Demographic trends show a definite tendency toward slowing of population growth, leading to reduction in global population. As people get more prosperous, they have fewer babies. While advances in medicine and food production led to an decrease in infant mortality and an increase in lifespan, in the longer term, lower infant mortality means that people don’t need to have 10 kids to make sure a few of them survive. In developing countries, children are your social safety net. They’re your retirement plan. When you don’t need to pump out an army of children, you don’t do so anymore. There’s no need to panic over population increase. What we do need to worry about however, is an aging global population, without so many young people to support old farts.
That raises the question of whether you can increase the wealth and prosperity of everybody quickly enough so that the poorest don’t need to have large families to survive. That seems like a race that cannot be won, especially because radicals are bent on making energy scarce and expensive.