The population explosion is not over. These are two separate problems, and Ben Wattenberg does a disservice by lumping them together. African fertility is still above five children and has only begun to decline slightly in a few countries. Desired fertility in the developing world is still above replacement nearly everywhere. Desired fertility is actually a very good predictor of actual fertility, so it is reasonable to expect that fertility will stay above replacement in many countries, including some very large ones such as India, Pakistan, Bangladesh, Nigeria, Ethiopia, and Indonesia for some time to come.
Population momentum is the critical issue.
Even in countries such as Brazil and China, where replacement level fertility has been achieved, the very young age structure of the population means that even if every couple only reproduces itself, fertility will remain high for some time to come. The high fertility of the recent past thus essentially guarantees that substantial future population growth is inevitable. John Bongaarts of the Population Council estimates that at least 2.5 perhaps 3 billion people will be added to the developing world's population over the next 50 years, through population momentum alone. Even if every couple wanted just two children and succeeded in achieving that goal tomorrow which will not happen we would still wind up with these additional billions. Fertility has fallen to well below replacement level in many European countries and Japan.