Is it correct to say "the more beneficial a mutation, the more often it arises independently"?

[AnonymousUserUse]

Is it correct to say "the more beneficial a mutation, the more often it arises independently"? @corneliusroemer

In my opinion, the benefit of a mutation and the independent appearance of a mutation are two different, not directly related features of a mutation. It is true that the independent appearance of a beneficial mutation is more likely to be found in the current surveillance system, but the independent appearance of a mutation itself is not related to the benefit of a mutation.

Even if one regards the sense of the independent appearance of a mutation found in surveillance, one cannot say with certainty that a beneficial mutation always arises independently and a mutation that arises frequently independently always has advantages. For the former, there are several beneficial mutations that have only been caught once, such as S:R346K in BA.1 and ORF1b:T1050N in BA.5.2. For the latter, this list includes a number of highly homoplasic mutations, most of which do not show any advantages.

It might be worth having a quantitative analysis for the correlation between the benefit of a mutation and the independent appearance (caught in surveillance) of a mutation, including or excluding the listed highly homoplasic mutations. I would not be surprised if there is a correlation between them, but I guess the correlation may only be moderate.