[EMAIL PROTECTED] wrote: [...]
> For example, when a sheep dies you get more > grass for the remaining sheep, which gets you more sheep again, > so you can do a reasonable job of predicting sheep population > without knowing anything about the fates of individual sheep. Actually as the cycle time for the sheep population & the cycle time for the grass are not the same or multiples of each other, what you get from a deterministic continuously variable model is wild oscillations of sheep and grass populations that make it nigh on impossible to predict the sheep population at any given time in the future. Things get more steady if you introduce predators that eat the sheep, but never completely predictable in the long run. The only way to know how the model system would stand at any time in the future beyond the typical cycle time is to do the sums. And there is no guarantee that the real world analogue of the model would be in a similar state at that time. One of the classic examples of what is now called "chaos" (a word that I don't like in this context). The exact trajectory taken by simple models of predator-prey systems is often very sensitively dependent on initial conditions. Of course in real life these things are stochastic anyway so the variables in your model should actually be probability distributions, which makes the sums much harder and leads to considerable handwaving. Known about since the 1920s, pretty exhaustively described by Robert May, John Maynard-Smith & others in the 1970s, but still argued about today. Whether or not more complex systems (more species, more levels of predation, more kinds of resource) are more "stable" is still a moot point, opinions tending to depend (sensitively) on what the opinionated one actually means by "stable". And on whether they have a background in maths, or physical sciences, or molecular biology, or real biology. This kind of thing has implications for economics & technology & markets of course (cf Santa Fe, ad infinitum). People who think like ecologists tend to assume that a more complex market, with more participants, and more kinds of interaction between them, will be in the long run more "stable" - perhaps because that is what they think they see in nature. People who think like engineers may disagree and talk of excessive market volatility, and the dangers of new forms of trading & so on, and they need for regulation, looking for a few global variables to track and control. Apologies for off-topicness, but this is probably the only subject that's come up here about which I suspect I'm better read than the list in general. I'm working towards a doctorate in which I intend to argue (in effect) that for many kinds of investigation (such as the relationship between complexity and stability of the whole system) you do need to know about the fates of the individual sheep. (Or, in my case, imaginary protobacteria, to keep it simple :-) > Similarly, if i cut a fart in an elevator, there's no telling where an > indvidual stink molecule will go, but in not too long they'll > be more or less uniformly spread throughout the elevator. I suspect they probably won't, not unless you spend a lot more time in the lift than is healthy for you. Whiffs will be whisked about chaotically, some being lost every time the door is opened or anyone walks around. So some poor guy on the 3rd floor will get a noseful, but someone else standing next to him might miss out entirely.
