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

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 (well, unless you’re Brian), 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, and perhaps because the system is stable at a larger spatial scale (maybe thanks to competition-colonization trade-offs or successional niches). 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. In general, 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.πŸ™‚ But I’ve been unable to find the strip online.

p.s. This is a slightly-edited version of a post that first ran in 2013. Sorry for the rerun, I’m swamped at the moment.

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

  1. I know the economist joke with a married couple queuing at the supermarket – partner to the economist: why don’t we switch the counter, the queue over there is shorter – economist: nonsense, if that was true, the other people would have switched already.

    Joke aside, I find this question is definitely one of the big ecological conundrums of our times. Classical theory / wisdom clearly doesn’t sufficiently appreciate the possibility of stabilizing / equalizing / mixing effect that could be created by dispersal limitation and slow adaptation in connection with spatio-temporal environmental variability.

    Yet, this insight doesn’t help much if we don’t have the empirical tools to measure how frequent 10$ bills on the street really are, and if there is no capacity to evaluate models that include all the effects that realistically determine community assembly.

    I don’t know if we have any chance at all to tackle this question at the macro scale, but if we have to I guess the starting point for me would be asking what it is precisely that we want to measure. I guess we are not only after 10$ bills alone. Maybe 10$ bills are not so common. But what about nickels – would people pick up a nickle on the street? Maybe nickles lie around everywhere. So, the question is: what are sensible measures of stability / drift / fit that are meaningful and measurable without going into the detailed processes.

    • I like that version of the joke. It’s easy to translate into ecological terms as a joke about the ideal free distribution.πŸ™‚

      Good question re: precisely what it is we want to measure. Population ecologists have more or less agreed on this, I think. You want to measure density dependence (association between per-capita growth rate and density, possibly with a lag), which in a time series is manifested as return tendency. There are various statistical approaches you can use to try to estimate that, but it’s not an unlimited range (see Ziebarth et al. 2010 and de Valpine et al. 2010 for instance). Community ecologists could take the same approach with the same sort of data–a community time series is just a multivariate version of a population time series. But getting community ecologists to all agree on one stability measure is probably futile (

  2. I know I headed down this road a bit in the previous comments on this topic. But I increasingly don’t think any communities are truly at equilibrium in any meaningful sense. Change is the number one reality of ecological systems. Just for example, a paper I was on, Dornelas et al 2014, found that 10% of the species turn over every decade. A book chapter I authored in Rohde’s book on nonequilibrium communities showed that even birds (homeothermic vertebrates and presumably among the most stable populations out there) show very little evidence of stable communities. For example density dependence explains only about 30% of the year-to-year variation and most communities are being exogenously forced to have non-stationary trends (i.e. the “setpoint” is moving).

    So the idea that most communities are stable and therefore special but typical because they’re all that can remain is not true. Apparently nature is very good at maintaining non-stable systems over extended periods of time. As Florian suggested, I think the spatio-temporal context and connectivity is a big part of this. And since the background climate is non equilibrial, I think its probably a very good thing nature is good at maintaining non-stable systems!

    • You could be right, dynamics of non-stationary systems is a huge unstudied problem in ecology. It becomes difficult to even define sensible questions to ask. Peter Chesson is working on this, drawing on ideas from applied mathematical work on non-stationary systems. Turns out there are stability concepts one can define in non-stationary systems that are analogous in some ways to those for stationary systems. But how useful those concepts are for either theoretical or empirical work in ecology remains to be seen. As far as I know, Peter hasn’t published this work, he’s just talked about it at the ESA meeting.

      Quibble: the fraction of year to year variation in abundance explained by density dependence is a total red herring. That has absolutely nothing to do with stationarity, or with the “importance” or “strength” of density dependence however defined. Indeed, if anything, systems in which density dependence explains little of the temporal variance in abundance are those in which density dependence is likely to be *strong*. See Ziebarth et al. 2010 Ecol Lett. Don’t misunderstand, if what you care about is explaining or predicting temporal variance in abundance, you might well not need to care much about density dependence, which is fine. But “I don’t need to know about X to answer the question I happen to be asking” and “X is weak/unimportant” are totally different things.

      • I understand your point about % of variance explained by density dependence. But I think you and I might have different goals which make it be or not be a red herring. To me two meanings of equilibrium (sensu latu) is that there is a set point and that dynamics of returning to that setpoint dominate the dynamics (i.e stochastic perturbations are “small” relative to return to equilibrium). My two metrics of non-stationarity (trends in set point) and % of variance explained by density dependence get at those two aspects. Not sure why you see Ziebarth contradicting my interpretation? Their sigma_infinity/sigma_E is at least conceptually in the same ball park (although linked as 1-x or going in opposite directions) as my percent variance explained by density dependence and as their number gets big (my number gets small) the return time gets large and approaches the zone (in their ARMA models) where there is no stationary equilibrium.

        To me the profound point is “non-stationarity” sounds so technical and ultimately likely to be tractable by technical solutions. But a much blunter version is equilibrial systems are rare or explain a small fraction of what is happening. I’m not sure I would reject that proposition like I would have 10 years ago. And it has pretty big implications for applying ecological theory to the real world.

      • The other thing I’d say in response to some of the empirical data you noted (rates of species turnover etc.) is that it might well be that “local”communities often are unstable/nonstationary, because that’s basically the wrong spatial scale to be looking for stability/stationarity.

        It’s possible that the differences in goals between you and me mirror the differences in goals among many ecologists and evolutionary biologists. I’m thinking back to the ASN meeting debate on ecological “limits” to continental-scale species richness. Much of the debate seemed to come down to different implicit definitions of “limit”. I have an old post in which I explained why I think some definitions are better than others ( Very curious if you’d agree with my definitional preference in the context of that debate. I’m guessing you woudn’t?

      • I’d definitely agree with your first paragraph. That is the core assumption of macroecology – that things get more deterministic and less stochastic as you increase scale.

        Yes – I would agree with your definition. Although more broadly I think you can define equilibria by two aspects. Behavioral which is a return tendency as you discussed. And mechanistic – some actual evidence of density dependence (too much leads to decline, too little leads to increase). They lead similar places. But have different statistical methods and perhaps different implications for thinking about them.

      • Cheers for this. I’m glad we returned to this topic. Until now, I had been worried that we had a fairly serious disagreement here. But now I see that we’re more or less on the same page, just perhaps differing in our interests or in emphasis.

        “And mechanistic – some actual evidence of density dependence (too much leads to decline, too little leads to increase). ”

        The trouble with that way of defining density dependence is that in practice, inability to identify the mechanisms often has led to the (incorrect) inference that density dependence doesn’t exist or is weak or whatever. That’s the big beef of field-oriented folks like Charley Krebs with time series analytic folks like Peter Turchin. Of course, fitting mechanistic models to time series data is one way to bridge that gap (see the work of folks like Kendall, McCauley, Bjornstad, Grenfell, King…). At least, it *should* be seen as bridging that gap. But I’m not sure that it is. Purely speculating, I suspect that to a certain sort of ecologist, only certain sorts of field experiments really count as “mechanistic” studies…

        Which maybe would be a good topic with which to start a fight in a future post. What’s a mechanism, and how do you test for one? Or maybe more interestingly, what are the pros and cons of searching for mechanisms, as a research program? I have an old post that sort of touches on this:

  3. While the scale is obviously different (ecology probably has a lot more wiggle room for its parameters), physicists also struggle over whether to invoke the anthropic principle over why the universe’s key parameters are how they are (‘there could be no other way for us to observe this universe’), or to search for more meaningful information (‘these are the governing dynamics of the parameters, and here’s why they are what they are’).

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