News reports suggest that the world is overflowing with people. Politicians in the U.S. and Europe talk about migrants—whether from Latin America or the Middle East—as a threat: They’ll steal jobs, depress wages and upend local ways of life. The backlash plays on deep-seated fears about a “population bomb.” The latest United Nations forecasts suggest that the global population will rise to 9.7 billion over the next 35 years, an increase of 2.4 billion. Where will they live, and what will they eat?

This narrative is sorely...