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For instance, let’s say the system is at equilibrium, meaning that predator and prey abundances aren’t changing over time. UPDATE: I’m not saying that ecology, or dynamical systems in general, aren’t causal systems. Found what I’m assuming is a billiard coin in the yard. 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. 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. 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. Ecology is about dynamical systems. 2: Nor am I saying that ecological systems are "nonlinear" or "nonadditive".

There are no sequences of events here. Rube Goldberg machines are sequences of causal events. But ecology is mostly not like billiards, or falling dominoes, or Rube Goldberg machines. It’s just a bit of ecology I know well. 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. 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. 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. 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…

Your cue strikes the cue ball, causing it to roll into another ball, causing that ball to roll into the corner pocket. He made a ball jump 34 centimetres high! Patrons walk along the first fairway before the start of play during the second round of the 2016 Masters Tournament at Augusta National Golf Club. Danny Willett of England walks along the 15th hole during the final round of the Masters on Sunday at Augusta National Golf Club. Danny Lee, of New Zealand, hits a drive on the second hole during the second round of the 2016 Masters Tournament at Augusta National Golf Club. American Scott Piercy creates a splash of sand as he hits out of a bunker during the third round of the Masters. Steven Bowditch of Australia celebrates after chipping in a birdie on the first hole during the first round of the 80th Masters Golf Tournament at the Augusta National Golf Club.

Lee Westwood of England chips on the second hole during the first round of the 80th Masters Golf Tournament at the Augusta National Golf Club. In any case, the Tournament Director must be called upon to restore the positions of the disturbed balls as soon as possible, but not during the shot. Inputs and outputs, not colliding billiard balls. Inputs and outputs are in balance. 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. Or, let’s say the predators and prey exhibit cyclic dynamics. Why do the predators and prey cycle? That’s why colliding billiard balls are a paradigmatic example of causality in philosophy. 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. And it’s wrong. Not "wrong in the details, what is billiards but basically right".