Shoshana Sorlie asked 6 days ago
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. 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 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. Predators convert consumed prey into new predators, and they die. “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. When humans think about causality, they find it natural to think in terms of sequences of events. 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.
If you’re brand new to the game of pool, you may be unfamiliar with the colors and numbers of billiard balls. Another reason could be that you purchased a cue ball from one brand and other balls from another. Your cue strikes the cue ball, causing it to roll into another ball, causing that ball to roll into the corner pocket. A scratch is broadly defined as a cue ball driven off the table or pocketed. A table scratch occurs when a player fails to hit an object ball with the cue ball. They use English to position the cue ball for the next shot. You have to consider dozens, even hundreds of things when selecting a shot. There are a total of 500 points available to a player, representing the combined value of a perfect score on all 76 shots, although not all games are played with the full shot catalogue. But before you start shopping for that perfect table, there are essential considerations to keep in mind. The process of alternately potting reds and colours continues until the striker fails to pot the desired object ball or commits a foul-at which point the opponent comes to the table to start the next turn-or when there are no red balls remaining.
The table is “open” at the start of the game, meaning that either player may shoot at any ball. For instance, let’s say the system is at equilibrium, meaning that predator and prey abundances aren’t changing over time. 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. 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. Players on the World Snooker Tour generally gain a two-year “tour card” for participation in the events. 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. No. A predator birth or death? 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. 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.
Which I think makes them positively misleading in many circumstances (as I say, much more on SEMs in a future post). That is, SEMs mesh with and reinforce our natural tendency to think about causality in terms of colliding billiard balls. Then you have to think about the cushions, sides, pockets, and any decorative additions that make the table look nice. Make sure your cue tip is always properly chalked. ’t just make it hard to teach ecology. 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. 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. There are no sequences of events here. They are, but that’s not my point here. 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. UPDATE: I’m not saying that ecology, or dynamical systems in general, aren’t causal systems.
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