In a recent article in Wired entitled “The World Might Actually Run Out of People” by Megan Molteni, the hypothesis was indeed provocative but it doesn’t factor in, or even mention, the likely effects of climate change, which will almost assuredly depress world population growth, turning it negative because of rising temperatures, lower crop yields and lower agricultural worker productivity. Increased mortality will be due to heat stroke; warmer and increasingly polluted oceans and overfishing will decimate fish populations and will lead to widespread starvation for billions living in maritime-dependent human societies; and the social and political stresses engendered by millions of climate refugees forced to relocate by rising sea levels. In the light of these life-threatening impacts of climate change, maternal fertility decisions will surely be affected, with the historical transition from high- to low-fertility in response to high-to low-infant mortality much slowed if not reversed.
The human population of the Earth is at risk, but by climate change, not by natural causes. The world is becoming a much less hospitable place for humans, and indeed for almost all forms of life. If humans were to die off as did the dinosaurs, the Earth would continue without us and eventually recover over a millennia if not millions of years.