That theory was argued by Thomas Robert Malthus and the scenario has come to be known as a Malthusian crisis or catastrophe. If you looked at a graph charting food production and population, food production increases as a steady rate (a straight line) while population increases exponentially at different points. Where the two lines meet would be a Malthusian crisis where population exceeds food thereby resulting in a decreases in population; however, population will then rebound as food production continues to increase. It must be noted that the Malthusian theory (coined prior to the Industrial Revoltuon) does not take into account technological advances that could drastically increase food production, transportation, and preservation.
