[Coyoteman]

As I understand the basic premise of evolution, it is mutations that are favored by natural selection pressures will be passed on to succeeding generations (and the corollary that those detrimental will cause the demise of the individual and not be passed). The accumulation of enough of these “favorable” mutations leads to the emergences of a new species. On the other hand, the accumulation of enough “detrimental” mutations leads to the extinction of a species. Is this an incorrect statement of the basic premise of evolution?

Yes, this is an oversimplification on the order of "See Spot run!"

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.

Try a close look at sickle-cell anemia. One single trait. Bad news, right? Right, except that it provides some resistance to malaria. So, the efficacy of this particular trait (out of millions) depends on--is there malaria here? If there is malaria here, then you have a slight advantage in that one area, while still maintaining the disadvantage of the anemia. If there is no malaria, the slight advantage of malaria resistance does no good, and the anemia is still detrimental.

Multiply this by thousands of traits. The folks with the best overall adaptations for here and now (and here and now is always changing) survive and reproduce a little better than those who do not. Toss in a few million years and stir well.

But forget the mathematical models until you have a handle on the variables. If you can't figure out all the variables, and correctly model them, your mathematical models don't mean much in the real world.

[Lucky Dog]

Yes, this is an oversimplification on the order of "See Spot run!"

Granted it is a simplification. However, such simplifications are sometimes very useful for clarification.

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

The folks with the best overall adaptations for here and now (and here and now is always changing) survive and reproduce a little better than those who do not.

It is this phenomenon that is at the core of the issue. Exactly how much better (quantitatively) is required for the mutations to be accumulated to the point where a new species will emerge?