity to peak at high and/or low disturbance, or even vary in some more complicated way, or not vary at all, with disturbance.

      Re: what arguments should be considered in posts on the Oikos blog, I think it’s best if I take this opportunity to clarify how the blog works. The opinions I express on the blog are my own; the same is true for Chris Lortie and the other occasional contributors. No post is peer-reviewed or has to go through any other pre-publication validation system, formal or informal. The blog is intended as another way, complementary to the journal, for Oikos to spark, promote, and engage with interesting conversations about ecology. I try to help achieve that admittedly loosely-defined goal with various sorts of posts, including posts that comment briefly on single papers or exchanges of papers. This post is an example–I’m simply giving my own opinion on the exchange of views about Adler et al. I think that exchange fully aired the issues that might be raised with the work of Adler et al., and that the arguments of Adler et al. are much stronger than those of their opponents. I am simply agreeing with Adler et al., and so I am not supporting my view purely with rhetoric. My view is that Adler et al. are right, and so the support for my view is the support that they offer for their view.

      I appreciate the invitation to comment on the other papers you cite. I’m flattered that you would want my view, and I do try to engage with commenters, so I will consider doing this. But I’m afraid I don’t have the time to extensively review this massive literature on my own. And if I were to do my own substantive commentary on the diversity-productivity relationship I would probably want to do more than just comment on the papers you cite. I think what I will do is look into the literature a bit, including but not limited to the papers you cite, in order to decide if I have anything new to say that has not already been said elsewhere. I have already written one post indicating my stance on the issues as debated by others. I will figure out if I have anything new to add and if I do I’ll post on it. If not, not.

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