The Folk Theorem of Alternative Hypotheses In Ecology

A folk theorem is a theorem that’s too informally stated to be proven true, and might not even be strictly true, but that nevertheless often seems to hold. For instance, here are the folk theorems of game theory. And here’s Andrew Gelman’s folk theorem of statistical computing.

Here’s my Folk Theorem of Alternative Hypotheses In Ecology. Imagine you have several reasonably plausible alternative hypotheses about how ecological variables X and Y will be related.* Some or all of your hypotheses make different predictions about the the X-Y relationship (e.g., one says it’s humped, another says it’s an increasing linear relationship, etc.). But you have little or no data on how X and Y actually are related. Or maybe there is a lot of data, but it’s scattered throughout the literature and so no one knows what it would show if it were compiled.** Then my folk theorem says that none of those predictions will hold in a substantial majority of the cases, and there will be no rhyme or reason to which prediction holds in any particular case.

Shorter folk theorem: if anything can happen in ecology, anything will happen.

Example: the intermediate disturbance hypothesis. Ok, there’s actually not that much mathematical theory predicting diversity-disturbance relationships (as distinct from verbal arm-waving, which doesn’t count). But what theory there is makes predictions that are all over the map. Change the model structure, or even just change the model parameter values or the diversity metric, and you predict totally different diversity-disturbance relationships–humped or linearly increasing or curvilinear or whatever (Wootton 1998, Buckling et al. 2000, Shea et al. 2004, Miller et al. 2011, Svensson et al. 2012). Which according to my folk theorem is why all sorts of different diversity-disturbance relationships are found in both observational data and in manipulative experiments, with no one particular qualitative form of relationship predominating (Mackey and Currie 2000, Shea et al. 2004, Svensson et al. 2012, Fox 2013). There are equally good reasons to expect just about any disturbance-diversity relationship, which is why many different diversity-disturbance relationships occur with appreciable frequency.

A second example: local-regional richness relationships. You can get either linear or concave-down (“saturating”) relationships between local species richness and the species richness of the surrounding region, just by tweaking the parameters of a dead-simple model (Fox and Srivastava 2006). And in nature linear and saturating local-regional richness relationships are about equally common, and there’s no rhyme or reason to when you see one or the other (see this old post for discussion and citations).

My folk theorem is the converse of Steven Frank’s (and others’) notion that simple patterns emerge in ecological data when there are many different processes or mechanisms that would generate the pattern, and few or none that would generate any other pattern. Think for instance of the fact that most every species abundance distribution is lognormal-ish in shape, with many rare species and few common ones. That’s presumably because a lognormal-ish species-abundance distribution is hard to avoid. As illustrated by the fact that most any plausible model of community dynamics, (and many implausible ones) predict a lognormal-ish species-abundance distribution. Contrast that with my folk theorem. My folk theorem says that, when different process or mechanisms all generate different patterns in data rather than all generating the same pattern, you won’t see a pattern at all. Rather, the data will vary idiosyncratically from one case to the next, thanks to case-specific variation in the details of underlying processes or mechanisms.

My folk theorem is consistent with how theoreticians go about their work. Theoreticians either develop their models to explain existing data, or to answer a hypothetical question: what would the world be like if [list of assumptions] were the case? There’s no reason to expect (or want!) the latter sort of model to describe the way the world usually is. And the former sort of model will only describe the way the world usually is if the existing data describe the way the world usually is. If the existing data just comprise a couple of suggestive case studies, or a “stylized fact” that might not actually be a fact at all, theory developed to explain those data isn’t likely to hold more broadly. After all, how common is it for the first few published examples of anything in ecology to turn out to be typical examples? Not that common, right?

What do you think? Is my folk theorem valid? Can you think of other examples? Can you think of counterexamples–maybe even enough so that it should no longer be regarded as a folk theorem? Looking forward to your comments, as always.

*Roughly equal plausibility of the alternative hypotheses is a key assumption here. You can always dream up some reason why anything would happen in ecology. But you can’t always dream up a plausible reason.

*Thus, my folk theorem doesn’t apply in cases where many different hypotheses are proposed to explain a known, well-established pattern in empirical data. The fact that there are seventy bazillion hypotheses to explain the latitudinal species richness gradient is not a counterexample to my folk theorem.


Are our students reading the textbook? And, if they are, is it helping them?

I recently went to a really interesting seminar hosted by Michigan’s Foundational Course Initiative. The seminar was given by José Vazquez from the University of Illinois. He raised a couple of issues that I’ve been reflecting on since the seminar, and that I thought would be worth blogging about. The first is: students are not reading the textbook, even when you try to force them to, and, if they are, it might actually make them less prepared. The second, which I’ll explain more in a future post is: one of our main roles as instructors is to motivate our students, and curiosity is a really important motivator; we can motivate our students by focusing their attention on a gap in their knowledge or understanding (as long as that gap isn’t too big).

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Who is doing interesting system-based research? And what is a model system anyway?

I will be organizing the American Society of Naturalists’ Vice Presidential Symposium next year, and think it would be fun to have the symposium focus on insights gained from system-based research. (Related: my old post on the merits of system-based research.) My thinking is to combine people who are working on well-established model systems (e.g., three spine sticklebacks, Arabidopsis, E. coli) with those working on more recently established systems (nascent model systems?). I’d like to include work that spans the breadth of the society (so, ecology, evolutionary biology, and behavior). I also want the symposium to feature the work of early career scientists. That’s where you come in! Tell me who you think is doing really interesting and exciting system-based research. I’m especially interested in hearing about early career folks, and am super duper interested in learning about early career folks who’ve done work to establish new model systems.

