Which premise are you talking about?

Now you introduce new terminology even before you explained the old. What is your definition of “sequential mutations”. I can guess but we apparently need to be exact here. You use the term “coordinated” without explaining in spite of I clearly asked for it. “simultaneous” how do you define that? Few thing in biology are exactly simultaneous.Your premise presumes that sequential mutations will produce a new function involving coordinated mutations at a faster rate than coordinated simultaneous mutations.

I certainly don’t. I even don’t know what it would mean.You also presume that the observed 1 in 10^20 rate of 2 coordinated mutations is due to it being a simultaneous mutation.

This takes us back to the question I asked in post #4 in this thread.And you also presume that two sequential selectable mutations that produce a new function will occur at a rate that is much faster than the 1 in 10^20 rate for resistance to chloroquine.

If your assumptions are factually accurate then we should have expected to observe many sequential coordinated mutations producing a new function at a much faster rate within the time it took us to observe malaria developing resistance to chloroquine.

The other possibility is that sequential mutations may not produce new a new function involving coordinated mutations any faster than simultaneous mutations.

- -

I will now again try to make my argument clearer, showing which assumptions I make, without using any new terminology.

My presumptions are:

- Mutations occur randomly and the probability of one specific mutation to occur in some specific DNA point during the lifetime of one individual is a fixed value P.

-Then the time (number of generations) until there is a will be a mutation depends on the value P and the population size. The more individuals there are in a population, the faster the mutation will occur (fewer generations are needed).

-If a mutation is beneficial it spreads to the whole population after some time. If it isn’t beneficial the mutation generally doesn’t spread.

Do you agree?

From that the following it is simple logic. It can be simulated by a simple computer program.

Assume that two different mutations M1 and M2 are needed to get a specific function (and assume they have to occur in that order) . Assume that both have the mutation rate P.

M1 will occur after G1 number of generations (in average) where G1 is depending on P and the population size, perhaps millions of individuals. If the M1 mutation isn’t beneficial it will not spread through the population and will be limited to a few individuals for the generations to come. That means that the population that is useful to get a mutation M2 is very small. From that follows that the number of generations until M2 occurs will be a great number (very approximatively G1 x G1)

On the other hand, if M1 is beneficial, the population of individuals the have the mutation M1 will spread and finally reach almost the total population. Then the number of generations until M2 occurs will be about the same magnitude as G1. If the time for spreading is Gs, the total time will very approximatively be G1 + Gs + G1. If G1 is a big number 2xG1+Gs is much smaller than G1xG1.

If four mutations is needed for a function and all the mutations are beneficial the number of generations will be G1+ Gs+ G1 + Gs + G1+ Gs+G1 = 4x G1 +3 x Gs. If they aren’t beneficial the number of generation will be of the magnitude of G1 x G1 x G1 x G1. If G1 for instance is 10^10 this number will be 10^40, so four specific non-beneficial nutations will never occur in one individual.

Here I don’t use any of your terminology: coordinated, selectable, sequential or simultaneous mutations. When you comment I ask you not to use those terms, at least without exact definitions.