  Agriculture operates within a global ecosystem for which planetary boundaries
have recently been defined. Efficiency in nitrogen use is essential for
maximizing the benefits of agriculture for humanity and minimizing adverse
socio-ecological impacts. The set of variables that support global system
efficiency also determine the food production boundaries of agriculture, which
govern the maximum supportable human population. Food production boundaries,
nitrogen loss and nitrogen self-sufficiency are combined here into the nitrogen
operating space of world food production. We position world regions and the
world trajectory (1961-2013) within the nitrogen operating space and show that
the maximum supportable human population ranges from 6 to almost 17 billion
people according to the share of grain used as feed and the nitrogen
fertilization regime. All UN population projections for the 21st century can
only be conditionally achieved. We discuss the growth rate requirements in
production and efficiency to meet food production boundaries and the nitrogen
planetary boundary by 2050.
