Historically, there has been a streak of doomsday in human thinking, where it was theorized that the human population would explode far past the food supplies and other commodities needed to support it. Massive famine, starvation, and general despair would follow. Due to continued human innovations, this has not occurred. The overpopulation fears of the 18th century were dealt with by the Agricultural/Industrial Revolution. And modern concerns of the "population bomb" were dealt with through GMO foods, and such factors as the average number of children a family has dropping.
The challenge is to have a global overpopulation crisis.