Hold one hand still, move the other

I saw this post about human population diversity the other day...and though it was interesting, there was something that stuck in my craw:

Actually, this will be sharper for genes under selection, since selection should be weaker in bottleneck populations.

I don't think this is true. Selection isn't weaker, random genetic drift is stronger. Consider the probability of fixation of a new mutation. If the mutation is neutral so selection is non-existent its frequency is being buffeted only by random genetic drift. As you probably know, the probability of fixation is 1/(2N_e), where N_e is the effective breeding population. So if a neutral mutant arises in a population of 10 in one of the individuals, it has a 1 out of 10 shot at fixation (with an expectation of fixation in 40 generations, that is 4N_e). If the effective population is 1000 the probability of fixation is 1 out of 1000, or 0.001 instead of 0.1. This is pretty straightforward, as N_e zooms up individual neutral mutants are less likely to fix (though remember there are more fizzing in the background, so the rate of substitution is constant and dependent only on mutation rate).

But what about selection? The probability of fixation of a new positively selected mutant is 2s, where s is the selection coefficient of the new allele vis-a-vis the population mean fitness. Consider that an allele, a^-, confers a fitness advantage of 0.1 when compared to the "wild type," a⁺. The probability of a single mutant fixing in a population 0.2 (in a diploid). Notice any population parameter? Exactly!

Hold selection still, but vary the power of drift! So the key with a population bottleneck is that random genetic drift overwhelms selection! In other words where 1/(2N_e) is far greater than 2s, ignore selection, where 2s is far greater than 1/(2N_e) ignore random genetic drift. In other cases, do the sums and the weight the parameters.

Does this minor technical point matter? I think it does. 2s is a powerful formula to keep in mind because you multiply it out for every introduction of a given allele. Neglecting the power of selection results in random genetic drift becoming a deux ex machina.