Abstract: 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 commonly cited explanation is the “grandmother hypothesis”, which applies only to higher, social mammals. We propose that post-reproductive life span evolves to stabilize predator-prey population dynamics, avoiding local extinctions. In the absence of senescence, juveniles would be the most susceptible age class. If juveniles are the first to disappear when predation pressure is high, this amplifies the population’s risk of extinction. A class of older, senescent individuals can help shield the juveniles from predation, stabilizing demographics and avoiding extinction. If, in addition, the life history is arranged so that the older individuals are no longer fertile, the stabilizing effect is further enhanced.