I am talking about nearly neutral mutations. Mutations that are barely deleterious or barely advantageous. They do become fixed in the population all the time.
You realize that the population size is also an incredibly important consideration when talking about nearly neutral/fixation theory, yes?
As population size grows - selection effects become more pronounced, to the point where selection 'notices' the nearly neutral deleterious mutations (and the nearly neutral beneficial ones too) and their frequency begins to alter accordingly.
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