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Which bits of science and academia are just fine?

Lots of attention, here and elsewhere, focuses on problems. Stuff that’s “broken” or otherwise Bad, that needs fixing or replacing. That’s for various obvious reasons.

We also pay attention to things that are New or Changing. And we pay attention to things that Great–outstanding in some positive way. Again, for obvious reasons.

Without wanting to downplay the importance of any of that stuff, I think it’s worth occasionally taking time to appreciate things that are Fine (no, not that way). They’re not perfect (what is?). They’re not great. But they’re not bad either. They’re fine. And they’ve been fine for a while, so we tend to just take them for granted and not even think about them. Which of course is a big reason why we have attention to spare for bemoaning and fixing Bad stuff, and celebrating Great stuff, and noticing New stuff. One measure of the health of an institution, organization, or society is the amount and importance of stuff that’s just Fine. It is good to be able to be able to take some perfectly adequate things for granted!

So: which bits of science and academia are Fine? The more broadly-applicable the better. (After all, something that’s Fine for a select few and Bad for most everybody else often isn’t really Fine…) Let’s take a few moments to appreciate the stuff that we needn’t either worry about or celebrate, because it merely needs to be–and is–good enough.

Here’s the first one that occurred to me off the top of my head: the quality of talks at ecology conferences. It’s fine. Are some talks better than others? Sure. Could the average quality be raised? I dunno, maybe. But the overall quality of ecology conference talks is fine. And it’s been fine at long as I’ve been attending conferences, which is…[counts fingers]…[removes shoes and socks, counts toes]…[runs out of appendages]…many years. Which means that whatever we’re doing to prepare our own talks, and teach others how to give talks, is also basically fine.*

But I’m sure y’all can come up with many more examples. Looking forward to a Great comment thread about things that are Fine. 🙂

p.s. If you’re feeling brave, you can also suggest things about science and academia that are in your view basically Fine even though they’re widely believed not to be. My opening bid in that category is “peer reviewers and editors performing the gatekeeping function at selective journals“.

*Note that in other fields the quality of conference talks may not be Fine.

Am I frantically juggling when I should be letting things go off the edge of a cliff?

When I started my first faculty position at Georgia Tech, I felt like I was juggling as fast as I could; every time it felt like I was starting to get a hang of things, a new ball would get tossed in. I mentioned this at some point to someone there who said: the key is to remember that some balls are glass and some are rubber.

I was thinking about that juggling metaphor again recently because I was involved in a discussion with other faculty about how we all have too much to do. There was some discussion of the root causes of this, including a major decline in administrative support and more expectations. Obviously those are huge issues that are worthy of much more thought and systemic solutions. But there was also a discussion of what we can do individually in the short term as we all struggle with this. At some point, someone said something to the effect of, “you need to accept that you are never going to be able to do it all, and you have to accept that some things are just going to go off the edge of the cliff”.

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Recommitting to email boundaries

In November 2016, I did a poll and wrote a post about how overwhelming email can be. About a quarter of respondents to the poll said they rarely or never feel overwhelmed by email. I am not one of them. I’m in the majority that are overwhelmed by email at least some of the time. Other notable poll findings were:

  • people with more emails in their inbox were more likely to feel overwhelmed by email, and
  • faculty were more likely than grad students and postdocs to have a lot of work-related emails in their inbox.

At the time I wrote up the results of that poll, one of the main strategies I settled on for trying to be less overwhelmed by email was to batch my inbox, so that my emails only arrived once or twice a day. The idea is to treat email like regular mail – a thing that arrives at a given time and that you deal with in a batch (or, um, toss on the table and leave there for a while).

After that poll, I switched to using batched inbox to batch my mail. (It was free when I signed up, but I don’t think it is now.) It was amazing how much less overwhelming email was! I wasn’t getting distracted by emails as they arrived in my inbox, I found I actually got less email than I thought, and dealing with them in batches really reduced the amount of time and energy I spent on email. (I’m not alone. Arjun Raj has a post about how much email filtering helped his peace of mind.)

So, I was a fan. But then I started “cheating” and checking the folder where the batched emails hang out until they get dumped into the inbox. And, in the years since then, I have gone through cycles where I recommit to batching, think “OMG, why did I ever stop doing this?!?! Dealing with emails in bulk is so much better!!!”, then start sliding and going back to more of a system of dealing with emails as they come in (why? why do I do this?!? I know it’s counterproductive!), then get completely overwhelmed by emails, then at some point remember that batching is supposed to help with that, at which point I recommit to it and once again think “OMG, why did I ever stop doing this?!?!”

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Bold opinion pieces, RIP?

A few weeks ago, I lamented the passing of papers like Janzen’s Why mountain passes are higher in the tropics (1969) or Janzen’s Herbivore and richness hypothesis (1970) (the Janzen half of Janzen & Connell hypothesis) or the Hairston, Smith & Slobodkin (HSS 1960) paper best known as “why is the world green” even though that is not really the title. These papers were highly speculative, waved a little bit of data around, but mostly put out a hypothesis that attracted researchers for decades. But you don’t really see these kinds of papers any more. Hence my question of whether we should assume this category of paper has come to rest in peace (RIP) (i.e. are dead). Continue reading