About Jeremy Fox

I'm an ecologist at the University of Calgary. I study population and community dynamics, using mathematical models and experiments.

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.

 

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.

Poll results: are EEB faculty job seekers receiving good advice about the EEB faculty job market?

Recently I polled y’all on the advice you received about the EEB faculty job market, focusing on the prevalence, sources, and nature of bad advice (or what respondents perceived to be bad advice). Thanks very much to everyone who took the poll! Here are the results, with some commentary.

tl;dr: A substantial majority of respondents reported receiving mostly or entirely good advice, though there’s an interesting discussion to be had about how to distinguish good advice from bad. And the very worst advice is…😬. I conclude with some advice on giving advice.

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A statistical profile of recent EEB faculty job applicants (UPDATED)

In my continuing quest to know All The Things about the ecology faculty job market, I compiled some data on recent EEB faculty job applicants. How many positions does the typical applicant apply for these days? How many publications do they have? How many interviews and offers do they get? And is there anything besides the number of applications they submit that predicts the number of interviews or offers they’ll receive? For the answers, read on!

Attention conservation notice: long-ish post ahead, but stick with it, the most important and surprising results are at the end. And I think it’s of broad interest to many of you, not just to current EEB faculty job seekers. And there are lots of graphs. 🙂

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Poll: are EEB faculty job seekers receiving good advice about the EEB faculty job market?

My recent post on when the ecology faculty job market first became so competitive sparked a lot of good discussion, here and on social media. One point that came up is that, because the ecology faculty job market has changed over time, what might once have been good advice to ecology faculty job seekers might now be bad advice. Anecdotally, I feel like I often see this complaint from faculty job seekers in ecology (and evolution): that too many profs these days are giving bad advice, because they don’t realize how much more competitive the faculty job market is today than it was back when the prof in question was on the job market.

I sympathize deeply with anyone who’s received bad advice about the EEB faculty job market, as some people have. It’s hard enough being among the many people chasing comparatively few TT faculty positions without also receiving bad advice! I was fortunate to receive uniformly excellent advice myself, and so I’d like to do what I can to help make sure others get good advice too.

In order to improve the advice that EEB faculty job seekers receive, it would help to first know something about what advice they’ve gotten, from what sources, and how good it was. So I got to wondering: how common is it for EEB faculty job seekers to receive bad advice, or at least what they consider to be bad advice? From what sources does bad advice most commonly come? In particular, how common is it for EEB faculty job seekers to receive outdated advice, as opposed to advice that’s bad for some other reason? I wonder about that last one because, as best I can tell, almost everyone who currently holds a tenured or tenure-track faculty position in ecology experienced a very competitive job market as an applicant (i.e. was hired in 1980 or later). Plus, it’s not as if current profs only know about the faculty job market from their own experience as applicants–many have since served on search committees, for instance.

Hence this short poll! This completely anonymous poll is for everyone who holds, has held, seeks, sought, or plans to seek a tenured or tenure-track faculty position in ecology, evolution, or an allied field. Please take 60 seconds or so to fill it out! I’ll summarize the responses in a future post.