Recent field studies suggest that it is common in nature for animals to outlive their reproductive viability. Post-reproductive life span has been observed in a broad range of vertebrate and invertebrate species. But post-reproductive life span poses a paradox for traditional theories of life history evolution. The only commonly-cited explanation is the ‘grandmother hypothesis’, which is limited to higher, social mammals. We propose that post-reproductive life span evolves to stabilize population dynamics, avoiding local extinctions. Predator–prey and other ecosystem interactions tend to produce volatility that can create population crashes and local extinctions. Total fertility rates that exceed the ecosystem's recovery rate contribute to population overshoot, followed by collapse. These local extinctions may constitute a potent group selection mechanism, driving evolution toward controlled rates of population growth, even when there is a significant individual cost. In this paper, we consider the question: what life history characteristics support demographic homeostasis at the least cost to individual fitness? In individual-based evolutionary simulations, we find that reduction in fertility is sufficient to avoid population instabilities leading to extinction, but that life histories that include senescence can accomplish the same thing at a lower cost to individual fitness. Furthermore, life histories that include the potential for a post-reproductive period are yet more efficient at stabilizing population dynamics, while minimizing the impact on individual fitness.