One common zombie idea about disturbance is that it prevents competitive exclusion by “interrupting” or “setting back” the process of exclusion. The idea is that disturbance, by temporarily reducing every species to low density, perturbs the system away from the equilibrium it was approaching, an equilibrium at which species would be competitively excluded. Repeated disturbances, so the argument goes, prevent the system from ever actually getting to equilibrium, and so prevent competitive exclusion from ever “going to completion”.
I’ve explained before why that idea is wrong (see my forthcoming paper in Trends in Ecology and Evolution, or use our search bar for old “zombie ideas” posts). But often it helps to have different ways of explaining the same thing, in case one way doesn’t “click” with everyone. And I just thought of a fun analogy to the zombie idea that “disturbance prevents competitive exclusion by interrupting it”. That zombie idea is kind of like Zeno’s paradox of Achilles and the tortoise.
Let me explain.😉 Zeno (c. 490-430 BC) was a Greek philosopher who proposed a number of paradoxes, the most famous of which all have to do with ideas of infinity, continuity vs. discreteness, and wholes vs. parts. The overall intent was to demonstrate the oneness of reality and the impossibility of any kind of change. Zeno was a follower of Parmenides, who famously argued that nothing can move and the appearance of movement is a mere illusion. Zeno’s paradoxes were defenses of Parmenides’ views.
In Zeno’s paradox of Achilles and the tortoise, Achilles is in a footrace with a tortoise. Suppose that Achilles allows the tortoise a head start of 100 m. After some finite amount of time, the fleet-footed Achilles will reach the point 100 m ahead of him, where the tortoise was when the race began. But during that time, the tortoise will have moved ahead a bit (say, 10 m), and so will still be leading the race. It will take Achilles some further amount of time to cover that 10 m–but by the time he does so, the tortoise will have moved ahead some further distance. Thus, whenever Achilles reaches a point where the tortoise has already been, he still has further to go. Meaning that he can never overtake the tortoise.*
The analogy to the notion that disturbances prevent competitive exclusion by “interrupting” it or “setting it back” isn’t perfect, but I think it’s close enough to be interesting. The system approaches competitive exclusion (=Achilles approaches the tortoise). But before it can get all the way there, its progress is set back by disturbance (=the tortoise moves ahead a bit). Ergo, competitive exclusion can never occur (=false conclusion). Further, you can actually tweak a lot of the details without changing the basic nature of the paradox, or the obvious falsity of the conclusion. For instance, Zeno’s “dichotomy paradox” differs in many details from the paradox of Achilles and the tortoise, but at bottom is basically the same paradox. So just as Achilles will in fact pass the tortoise, competitive exclusion will in fact occur despite periodic interruptions or setbacks.
But of course, just pointing out that the conclusion of a chain of reasoning is false doesn’t on its own give any insight into why it’s false (When he first heard Zeno’s arguments about the impossibility of motion, Diogenes the Cynic apparently refuted them by saying nothing, getting up, and walking out) What’s wrong with Zeno’s reasoning about Achilles and the tortoise, and what, if anything, does it tell us about the zombie idea that periodic disturbances can prevent competitive exclusion simply by interrupting it? Surprisingly, there’s no universal agreement on precisely how Zeno goes wrong. And in any case, I suspect that claims about how interruptions can prevent competitive exclusion go wrong for rather different reasons than Zeno does. Zeno does recognize that Achilles gets closer and closer to the tortoise, he just denies that Achilles can ever catch up entirely. In contrast, verbal arguments about how periodic disturbance interrupts competitive exclusion tend to forget that, in between each disturbance, the system gets closer and closer to equilibrium (they also tend to forget that adding disturbances to a disturbance-free system changes the location of the equilibrium, but that’s another issue).
So no big conceptual insight into ecology here, which actually disappoints me a bit. When the idea for this post popped into my head the other day, I thought it would be really fun to show how zombie ideas about the IDH actually predated Christianity and had been refuted by Aristotle or something.🙂 But while that didn’t quite pan out, I still thought the analogy was sufficiently off the wall, and sufficiently close, to be worth sharing.
See The Stanford Encyclopedia of Philosophy for further discussion of Zeno’s paradoxes, on which I drew for this post.
*Zeno took his paradoxes as proof that time and space are fundamentally indivisible, since assuming that they are divisible leads to absurd conclusions.
UPDATE: xkcd on Zeno’s paradoxes.😉