I agree...Nils wrote: ↑Mon Jan 10, 2022 5:45 am What I wrote about was an imagined example where there is one case with possible non-beneficial mutations and one case with possible beneficial mutations and I compared the rate between these two specific cases. The motive for this example was to show that there are two different mechanisms, one linear and one exponential (to which you agree). That doesn’t mean that every case with beneficial mutations is more rapid than some case with non-beneficial mutations.
But we do have a fixed point of agreement that six non-beneficial mutations working together to provide a new function exceeds the capability of all life that has ever existed on this planet.
We also have an empirically observed example of two non-beneficial mutations working together to provide a new function at an inverse exponential rate.
And we have the premise that beneficial mutations not only can but actually do (by orders of magnitude) exceed the inherant inverse exponential rate of non-beneficial mutations.
(btw I agree with your statement that beneficial mutations will not necessariy generate new functions at a more rapid rate than non-beneficial mutations for the reasons you describe.)
That all begs the question...
Where are the empiricaly observed examples of beneficial mutations that DO generate new functions at a rate faster than non-beneficial mutations?
You can't create the tree of life with a series of non-beneficial mutations.
You can't create the tree of life with a series of beneficial mutations that, for whatever reason, is slower than non-beneficial mutations.
In order order to create the tree of life you require a series of beneficial mutations that exceed by orders of magnitude the frequency of non-beneficial mutations.
Stipulating to your statement:
"That doesn’t mean that every case with beneficial mutations is more rapid than some case with non-beneficial mutations."
Do you agree with the following statement...
In order to create the tree of life, the number of empirically observable examples of combinations of x beneficial mutations should exceed (by orders of magnitude) the number of empirically observable examples of combinations of x non-beneficial mutations.