As the New York Times reported today, a higher than ever percentage of children are surviving until their fifth birthday.

This public health triumph has arisen, Unicef officials said, partly from campaigns against measles, malaria and bottle-feeding, and partly from improvements in the economies of most of the world outside Africa.

So, with more babies surviving through early childhood, will there be a population boom? Maybe not.

If you live in a culture where children are the only feasible retirement plan–i.e. most of the world–it’s really important one child survives through your retirement, right? And if there is about a one in three chance that any given child won’t survive to see his or her fifth birthday (where Sub-Saharan Africa was a few decades ago), you better have several children.

Here comes some math to back up this notion. If your only willing to risk a one in a hundred chance of ending up destitute in old age, and there is a thirty percent chance than any given child will perish, the math tells us you’ll need to have four kids. Drop the mortality to fifteen percent–where Sub-Saharan Africa is today–and three kids will cut it. Five percent chance of perishing before five, like present day North Africa? Two kids will cut it. Magic. Smaller families through better survival.

Logic like this helps us understand why people in economically marginal areas of the world continue to have large families–further stretching resources, resulting in higher childhood mortalities, causing larger yet families–and how this pattern can be broken by public health.