Explaining the stability of human populations provides knowledge for understanding the resilience of human societies to environmental change. Here, we use archaeological radiocarbon records to evaluate a hypothesis drawn from resilience thinking that may explain the stability of human populations: Faced with long-term increases in population density, greater variability in the production of food leads to less stable populations, while lower variability leads to more stable popula- tions. However, increased population stability may come with the cost of larger collapses in response to rare, large-scale environmental perturbations. Our results partially support this hypothesis. Agricultural societies that relied on extensive landscape engineering to intensify production and tightly control variability in the production of food experienced the most stability. Contrary to the hypothesis, these societies also experienced the least severe population declines. We propose that the interrelationship between landscape engineering and increased political-economic complexity reduces the magnitude of population collapses in a region.