Why “Suboptimal” Is Optimal: Jensen’s Inequality and Ectotherm Thermal Preferences

Body temperature (T(b)) profoundly affects the fitness of ectotherms. Many ectotherms use behavior to control T(b) within narrow levels. These temperatures are assumed to be optimal and therefore to match body temperatures (Trmax) that maximize fitness (r). We develop an optimality model and find that optimal body temperature (T(o)) should not be centered at Trmax but shifted to a lower temperature. This finding seems paradoxical but results from two considerations relating to Jensen's inequality, which deals with how variance and skew influence integrals of nonlinear functions. First, ectotherms are not perfect thermoregulators and so experience a range of T(b). Second, temperature-fitness curves are…