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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… 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. 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. You’ve got some prey that reproduce and die, and some of those deaths are due to predators. One way to see this: The main issue are corners.

See the linked post from Nick Rowe, below, for further clarification. This post was inspired by a post on the same topic by Nick Rowe. Which I think makes them positively misleading in many circumstances (as I say, what is billiards much more on SEMs in a future post). 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. Introduced at the 1959 News of the World Snooker Plus Tournament, this variant failed to gain popularity and is no longer played. Some early world finals had much longer matches, such as the 1947 World Snooker Championship, which was played over the best of 145 frames. 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. 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.

It’s also a good idea to make sure that your pool table lighting is installed before you start setting up your pool table. The lighting in your rec room is going to have a significant impact on the look of your felt, no matter what color you choose. We have a brief glimpse outside of the hall which is staged to look like that of Luton Hoo but is not. If you have a clean proof of the conjecture, that's very interesting (but not an acceptable answer). If you can refute the conjecture, that's an acceptable answer. I haven't written an argument down; if you can refute this claim that's an acceptable answer. This kind of narrows your options down, so if you're having trouble running the game with your GPU there's a plain and functional toon shaded codepath that you can try but you'll miss out on the fancy shading. If an attempt is made to pocket a ball, and the ball hits the pocket, bounces out and lands on the ground, the ball is placed in the pocket and the game continues. Some people think that games like billiards is not a sport because there really is no team and there maybe no strategy involved because all you do is hit a ball into a pocket.

And while there are lots of different types of billiard games that you can learn and play, pool is by far the most popular, at least in America. Green and blue are by far the most popular felt colors used today - specifically, Tournament Green (aka Classic Green) and Tournament Blue (aka Electric Blue). There are no sequences of events here. You cannot think about this dynamical system in terms of sequences of causal events. 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. Simultaneity, not sequences. Feedbacks, not one-way traffic. 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. 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.