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.