Performance in a variable world: using Jensen's inequality to scale up from individuals to populations.

Body temperature affects plants' and animals' performance, but these effects are complicated by thermal variation through time within an individual and variation through space among individuals in a population. This review and synthesis describes how the effects of thermal variation-in both time and space-can be estimated by applying a simple, nonlinear averaging scheme. The method is first applied to the temporal variation experienced by an individual, providing an estimate of the individual's average performance. The method is then applied to the scale-dependent thermal variation among individuals, which is modelled as a 1/-noise phenomenon. For an individual, thermal variation reduces average performance, lowers the temperature of maximum performance ( ) and contracts the range of viable temperatures. Thermal variation among individuals similarly reduces performance and lowers , but increases the viable range of average temperatures. These results must be viewed with caution, however, because they do not take into account the time-dependent interaction between body temperature and physiological plasticity. Quantifying these interactions is perhaps the largest challenge for ecological and conservation physiologists as they attempt to predict the effects of climate change.