Dispersal as a stabilizing force against adaptation-induced oscillations under climate warming

Global warming threatens biodiversity by increasing habitat temperatures that impact species performance and survival. Species can cope with warming through two key mechanisms: thermal adaptation, by shifting their thermal optima, and dispersal, by moving to habitats with more favorable conditions. Here, we examine how these mechanisms affect species interactions and persistence in predator–prey systems using a temperature-dependent version of the Rosenzweig–MacArthur model, in which demographic rates depend on temperature, thermal traits evolve through adaptation, and populations disperse among spatially structured patches. We find that both mechanisms increase persistence by lowering extinction thresholds under warming, but adaptation does so in a destabilizing manner, shifting dynamics from a stable equilibrium to a limit cycle and increasing extinction risk. In contrast, dispersal buffers adaptation-induced fluctuations, stabilizing the system and favoring equilibrium persistence. Prey adaptation also indirectly benefits predators by enhancing prey persistence, even when predators do not adapt. Together, these results show that adaptation and dispersal interact in non-trivial ways, jointly shaping species persistence and stability under climate warming.