Thermal games: frequency-dependent models of thermal adaptation

1. Most models of thermal adaptation ignore biotic interactions, and those that do consider biotic interactions assume that competitors or predators cannot respond to adaptation by the focal species. Nevertheless, real biotic interactions involve responsive entities, which can be more accurately modelled using evolutionary game theory. 2. We present a two-part analysis of a thermal game between prey and predators. First, we model a game in which prey choose patches on the basis of operative temperature and predation risk, whereas predators choose patches on the basis of prey density. Second, we consider how this thermal game influences the evolution of the prey’s thermal physiology. 3. The solution of the thermal game is an evolutionarily stable Nash equilibrium in which prey divide their time equally among a range of thermal patches while predators bias their hunting efforts toward warmer patches, even though they derive no thermoregulatory benefit from doing so. Furthermore, the optimal range of temperatures selected by prey and predators increases as the lethality of predators increases. 4. This thermal game potentially influences the evolution of the prey’s thermal physiology. When predators are less lethal, prey should thermoregulate over a narrower range of temperatures, resulting in selection for thermal specialization of physiological performance. But when predators are very lethal, prey should thermoregulate over a broad range of temperatures; in this case, prey pay no fitness cost for being thermal generalists. 5. Evolutionary game theory provides a powerful tool for generating hypotheses about the effects of biotic interactions on evolution in heterogeneous environments.