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According to the survey, there is a lot of awareness among people regarding a healthy lifestyle, but they are of the opinion that since healthy foods are very expensive, they try to spend most of their time doing extracurricular activities so that they can maintain their physique even when they cannot follow a very healthy diet for that matter. 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. Births and deaths are happening instantly and continuously. 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.

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. 2: Nor am I saying that ecological systems are "nonlinear" or "nonadditive". UPDATE: I’m not saying that ecology, or dynamical systems in general, aren’t causal systems. Ecology is about dynamical systems. It’s just a bit of ecology I know well. 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. 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.

A prey individual was born, which caused prey abundance to increase by one, which caused… 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. Falling dominoes are sequences of causal events. Billiards is all about sequences of causal events. Rube Goldberg machines are sequences of causal events. But ecology is mostly not like billiards, or falling dominoes, or Rube Goldberg machines. I think it also makes it hard for professionals to do ecology. You cannot think about this dynamical system in terms of sequences of causal events. 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. If you have played both snooker and pool, you might have questioned yourself is the cue ball smaller in snooker? Puddy, David. "Snooker for beginners". Team Europe members (Thomas Engert and David Alcaide). Perhaps it reminds them of their first game, an ancestral home, or even their favorite sports team. It is the second most played professional pool game, after nine-ball, and for the last several decades ahead of straight pool.

The first is ball-in-hand behind the head string and the second is ball-in-hand anywhere on the table. In most areas table scratches are rare and the results are much the same as common pocketed cue ball scratches. There are no sequences of events here. When humans think about causality, they find it natural to think in terms of sequences of events. 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. For concreteness, let’s say it’s a limit cycle in the Rosenzweig-MacArthur model. Why do the predators and prey cycle? That’s why colliding billiard balls are a paradigmatic example of causality in philosophy. But you truly are able to touch the lowest level of billiard god-hood when you realize that the game is based on a very simple skill.

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