Demographic feedbacks during evolutionary rescue can slow or speed adaptive evolution.

Populations declining toward extinction can persist via genetic adaptation in a process called evolutionary rescue. Predicting evolutionary rescue has applications ranging from conservation biology to medicine, but requires understanding and integrating the multiple effects of a stressful environmental change on population processes. Here we derive a simple expression for how generation time, a key determinant of the rate of evolution, varies with population size during evolutionary rescue. Change in generation time is quantitatively predicted by comparing how intraspecific competition and the source of maladaptation each affect the rates of births and deaths in the population. Depending on the difference between two parameters quantifying these effects, the model predicts that populations may experience substantial changes in their rate of adaptation in both positive and negative directions, or adapt consistently despite severe stress. These predictions were then tested by comparison to the results of individual-based simulations of evolutionary rescue, which validated that the tolerable rate of environmental change varied considerably as described by analytical results. We discuss how these results inform efforts to understand wildlife disease and adaptation to climate change, evolution in managed populations and treatment resistance in pathogens.