Michael — I’m not an expert on these matters, either, and the article doesn’t spell out the theory as precisely as I might have liked. But this is my general interpretation:
In r-selection, you have a bunch of kids, knowing that many will fail to reproduce. In K-selection, you have fewer kids but invest in them to make sure that they will be able to reproduce. The problem is that among modern humans, virtually no one dies before they reach reproductive age, and virtually anyone who wants to have children can have them. So K-selection is kind of pointless from a purely evolutionary standpoint: You don’t need to invest in kids to guarantee they can reproduce; you just invest in them to make their lives more pleasant.
With modern birth control, a major driver of human reproduction will be the simple question of who wants to have kids. My expectation is that the K-selection trend The Economist speaks of will slowly decline over time as the desire to have children is heavily selected for.