[PatrickHenry]

Additionally, I must also ask how many mutations are required for one species to “evolve” into another completely different species. While you generously (for my benefit) postulate a 1% beneficial rate, from a mathematical perspective, I must also inquire as to how many of these mutations must be sequential for a new species to appear.

That depends on the mutations, doesn't it? The key point is that after thousands of generations, numerous mutations have been favorably selected, and have spread through the population. Others have been de-selected (by early death or reproductive failure) and have been removed from the population. The gene pool (that's the ball to keep your eye on) is then different from what it once had been. It changes every generation, somewhat, but over a great many generations the changes are cumulative. The creatures in the breeding population never notice this, because from one generation to the next, the effect is minimal. It's mostly apparent only when an ancestral fossil is found and compared to the current version.

It can also become apparent if the population is divided, perhaps by a river or something, and each takes it's genetic material and goes a separate way. In time (again, we're talking about thousands of generations) the two populations -- if they were reunited -- probably won't be one breeding population any more.

[Lucky Dog]

That depends on the mutations, doesn't it?

Presumably, your postulate stands. However, for the sake of calculations, one must have some dividing line. Without such, there is no way to evaluate the probabilities.

The key point is that after thousands of generations, numerous mutations have been favorably selected, and have spread through the population. Others have been de-selected (by early death or reproductive failure) and have been removed from the population.

By observation, there are species currently in existence that are nominally evolutionary “precursors” of those that came at later times ostensibly as a result of the accumulation of enough mutations in the “gene pool” to have created these new species. By these observations, on can conclude that one of the “gene pools” did not accumulate mutations and another did. Therefore, to calculate the likelihood of enough favorable mutations having occurred in an alternate “gene pool” to qualify as a new species, there must be a definition of the number of mutations