Ecology is mostly not like billiards (but lots of people think it is) (UPDATEDx3)

Submitted by drupaladmin on 8 June 2012.

Billiards is all about sequences of causal events. Your cue strikes the cue ball, causing it to roll into another ball, causing that ball to roll into the corner pocket.

Falling dominoes are sequences of causal events. You knock over the first domino, which knocks over the second, which knocks over the third.

Rube Goldberg machines are sequences of causal events. The toy car is pushed into a line of dominoes, the last of which falls onto another toy car, which rolls down a ramp and runs into a ball, which rolls down another ramp...[skipping ahead]...which causes a piano to fall...[skipping some more]...which causes paintball guns to fire at a rock band.*

When humans think about causality, they find it natural to think in terms of sequences of events. That's why colliding billiard balls are a paradigmatic example of causality in philosophy.

But ecology is mostly not like billiards, or falling dominoes, or Rube Goldberg machines. Like history, ecology is (mostly) not "just one damned thing after another." But it's hard not to think of it that way, and to teach our students not to think of it that way.

(UPDATE: I'm not saying that ecology, or dynamical systems in general, aren't causal systems. They are! I'm just saying that the nature of that causality is such that it's misleading to think about it as "Event A causes event B which causes event C which causes event D...")

(UPDATE#2: Nor am I saying that ecological systems are "nonlinear" or "nonadditive". They are, but that's not my point here. For instance, you can have a sequence of causal events in which the magnitude of the effect is nonlinearly related to the magnitude of the cause. See the linked post from Nick Rowe, below, for further clarification. Sorry the original post wasn't better, it's clear that I did a lousy job of anticipating the ways in which readers might misunderstand what I'm trying to get at here).

Ecology is about dynamical systems. Stocks and flows, not falling dominoes. Inputs and outputs, not colliding billiard balls. Simultaneity, not sequences. Feedbacks, not one-way traffic.

Here's an example. It's a population ecology example, but not because population ecology is the only bit of ecology that's about dynamical systems. It's just a bit of ecology I know well. I could equally well have picked an example from physiological ecology (e.g., to do with individual growth), or from community ecology, or from ecosystem ecology, or from island biogeography, or conservation biology, or spatial ecology, or macroecology, or etc.

The example is predator-prey dynamics. You've got some prey that reproduce and die, and some of those deaths are due to predators. Predators convert consumed prey into new predators, and they die. Purely for the sake of simplicity (because it doesn't affect my argument at all), let's say it's a closed, deterministic, well-mixed system with no population structure or evolution or anything like that, so we can describe the dynamics with just two coupled equations, one for prey dynamics and one for predator dynamics. And again for the sake of simplicity, let's say it's a constant environment and there's no particular time at which organisms reproduce or die (e.g., there's no "mating season"), so reproduction and mortality are always happening, albeit at per-capita and total rates that may vary over time as prey and predator abundances vary.

You cannot think about this dynamical system in terms of sequences of causal events. For instance, let's say the system is at equilibrium, meaning that predator and prey abundances aren't changing over time. That does not mean nothing's happening! In fact, there's a lot happening. At every instant in time, prey are being born, and prey are dying, and those two rates are precisely equal in magnitude but opposite in sign. And at every instant in time, predators are being born and predators are dying, and those two rates are precisely equal in magnitude but opposite in sign. Inputs and outputs are in balance. You cannot think about equilibria in terms of sequences of causal events, it's like trying to think about smells in terms of their colors, or bricks in terms of their love of Mozart. What "sequence of events" keeps the system in equilibrium?

Or, let's say the predators and prey exhibit cyclic dynamics. For concreteness, let's say it's a limit cycle in the Rosenzweig-MacArthur model. Why do the predators and prey cycle? This is a case where it's sooo tempting to think in terms of sequences of events; I know because my undergrad students do it every year. "The prey go up, which causes the predators to go up, which causes the prey to crash, which causes the predators to crash." In lecture, even I've been known to slip and fall back on talking this way, and when I do the students' eyes light up because it "clicks" with them, they feel like they "get" it, they find it natural to think that way. And it's wrong. Not "wrong in the details, but basically right". Not "slightly wrong, but close enough." Wrong. Births and deaths are happening instantly and continuously. There are no sequences of events here.

Now I can hear some of you saying, ok, that's true of the math we use to describe the world, but it's not literally true of the real world. In the real world one could in principle write down, in temporal order of occurrence, all the individual birth and death events in both species. But my point would still hold. A prey individual was born, which caused prey abundance to increase by one, which caused...what, exactly? What's the next domino to fall in the sequence? Another prey birth? No. A prey death? No. A predator birth or death? No. What that increase in prey abundance did was slightly change the expected time until the next birth or death event, by increasing prey abundance and (in any reasonable model) feeding back to slightly change the per-capita probabilities per unit time of giving birth and dying. Now, you could try to drill down even further, down to the underlying physiological (or whatever) causes of individual births and deaths, and the underlying mechanisms linking per-capita birth and death probabilities to species' abundances. But you're never going to find something that lets you redescribe predator-prey dynamics in terms of sequences of events, each causing the next. (UPDATE #3: And to clarify further, no, I'm not trying to argue against the notion that population dynamics are ultimately a matter of individual organisms giving birth, dying, and moving around. I actually heartily believe that! My point is to do with how to interpret the causality of what's going on, whatever level of organization (individuals or populations) we choose to focus on.)

Our deep-seated tendency to think in terms of causal sequences of events rather than in terms of rates of inputs and outputs (i.e. rates at which the amount of something increases or decreases) doesn't just make it hard to teach ecology. I think it also makes it hard for professionals to do ecology. For instance, to preview a future post, much of the appeal and popularity of structural equation models (SEMs) that they let researchers take causal diagrams (variables connected by arrows indicating which ones causally affect which others) and turn them directly into fitted statistical models. That is, SEMs mesh with and reinforce our natural tendency to think about causality in terms of colliding billiard balls. Which I think makes them positively misleading in many circumstances (as I say, much more on SEMs in a future post).

This post was inspired by a post on the same topic by Nick Rowe. Nick's post is about economics. His post is way better than mine. You should click through and read it (no training in economics required; stop when you get to the bit at the end about "concrete steppes", which is where the post segues into technical economics issues).

*Click the link to see what I'm talking about. ;-)

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