We use evolutionary game theory to generate novel and testable predictions about optimal thermoregulation and evolution of thermal performance curves. Existing theory of optimal thermoregulation describes the strategies that maximize net energetic gain in heterogeneous environments (Huey and Slatkin 1976); this theory assumes that the optimal strategies do not depend on the responsive behaviors of other organisms. Here, we apply game theory to derive the evolutionarily stable behavioral strategies for both thermoregulating prey and their predators in thermally heterogeneous environments; we consider a range of environment types comprising a) two patch types, b) n>2 patch types, and c) a continuous distribution of patch types. Next, we model the effect of the thermal behavioral game on the evolution of the prey’s thermal performance curve.  We obtain our results using a combination of analytical and numerical techniques.
Results/Conclusions

The thermal game predicts that prey should thermoregulate over a broader range of operative temperatures as predator lethality increases. At low predator lethality, prey should thermoregulate in habitats characterized by operative temperatures near the peak of their thermal performance curve. But at higher predator lethality, prey should attempt to reduce their predation cost by spreading the time over a greater proportion of the environment, thereby reducing their energetic benefits. The behavioral thermal game can also drive the frequency-dependent evolution of the prey’s thermal performance curve, as  high predator lethality sustained over evolutionary time can permit the successful invasion of mutants with broader (less specialized) thermal performance curves.