Historical examples of demographic change, in China, Italy, Nigeria, Utah, Easter Island, and elsewhere, together with simple mathematics and biological principles, show that stabilizing world population before it is limited by food supply will be more difficult than is generally appreciated. United Nations population projections are wrong because they assume, in spite of the absence of necessary feedbacks, that all nations will converge rapidly to replacement-level fertility and thereafter remain at that level. Education of women and provision of contraceptives have caused dramatic reductions in fertility, but many groups, including some that are well-educated, maintain high fertility. Small groups with persistent high fertility can grow to supplant low-fertility groups, resulting in continued growth of the total population. The global average fertility rate could rise even if each country's fertility rate is falling. In some low-fertility European countries where deaths exceed births, the population continues to grow because of immigration. Producing more than two offspring is normal for all animal species with stable populations because their populations are limited by resources or predation rather than birth control. It may therefore be appropriate to view the growth of human population as the result not of excess fertility but rather of excess food.