Belz:
Nonlinear systems
WP include chaotic systems, which includes turbulent flow amongst others which affect the weather, itself a classic example of a chaotic system.
Many (ETA: maybe most) systems with lots of positive feedback loops are likely to be nonlinear; they would at least be bistable or multistable, and probably oscillatory. Negative feedbacks loops could increase temoporary islands of stability. All these are present in biological and ecological systems, for example the reduced adult cod population has probably resulted in increased predation of cod fry by the prey of adult cod, keeping the Grand Banks cod population low, despite fishing controls. This is an examople of a positive feedback loop.
Here is a transcription of a 1989 New Scientist article about chaotic systems in biology, including population dynamics by
Robert May, former president of the Royal Society ( I am slightly dubious about the site host of the transcript, but the article seems fine):
The first few paragraphs talk about chaotic population dynamics.
Until recently, conventional analyses of population genetics showed that such selective effects could maintain variability within a species, but these static analyses tended to assume that the proportions of the different genotypes remained constant overtime. William Hamilton at Oxford, Simon Levin and David Pimentel at Cornell, Roy Anderson at Imperial College, London, and I have more recently studied the dynamic properties of the interactions among hosts and pathogens. The studies show that the proportions of any one genotype are likely to fluctuate chaotically from generation to generation. Such chaotically fluctuating polymorphisms are likely to be the rule rather than the exception.
One thing is certain. Biological systems, from communities and populations to physiological processes, are governed by nonlinear mechanisms. This means that we must expect to see chaos as often as we see cycles or steadiness. The message that I urged more than 10 years ago is even more true today: "not only in [biological] research, but also in the everyday world of politics and economics, we would all be better off if more people realised that simple nonlinear systems do not necessarily possess simple dynamical properties."
In the example from your post:
jimbob said:
Doesn't the statement that "evolution is non-random" imply that its course is inevitable, even if not predictable? In other words as soon as life emergerd it was inevitable that about 3.8 billion years later the ecosystem would look as it does now with only insignificant differences? Doesn't that also mean that in 100 or 1000 years from now the ecosystem is already determined with only insignificant differences?
Yes. But then it depends what you mean by random. By the definition you gave above, what you describe here is entirely deterministic and the answer to your question is yes. If you want it to be partially random you're going to have to change your definition.
I would disagree. Near-identical nonlinear systems tend to diverge over time.
Slight differences get magnified, all the way up from the alpha particle to a weather system.
3.8 billion years ago, as life first emerged, there was no inevitibility about the shape of the ecosystem now. Even just after the KT event, the shape of the current ecosystem would not have been determined. A few hundred thousand years ago, most of the ecosystem might, except for those species later rendered extinct due to chance technological developments of mankind, some of which were more probable than others. (Agriculture seems to have been developed independently in the Fertile Crescent, South America, and China for example)
Wowbagger:
The maths says that these systems
are significantly affected by truly random events*, i.e. it isn't just because of a lack of measurement accuracy that prevents me from knowing what quarter the wind will blow from over my house in 100 days time but that it will be significantly* influenced in effect by random events that haven't happened yet. Similarly for other weather conditions. There are also
predictible factors that affect the weather, and it
probably will be warmer.
Linear systems are not significantly affected, but chaotic systems are.
This doesn't mean that analyses are impossible, just that there has to be a probabilistic slant.
An anlogy: When running simulations of planetary formation, sometimes the orbital mechanics are chaotic. To see what would tend to happen, one can run many simulations with very similar starting conditions and see how many times certain outcomes occur. "With a Jupiter sized body in the position of Jupiter's orbit, an Earth-like planet formed in the correct orbit in x% of the simulations" A bit of googling could probably dig out real examples.
You can run the experiment many times and see how often particular outcomes occur; this can sometimes be a "virtual" experiment, if you know the interactions.
Here is a recent BBC news story which includes a probabilistic treatment of evolutionary outocmes by
Professor Andrew Watson
"We now believe that we evolved late in the Earth's habitable period, and this suggests that our evolution is rather unlikely. In fact, the timing of events is consistent with it being very rare indeed," he says.
"This has implications for our understanding of the likelihood of complex life and intelligence arising on any given planet."
Previous models are founded on the rationale that intelligent life on Earth emerged from a sequence of unlikely "critical steps".
Prof Watson identifies four - the emergence of single-celled bacteria; complex cells; specialised cells allowing complex life forms; intelligent life with an established language.
He estimates that the probability of each of these "critical steps" occurring in relation to the lifespan of Earth is no more than 10%.
Thus, the chances of intelligent life on any given Earth-like planet is tiny - less than 0.01% over four billion years.
Of course you could argue that this could be simply the lack of knowledge, but given the nonlinear systems involved, I would argue that it is essentially chance.
(The factor that he doesn't mention is the unknown potential number of habitible planets, "less than 0.01%" over the galaxy for Earth-like planets could still be a lot).
*whether or not an alpha particle ionises a few molecule of air does eventually lead to totally different weather patterns (at least according to the maths).
**i.e whether there is any wind at all, what speed it is, which direction (any of 360°)...
