Challenge generality of prediction based on Jensen's inequality: Moderate and large temperature fluctuations can lead to opposite performance deviation at high mean temperature

Living organisms should be able to endure increased mean temperature and temperature variations under context of global warming. Jensen???s inequality predicts that the performance of an organism under fluctuating temperature conditions is inferior to that under the equivalent constant temperature condition when the mean temperature approaches or exceeds the thermal optimum. However, we found this prediction is not always valid by checking the independent data from different species. By simulating the present and future thermal scenarios, we studied the fitness-related responses of a global pest, the English grain aphid Sitobion avenae, under different constant and equivalent fluctuating temperatures with different variances and made predictions based on Jensen???s inequality. We found that the effects of temperature variation are dependent on the temperature fluctuation range when the mean temperature approached or exceeded the thermal optimum; moderate fluctuations (vs. constant temperature) had positive or no effects on the developmental rate, fecundity, intrinsic rate of increase, and net reproductive rate, whereas large fluctuations considerably reduced these fitness-related responses. Our findings suggested that Jensen???s inequality is not always powerful in thermal biology, especially when the natural temperatures are high. Jensen???s inequality could not predict the performance improvements at moderate fluctuations and the large reductions in performance at large fluctuations. Therefore, more attention is needed in the directional deviations at a high mean with small-to-moderate fluctuations and the quantitative deviation at a high mean with large fluctuations, while using Jensen???s inequality to predict the responses to climate warming.