[Ichneumon]

[There is no one "favorable" or "detrimental" in most individuals. There are thousands of benign (here and now), slightly detrimental (here and now), slightly beneficial (here and now), etc. The range is huge. That seems to be the point you are missing.]

Thank you for the expansion. However, I wish to understand the process at its basics. To do so, Gaussian distributions can be modeled at their means.

No, they can't -- not without introducing error. For *some* modeling this error is small or cancels out, and is a useful way to simplify the calculations without sacrificing a significant amount of accuracy. For others, however, it causes the model to become entirely invalid.

For the sake of clarity, those mutations that are only “slightly” detrimental or “slightly” beneficial can be regarded as benign.

No, they can't, because in evolutionary processes, a great deal of fitness increase occurs due to the slightly beneficial mutations. Even worse for your attempt at a simplifying assumption, the fact that "slightly beneficial mutations" are amplified through the population means that their you're attempting to hand-wave away a "butterfly effect", whereby small inputs can potentially have large consequences for the system. And if you know as much math as you try to portray, you'll know that nonlinear/chaotic systems do *not* lend themselves to the kinds of simplified linear analysis you're attempting to do here.

[Lucky Dog]

No, they can't -- [modeling Gaussian distributions at their means] not without introducing error. For *some* modeling this error is small or cancels out, and is a useful way to simplify the calculations without sacrificing a significant amount of accuracy. For others, however, it causes the model to become entirely invalid.

It is not that your assertion is incorrect… quite the contrary in many cases. However, the degree of accuracy required of a model is dependent upon its intended purpose. If the model’s purpose is predictive (either, postscriptive or prescriptive) then a relatively high degree of accuracy is necessary. On the other hand, if the purpose is the investigation of mere plausibility, the degree of accuracy need not be nearly as high.

In the case I was proposing, I merely wished to determine if a sufficiently strong, statistical correlation exists among mutation rate, natural selection pressure and emergence of new species. Since such a goal is merely a plausibility estimate, it requires only a modest degree of accuracy.

What is required is a mutation rate (one has been postulated by Campbell, noted earlier), a quantification of natural selection pressure and its changes, and the demarcation line from one species to the next in measurable terms. What I have not found is a quantifiable (measurable) estimate of the influence of, or change in, natural selection pressure or a measure of how many “favorable mutations must accumulate (both simultaneously and/or sequentially) to qualify the emergence of a new species. Obviously, there must be an agreed upon demarcation line from one species to the next in measurable terms.

No, they [quantifying slightly beneficial or detrimental mutations as benign] can't, because in evolutionary processes, a great deal of fitness increase occurs due to the slightly beneficial mutations.

If one chooses to extrapolate in one direction, then one must, likewise, extrapolate in the opposite direction as well. Consequently, your assertion is a little one sided, it seems, as it ignores the corresponding probability that “slightly detrimental mutations” would have counterbalancing effect [a great deal of “unfitness”] mathematically.

Even worse for your attempt at a simplifying assumption, the fact that "slightly beneficial mutations" are amplified through the population means that their you're attempting to hand-wave away a "butterfly effect", whereby small inputs can potentially have large consequences for the system.

If there are no reasonably stronger correlations among mutation rate, natural selection pressure and new species emergence that your postulated “butterfly effect,” then it would seem that those who wish to challenge the validity of the theory are justified in their doubts.

Sorry, I must, again, leave the forum for an extended period. I will check back later for your reply. Regards, Lucky Dog