Why do we live longer than we can procreate?

It's always been a puzzle why it is that people live longer than they can possibly produce offspring. Women usually have menopause at around age 50, so we'd expect that people would pretty much expect people to die around 50, since after that age they can't reproduce, and thus there would be no selective pressure for longer life.

One recent study suggests that longevity past 50 can be explained by male procreation with younger women (ht Robin Hanson). As explained in the abstract:

We analyze a general two-sex model to show that selection favors survival for as long as men reproduce. Male fertility can only result from matings with fertile females, and we present a range of data showing that males much older than 50 yrs have substantial realized fertility through matings with younger females, a pattern that was likely typical among early humans.

In other words, the longer a man lives the more children he'll end up having: younger men with a woman around their age, older men with younger women, and really, really old men with much, much younger women. So, since men who live longer would have more children, their genes would tend to dominate and would be selected for. Furthermore, these genes for longevity wouldn't just apply to men since they would be passed on to both the women and the men.

Personally, I've always though the explanation for longevity was due to some sort of group selection. Humans really aren't just competing with other individuals, but groups of humans are also competing with other groups. The groups sometimes completely wipe out the other so that the survivor group would be the only ones to pass on their genes. Think of the two competing groups of proto-humans in 2001: A Space Odyssey. The group that discovered tools, chased the other group from the watering hole, ensuring the survival of the tool-using group, and probably leading to the death of the non-tool-using group. Thus, the genes of this tool-using group would be passed on.

I've always thought this was a good explanation of how morality developed. Groups of humans that followed certain morals would be more united, and thus would be able to hunt/gather/farm better and succeed more in wars against non-moral groups which would be more disunited (especially think about how we usually have a sort of "us vs them" morality, where it is a sin to do things to one of our own that are perfectly acceptable to do to our enemies).

Similarly, this is how I'd explain longevity past the age of procreation. Old people are an asset to a community. They bear valuable knowledge and experience and are the best teachers. Especially in times before writing, old people are your best receptacles of knowledge. Most people would die before reaching their 30s due to disease, warfare, starvation or the dangers of hunting and childbirth, but a very small few would carry on, and probably carry on as long as our oldest members. These few old persons, though not as productive, would be a great asset because of their knowledge. Thus, groups with some old people would tend to outcompete other groups, and so genes for longevity would be selected for.

Admittedly, the story of older men procreating with younger women is more interesting. Then again, these two explanations aren't really mutually exclusive. Maybe it's both.