This question is motivated by two other questions that hinged on this one but did not explicitly ask the question.
Is intelligence declining due to the lack of selection pressure?
Is human evolution slowing down?
These two questions actually hit two sides of the same coin. The first asks whether natural selection is sufficiently strong to prevent deterioration of adaptive traits due to mutation pressure. The second asks whether novel beneficial traits are spreading in the human population. Both ultimately depend on the strength of natural section and the effective population size. These determine whether a genetic variant subject to natural selection persists or disappears.
Natural selection requires the existence of heritable variation in reproductive rate (i.e. fecundity). People frequently claim that this variation has been greatly reduced in modern human society. Here, I will think out-loud about the factors that may influence the level of heritable variation in fecundity, in the hopes of guiding someone to an answer.
Perhaps the most common claim along these lines is that the variation in reproductive rates has substantially decreased, and therefore natural selection cannot act on genetic variation in the population. This claim is first based on the fact that in wealthy societies, a larger fraction of people are surviving to adulthood, thereby reducing selection on traits linked to childhood mortality. Complementing this is the fact that large families are less common than in the past.
I don't see any way to interpret this supposed reduction in reproductive variability without information of how heritable traits contribute to this variability. Even if there were greater variation in the past, it could have been due to "luck" (i.e. stochasticity in the environment), not any genetic variation.
To the extent that there is variation in reproduction rates among humans, much of it occurs at at the level of entire societies and be driven by cultural and economic factors. Therefore it is not be due to the genetic variations of humans within those societies. It's unclear when this pattern first developed. It also is unclear if this negates natural selection, since between-group variation could theoretically allow for kin selection. While culture and capital may be considered "heritable variation", let's limit ourselves to genetic variation.
Even if these developments are reducing the scope for natural selection in today's society, it is unclear whether these conditions will persist over an evolutionarily relevant timescale (hundreds of generations). For instance, Western Europe today has very low levels of pre-reproductive mortality, but had very high rates of mortality 2-3 generations ago. Likewise, the Chinese state has placed strict limits on the upper reproductive rate within the population it rules, yet this has been followed by a substantial imbalance in male:female ratio, which will likely produce substantial variation in the reproductive rate of males in that population (similar sex imbalances exist in other countries).
Another factor to consider is that today's human population is much larger than in the past, and is less structured. We can expect continued population growth for the near future, and continued mixing of subpopulations, thereby reducing linkage disequilibrium. Both of these factors increase the amount of genetic variation on which natural selection can act.
I'll shut up now and restate my question. Is there any solid evidence that natural selection is having a reduced impact on modern human populations? One line of evidence would be to actually measure the impact of natural selection on various traits, but I really doubt that this is possible. It will be especially difficult to detect a change that has started only a few generations ago. An alternative form of evidence would be a thorough consideration of the factors that are believed to affect the efficacy of natural selection, how they have changed, and what their combined impact is on natural selection.
