For neutral genetic diversity, the effective population size is the harmonic mean of the population over time. That is, you take the inverse of the population size, average that over the population history, and then invert it. This harmonic mean is dominated by periods in which the population is very low – so, judging from the amount of neutral diversity, the effective human population size is about 20,0oo or so, rather than the census size of 7 billion. Small population sizes back in the Old Stone Age, and possibly ancient bottlenecks associated with population crashes and expansions of small groups, probably explain this.
The story is very different for beneficial mutations. Mutations that confer much advantage are rare – sometimes very rare, when only a specific molecular change will do the job. This means that in a small population, you may have to wait a long time for the right favorable mutation – as much as hundreds of thousand of years in ancient humans, when you consider than most favorable mutations are lost by chance.
Anyhow, you improve the chances, shorten the waiting time, with a larger population. And if the population stays large, avoids a crash, for very long – then many of the favorable alleles generated during the period of large population size will have had time to spread and become common, so they’re not likely to be lost in later crashes.
So, with beneficial mutations, the effective population size is very different. Instead of being dominated by bottlenecks, it is more influenced by eras of large population size – more and more so as the selective advantage of the mutation increases. In the limit, if we imagine mutations so advantageous that they spread very rapidly, the effective population size approaches the population mean.
For example, -13910*T , the European lactase persistence mutation, occurred in the context of a fair-sized population that was using milk from domesticated animals (probably cows, maybe horses or goats). Suppose that Europeans go through a bottleneck – let 100 adults of reproductive age make it to Alpha Centauri and start a colony.
Mutations like -13910*T won’t be lost. On the other hand, recent advantageous mutations that have not had much time to spread, like that apoliprotein mutation in Limone Sul Garda, probably would be.
So the effective population size for advantageous mutations is a function of the population size and the degree of selective advantage. I’ve never seen this in the texts, although I’ve seen Nick Barton mention it in an article about the evolution of pesticide resistance. We ran into this when we were thinking about how the post-agricultural population expansion must have greatly increased the rate of creation of advantageous mutations (as well as putting strong new selective pressures on the farmers).