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Differnet mutations can be fixing throughout the population simultaneously. There is no genetic constraint that one must fix throughout the entire population before the next one can begin doing so.

Even, given the number of genes and number of alleles per gene in a typical organism, the number of zeroes after the decimal required for probabilities to combine to produce a new species is a number staggeringly small (astronomically small is not an adequate description)

Factor in what I mentioned above and redo your calculation. And I recommend you show the values you use and the workings if you want anyone to accept your conclusion. Otherwise it looks like you have just plucked the conclusion of "staggeringly small" out of thin air to support what you already believed.

Of course, the above probabilities are for a single favorable mutation to occur and become species-wide. One must now address the probability that a favorably mutated species undergoes a second favorable mutation and that the second mutation becomes species-wide and so forth until enough favorable mutations have accumulated to result in a completely new species.

Differnet mutations can be fixing throughout the population simultaneously. There is no genetic constraint that one must fix throughout the entire population before the next one can begin doing so.

You are correct in that multiple mutations can occur simultaneously. However, you must assume that the environmental natural selection pressures are simultaneously favorable to every mutation so produced and remain so long enough for propagation. Additionally, assuming that such does occur, you must then include the probability that organisms, each possessing different favorable mutations, can combine to produce offspring having both favorable mutations and no detrimental mutations. Following such a combination, that offspring must find and combine with yet another mutated organism have a different one of your postulated, simultaneously favorable mutations, again, with no detrimental mutations and the environment, again, obligingly provides the natural selection pressure for the combination to have a survival advantage, etc. At each step, there is a probability multiplied by a another probability which, as fractions, produces an even smaller number for multiplication at the next step.

Even, given the number of genes and number of alleles per gene in a typical organism, the number of zeroes after the decimal required for probabilities to combine to produce a new species is a number staggeringly small (astronomically small is not an adequate description)

Factor in what I mentioned above and redo your calculation. And I recommend you show the values you use and the workings if you want anyone to accept your conclusion. Otherwise it looks like you have just plucked the conclusion of "staggeringly small" out of thin air to support what you already believed.

I beg you not to require my typing all of the probability calculations as it would require a huge amount of time. Rather, allow me just to pose one calculation, if you please.

Even given your earlier postulation of multiple, simultaneous mutations, I think you will agree that at least some mutations must occur sequentially for the appearance of a new species. Given Campbell’s mutation rate cited in my earlier post of "one mutation per locus per 10^5 to 10^6 gametes," one sequential mutation would 10^6 times 10^6 or 10^12. Add only one more sequential mutation and you have 10^18. I think you would agree that it would take many more than three sequential mutations for the emergence of a new species. From this, I think my assertion that the number quickly becomes staggering small is justified, especially given that each mutation has the probability of being detrimental or benign rather than beneficial or that even if the combination is beneficial that no additional detrimental mutation occurs and that the probability that the environmental selection environmental pressures must remain unchanged.