Using a global ecological and evolutionary model of competing branching and mounding coral morphotypes, this study shows symbiont shuffling was more effective than symbiont evolution in delaying coral-cover declines, but stronger warming rates outpace the ability of these adaptive processes and limit coral persistence. Global patterns in coral reef vulnerability to climate are sensitive to the interaction of warming rate and adaptive capacity and cannot be predicted by either factor alone. Overall, the results show how models of spatially resolved adaptive mechanisms can inform conservation decisions.