There is much debate about potential sustainable paths for both humans and ecosystems. The Earth's biocapacity is unable to meet current demands, let alone future demands. Past civilizations have managed to subvert the Malthusian trap through innovations in food supply and technological advances. How contemporary societies will organize a growing population (projected to reach approximately 11 billion by the end of the 21st century), dwindling resources and saturating crop yields is uncertain. We model human population over the next century, emphasizing feedbacks between natural and agricultural resource availability and human demography. We argue that an intensive agriculture approach to feeding the growing population is ill-conceived, without considering biodiversity and ecosystem services. The productivity of agricultural land and human population dynamics are dependent on the area of natural land and the rate at which natural land is degraded — generally, tipping at 5 billion ha of natural land (approximately 40% of the Earth's terrestrial area).