Stylized facts in ecology

In economics and other social sciences, “stylized facts” are broad empirical generalizations that are essentially true, although they may be inaccurate in some details, gloss over some nuances, or have some exceptions. The term was coined by Kaldor (1961), who identified several stylized facts about macroeconomics; they’re now known as the “Kaldor facts”.

Stylized facts are widely seen as a key raw material for healthy social scientific research (Summers 1991, Abad & Khalifa 2015). Stylized facts give theory a target to shoot at–something to explain. Indeed, the most useful ones will suggest (though of course not prove) theoretical hypotheses that might explain them. Stylized facts allow you to evaluate theory: your theory is importantly wrong if it can’t reproduce all the stylized facts it should reproduce. Stylized facts guide theory improvement: knowing which stylized facts your theory does and doesn’t reproduce suggests ideas for how to improve your theory. Finally, stylized facts aid feedback from theory to empirical work. Theory that predicts new stylized facts for empiricists to look for is highly valued. Theory that’s hard to test because it doesn’t predict any new stylized facts is much harder to test and so much less valued. Summers (1991) basically argues that if empiricists aren’t producing stylized facts, and theorists aren’t explaining and predicting stylized facts, they’re both Doing It Wrong.

I wouldn’t go that far. But I do think Summers and the many economists who think as he does have a point from which ecology could draw some lessons.

Where do our stylized facts come from in ecology? One obvious answer is “meta-analyses”, but I’m not so sure about that. In a recent post I noted that meta-analyses in ecology often don’t produce stylized facts that give new theory a “target to shoot at”, and so often end up functioning more as endpoints rather than as jumping-off points for further theoretical and empirical work. Which I guess is fine if you don’t expect or want ecological research to do more than statistically summarize what happens at various places and times. But personally, and without denying the value of those summaries, I’d  think ecologists sometimes can and should do more than that. I don’t agree that the undoubted complexity and variability of our study objects entails that ecology will never be anything more than a bunch of unique case studies that defy any theorizing. (aside: I recognize that there are other purposes meta-analyses can and do sometimes serve, such as testing existing theory and summarizing information bearing on a specific management issue.)

Then again, perhaps we shouldn’t be looking to meta-analyses for stylized facts. Abad & Khalifa (2015) argue that we should distinguish stylized facts from “bare facts”. They say that stylized facts, in contrast to bare facts, are not validly and rigorously inferred from reliable data. Lack of a rigorous basis in reliable data is what makes a stylized fact stylized. They also say that stylized facts aren’t merely facts a theory ought to explain (as with bare facts), but that stylized facts play a “methodologically beneficial role” above and beyond giving theory something to explain. And here’s the clincher: they argue that the stylization of stylized facts is crucial to their methodologically beneficial role. Basically, stylized facts give you something to go on when otherwise you wouldn’t have anything to go on. Having something to go on is really valuable.*

So, what are ecology and evolution’s most important, interesting, or fruitful stylized facts? Some opening bids:

• My favorite stylized fact in ecology is from Murdoch et al. (2002): generalist consumers that exhibit cyclic population dynamics cycle with low amplitude and short period. In contrast, specialist consumers that cycle do so with high amplitude and long period. (those could be stated more precisely, but that’s close enough for government work)
• My second-favorite stylized fact is closer to being a stylized fact in Abad & Khalifa’s sense: a plausible empirical claim that might be true, and that provides a particularly fruitful basis for theorizing. It’s Bjørnstad’s (2000) observation that large-scale spatial synchrony of cycling populations is lost if those populations stop cycling. The recent collapse of population cycles of many European mammals provides an opportunity to test whether this actually is a fact.

Most of the other stylized facts on my list are less stylized and better-grounded in reliable data than the one from Bjørnstad (2000), and so fall more towards the “bare facts” end of the continuum from bare facts to stylized facts:

