Anyone interested in taking on Syamsu in a "Great Debate"?

Do you know what stochastic processes look like really? Just because something is stochastic doesn't mean it’s random. Systems can lie in the ordered regime, complex regime, chaotic regime, and in various borderland spaces.I just finished modeling a stochastic system used for cell types. It’s a model of gene expression with varying degrees of noise involved. The system "gravitates" towards an attractor point but is pertabated back and forth by various noise.Let me give this to you visually, these are occupancy graphs. About 100,000 times steps of where the system is at any given point. This is with a very low amount of noise, the point near the center of the blob is where the system would go if there was no noise. The fluctuations around that point range in the 0.0001 range on a system that has values that can fluctuate from 0-3. That is a VERY tiny fluctuation. Basically this is deterministic, we know where the system is at any given time step even though it is stochastic.Here is a few more with increasing noise values: You can see the system becomes a little more stable, but 990,000 its is basically with in the stable state.This is an example of the system with a LARGE amount of noise: While the fluctuations here are too much to declare it stable any longer there is still very convincing attraction to a stable point.So before you decide that something being stochastic makes it random you have to look at some important features. Most basically:How sensitive is the system to noise? How much noise is there in the system?Natural selection is not that sensitive to noise. Random day to day fluctuations do not pertabate the system around randomly. Selection for optimal reproduction plods ahead through a lot of noise. That doesn’t mean there isn't some noise but not enough to perturb it. If conditions change so the noise increases considerably (such as small populations) then the power of natural selection decreases and the system becomes more unstable.Actually the variance we see in organisms in a fitness landscape fits stochastic process very well. The reason there is continuous variance in any trait is because of these stochastic processes. Variation with in a species would disappear with out them. But that does not mean that the whole system doesn’t move towards an optimal state and then stay around that optimal state. Very much like the graphs above show.

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Let me try this again, a population of organisms exist with a basic survival probability (we will use survival rather than reproduction for simplicity) lets say P(S). Let’s say every organism is the same phenotype so probability of survival is only dependent on the environment. In a totally deterministic system every organism would either survive or die. So P(S)=1 or P(S)=0 and any organism X=P(S). But the environment is not deterministic it is stochastic so lets say the probability of survival for a given organism is X=P(S)-R (lets have P(S)=1 and R any random fluctuations in the environment). R is a stochastic effect. If R is small then the total probability of all the organisms tends towards P(S). If R is large then the system is chaotic. Now let’s change so that there are two new phenotypes one of which decreases survival the other which increases survival.In this case the less fit phenotype might be described as Z=(P(S)-R)*0.5. The fitter phenotype as Y=(P(S)-R)*2. So X is now half as likely to survive as the original population and Y is twice as likely to survive. So does having R (a stochastic element) in the system destroy the idea that Y should out survive Z and X and that X should out survive Z? Well that depends on how large R is doesn't it? If R is really small then it has no effect if R is HUGE then nothing holds.So do you see now how the size of the noise has to be defined? And that’s just one side of the equation, the sensitivity to noise also has to be addressed but that’s a lot more complicated.You HAVE to define the size of R. So how large do you think R is in the natural environment on average?If R is not large than natural selection will select phenotypes of comparative advantage.