Are unstable communities like $10 bills lying on the ground?

Attention conservation notice: this post is old wine in a new bottle. But my old post was a long time ago and didn’t get many readers (or any comments!), so I thought I’d try again.

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Here’s an old joke about economists:

Two economists are walking across a college campus. Suddenly the first economist looks down and says “Hey look, a $10 bill on the ground!” The second economist replies “That’s impossible. If it were there, someone would’ve picked it up by now.”

The joke is about the idea that, in a well-functioning market, there are no risk-free profits to be had. No $10 bills just lying on the ground, waiting for someone to pick them up. Opportunities for easy, risk-free profits get exploited very fast (for instance via arbitrage), causing them to vanish. But just because something shouldn’t exist in theory doesn’t mean it can’t exist in practice, which is the point of the joke.*

Having said that, the situation described in the joke is indeed unlikely. You really do hardly ever see $10 bills lying on the ground, for exactly the reason the second economist gives. In general, you don’t expect to observe anything that can’t last very long. That’s why you never see raw sodium floating around in the water. Or see much ununoctium anywhere.

This “no $10 bills lying around” principle often gets invoked, implicitly or explicitly, to explain ecological phenomena. For instance, numerous papers argue that observed food webs, or other ecological “networks” like plant-pollinator interaction networks, are structured so as to be stable in some sense. The implicit argument is that this explains why those networks look the way they do. If they looked any different, they’d be unstable and so wouldn’t persist long enough to be observed. Conversely, many papers on omnivory in food webs are motivated by the observation that, in theoretical models, food webs with ominivory are prone to instability. The commonness of omnivory in natural food webs therefore is a puzzle that needs solving. From the perspective of simple theoretical models, food webs with lots of omnivory are like $10 bills lying on the ground.

Further back, this argument was deployed by advocates of density-dependence in population ecology against advocates of density-independence like Andrewartha and Birch. Any population that doesn’t experience at least weak negative density-dependence will do a random walk to extinction, so we shouldn’t expect to observe such populations. The community ecology equivalent is our focus on conditions for stable coexistence (I say “our” because I certainly share this focus). When analyzing theoretical models, we focus on the conditions that lead to stable coexistence rather than exclusion or priority effects or etc. And when we do empirical studies we expect to find that those conditions hold in nature. Because we shouldn’t expect to observe species that are on their way to being excluded. “If they were there, they’d have been excluded by now” would be the punchline to the coexistence theory version of the economist’s joke. I’m sure this sort of argument has been deployed in many other ecological contexts.

I find this argument appealing as an explanation for why the world is the way it is. But I’m also suspicious of it, as it’s often deployed without much critical evaluation. For instance, you might actually expect to see lots of $10 bills on the ground if picking up $10 bills were really costly. In economics, transaction costs can prevent otherwise-profitable arbitrage opportunities from being exploited. Or (and this is really another way of saying the same thing), maybe $10 aren’t actually worth much, so it’s not worth the effort to pick them up. That’s why you often do see pennies on the ground. Or maybe $10 bills are really hard to pick up because they blow around in the wind. Or maybe you see $10 bills on the ground because for some reason they’re being dropped on the ground even faster than people can pick them up. That does happen on occasion.

Analogous possibilities can occur in ecology. For instance, you might expect to observe density-independent populations even though they’re doomed to eventual extinction because a random walk to extinction is a slow process, at least under some circumstances. That’s an analogue to $10 bills being hard to pick up because they’re blowing in the wind. Or maybe new density-independent populations can be established via immigration or speciation fast enough to balance the rate at which they vanish. That’s an analogue to $10 bills being dropped as fast as they’re picked up. Steve Hubbell made precisely this argument in his “neutral theory of biodiversity”, although his argument has been strongly disputed (speciation is probably too slow to balance even the slow rates of extinction produced by stochastic drift in a neutrally-stable system). As another example, grassland communities established during old field succession are unstable, in the sense that they’re eventually replaced by forests. But nevertheless, we observe them, because old field succession is a slow process. As a third example, many species that are thought to be doomed to eventual extinction due to habitat loss are still around, and will be for decades at least, because that’s often how long it takes to pay the “extinction debt”. As a final example, Kristensen (2008) is a really nice theoretical paper showing that model food webs constrained so that all species must exhibit positive, finite densities don’t actually differ much in their structure from food webs not so constrained. In other words, lots of unobserved food web structures would be just as “stable” as observed ones. So you can’t argue that we only observe the food web structures that we do because the alternatives would be unstable.

Evolutionary biologists have thoroughly studied the various factors that prevent natural selection from always and everywhere producing populations in which all individuals have the same, perfectly-optimized phenotype. There are lots of well-studied reasons why we might observe less-than-maximally-fit individuals, the evolutionary equivalent of a $10 bill on the ground. Same in economics–there’s a huge body of research on why real-world markets might not be perfectly efficient or might fail to “clear”. But I don’t know that ecologists have been as thorough and systematic about studying the analogous problem. There are some papers like Kristensen (2008), but not nearly as many as there should be, I don’t think. As I noted in that old post linked to at the beginning, there are various reasons why ecological systems might look the way they do. “If they weren’t this way, they wouldn’t persist” isn’t necessarily the tightest constraint on what we observe, or even a constraint at all. Maybe the ecological world is actually full of $10 bills on the ground, and our task is to explain why. Or maybe it doesn’t even matter if there are $10 bills on the ground or not.

*There’s an old Bloom County cartoon about this. In it, boy genius Oliver Wendell Jones discovers the fundamental theory of physics, which predicts that penguins shouldn’t exist. Thereby causing Oliver’s friend Opus, a penguin, to vanish. But then Oliver realizes he made a mistake (“Forgot to carry the two”), causing Opus to reappear. 🙂 But I’ve been unable to find the strip online.