• Another stylized fact from population ecology: negative density dependence is ubiquitous, although mostly too weak and/or restricted to low population sizes to distinguish against the background of sampling error given the typical length of ecological time series (Hatton et al. 2015, Ziebarth et al. 2010).
• Many stylized facts in ecology are from macroecology and biogeography; ecologists usually call them “large-scale patterns”. Many of them are very well-established and so very much towards the “bare facts” end of the spectrum. Species abundance distributions comprise a few common species and many rare ones (or more precisely, they always have something approximating a lognormal or logseries distribution). Species richness increases as a power law function of area with an exponent of about 0.25 (aside: is “quantitative stylized fact” an oxymoron?) Species richness is highest at low latitudes. Bergmann’s Rule. In my anecdotal experience, macroecologists and biogeographers are very proud of their stylized facts and like to think they have more of them than other subfields of ecology. 🙂
• Many stylized facts in ecology involve comparing different species. And many of the most fruitful comparative stylized facts (meaning, the ones that have inspired the most successful theory) are those from evolutionary ecology. Though many of those arguably are too quantitative to be considered “stylized”. Quarter-power allometric scaling. Rensch’s Rule. Life history invariants. The island rule.
• Evolutionary biology sensu stricto has its own stylized facts. Haldane’s Rule. Spatial variation in selection always leads to the evolution of fitness trade-offs. Quantitative genetic variation mostly is due to many different loci of small effect. Genetic variation for fitness is minimal.
• I used to be a food web ecologist, so I know a bunch of stylized facts about food webs. Food web connectance ranges from about 0.03 to about 0.3. Connectance declines on average with increasing species richness because high-connectance, high-richness food webs don’t exist. Food chains are short (just a few links, usually). All food webs fall into one of two structural classes (roughly, those with lots of omnivory and poorly-defined trophic levels, and those with little omnivory and well-defined trophic levels).
• Contrary to what you might think, community ecology has some stylized facts, though perhaps they tend to be more stylized than those from, say, macroecology. Trophic cascades are ubiquitous, but attenuate as they propagate to lower trophic levels (Shurin et al. 2001). Total biomass, productivity, or resource use of a trophic level increases in a saturating fashion with increasing species richness of the trophic level, all else being equal.
• Community ecology also provides many examples of what Abad and Khalifa (2015) call “discredited stylized facts”–stylized facts that turned out, upon further empirical investigation, not to be facts at all, so got discarded rather than getting converted into bare facts. Or rather, they should have been discarded, but they haven’t been–they live on as zombie ideas, or perhaps as ghost ideas. The IDH, humped diversity-productivity curves, and predominantly linear local-regional richness relationships are three examples. Those research programs all kicked off because of a few suggestive empirical examples–stylized facts. This illustrates one of the occupational hazards of basing the early stages of a research program on stylized facts: if the facts turn out not to be facts at all, you’re hosed–but the research program is likely to keep on keepin’ on for a long time because research programs have their own internal momentum.
• A large part of the revolution in ecology in the 1950s and 60s was based on (highly) stylized facts and theorizing about them. Odum (1969) famously suggested a bunch of stylized facts about ecosystem development as succession proceeds. And Robert MacArthur was a great one for identifying (highly) stylized facts and then theorizing about them. Of course, many of the stylized facts Odum and MacArthur identified have since been discredited.

It’s interesting to think in a comparative way about stylized facts. For instance, are there different types? Tentatively, I’d suggest that many stylized facts of macroecology are what Steven Frank would call “statistical attractors” analogous to the central limit theorem (a suggestion that I’m far from the first to make, of course). These stylized facts are explained by “multiple realizability”. Roughly, there are many possible worlds in which these stylized facts are facts, and few or no possible worlds in which they’re not facts. In contrast, I think of the stylized comparative facts of evolutionary ecology as reflecting the strong constraints that evolution by natural selection places on the possibilities. Rather than there being many roads leading to the same endpoint (and no roads leading any other direction), there’s only one road leading to the endpoint; all other roads lead to dead ends. But some stylized facts don’t fall into either class, or at least it’s not obvious to me that they do.

*To say that one shouldn’t leap into theorizing until one has more to go on than stylized facts implies an overly-inductivist, empiricist view of how successful research programs proceed. That overly-inductivist view was expressed by some of Charles Darwin’s opponents following publication of the Origin of Species. They claimed that Darwin was speculating wildly, deviating from the slow but sure path of first accumulating a mass of facts without any preconceived ideas as to what might explain them, how they might relate to one another, or even what facts were worth accumulating in the first place. Darwin in contrast famously referred to evolution by natural selection as “a theory by which to work”–an idea that made sense of the available stylized facts and provided guidance as to the most productive new lines of empirical and theoretical investigation. Thereby allowing the research program to reach an ideal endpoint–well-established “bare facts” plus a well-tested theory to explain them–more quickly than it otherwise would have. History justifies Darwin’s procedure.