Incorporating thermodynamics in predator-prey games predicts the diel foraging patterns of poikilothermic predators

Models of foraging behaviour typically assume that prey do not adapt to temporal variation in predation risk, such as by avoiding foraging at certain times of the day. When this behavioural plasticity is considered-such as in predator-prey games-the role of abiotic factors is usually ignored. An abiotic factor that exerts strong influence on the physiology and behaviour of many animals is ambient temperature, although it is often ignored from game models as it is implicitly assumed that both predators and prey are homothermic. However, poikilotherms' performance may be reduced in cold conditions due to reduced muscle function, limiting the prey-capture ability of predators and the predator-avoidance and foraging abilities of prey. Here, we use a game-theoretic predator-prey model in which diel temperature changes influence foraging gains and costs to predict the evolutionarily stable diel activity of predators. Our model predicts the range of patterns observed in nature, including nocturnal, diurnal, crepuscular and a previously unexplained post-sunset crepuscular pattern observed in some sharks. In general, smaller predators are predicted to be more diurnal than larger ones. The safety of prey when not foraging is critical, explaining why predators in coral reef systems (with safe refuges) may often have different foraging patterns to pelagic predators. We make a range of testable predictions that will enable the further evaluation of this theoretical framework for understanding diel foraging patterns in poikilotherms.