The idea of population engineering is anathema. The result of the one baby policy in China has resulted everything from dramatic abortion rates, to episodes of infanticide (due in part to a cultural preference for male children), to creating an entire generation with an artificial imbalance of gender as well as many other highly problematic (to say the least) social issues. We have not yet encountered the social/political results of that last bit. I doubt it will end well.
Above it was mentioned that improved economics is the solution to population explosions. To my current knowledge, that is correct. There was a fairly comprehensive study of this phenomenon in the nation of Columbia, originating I believe in the late 1960′s. It’s been so long I don’t remember details but essentially, once the population realizes that their children are mostly surviving to adulthood, that the value of children as agricultural workers can be replaced more cheaply/efficiently by equipment and that on balance in a developed economy that children cost rather than produce economic value, birth rates drop quickly and precipitously.
Anecdotally, my great grandfather (Ebeneezer – I’m not kidding) marrying in rural Kansas in the late 1800′s fathered 14 children (aka, farm hands). His oldest (my grandfather), fathered 9. The following generation coming after the end of the Great Depression, WWII and the rise of the middle class, averaged between 2 and 3. The number is (give or take as I’ve lost touch with a good number of cousins) is now 1.9.