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My concern is that that it is extraodinarily imrpobable to have occurred by random chance. Nature's Selection Process, that is.

Also, what do you mean by "random", and what do you mean to distinguish from "random" by "stocahstic"? So far, the argument you make seems to be that no selection predicts any other selection, which is as best I understand a perfect description of a random process. If not so -- and likely you'll find it not so, in what ways is it not so?

"My concern is that that it is extraodinarily imrpobable to have occurred by random chance. Nature's Selection Process, that is."

Natural selection is not random. It is anti-random.

" Also, what do you mean by "random", and what do you mean to distinguish from "random" by "stocahstic"?"

Stochastic means it is probabilistic. Natural selection doesn't automatically pick the best; there IS a chance element. What it says is that those organisms better adapted will have a better chance at reproductive success. Look at from a sports analogy. The '27 Yankees were a great team, one of the best ever. The '62 Mets stunk, horribly. If you had them compete head to head, the Yankee's would demolish the Mets. But not every game. There is still the probability that the Mets could beat the Yankees, and by a lot in some games. Just because an organism is better adapted to the environment, doesn't mean that a chance event like a falling tree or a rare disease could not kill the *better* adapted organism. Chances are though that it will leave more offspring than other, less fit organisms. What determines *fitter*? The totality of the environment.

"So far, the argument you make seems to be that no selection predicts any other selection, which is as best I understand a perfect description of a random process."

No, it isn't random at all; it is just undirected. Those organisms that survive to reproduce are not randomly selected. Organisms can't look ahead to see what the environment will be in the next generations; they can't direct the variation. There is no direction to the the variation. This is a good thing, as the environment is unpredictable. Natural selection is properly speaking a two step process; the production of genetic variation, and the probabilistic selection of those organisms with the best genetic variation at that time and that place.