Even a small differential in reproductive rates would lead to a rapid increase in the prevalence of the trait. Just look at the example of blue eyes -- 15000 years ago nobody had them and now nearly 7% if the world's population do.
Do people with blue eyes reproduce more? I've not heard that before. I thought the ratio of blue to not blue eyes was due to the whole dominant/recessive gene thing (do I mean gene, or maybe allele? a long time since I learned this stuff at school).
Of course the trait was advantageous either in terms of natural selection, or more likely sexual selection. All the blue eyed people on earth can be traced back to a single ancestor living in the black sea region about 10,000 years ago. It is a recessive trait, but allele frequencies don't magically increase just because a trait is recessive. Without selection pressure, the ratio of blue eyed people would not have kept increasing after the emergence of the mutation.
If not requiring a lot of sleep has an advantage in our society (which presumably it does) then all else being equal, a non-sleeper will produce more offspring. This is just evolution 101.
That's only true for women. And it doesn't mean that there aren't still evolutionary incentives for women. If they are successful because they don't need to sleep, they can probably find a better mate (which will lead to an evolutionary advantage of the no-sleep gene long term).
