Vasseur, D. A.; Bieg, C.; Kummel, M.; Robey, A. J.

Thermal Performance Curves (TPCs) have become a popular tool for assessing the risks imposed by climate warming and variability on ectotherms. These assessments typically measure the match between an organism or population's TPC and the distribution of its current or future thermal environment as a proxy for extinction risk. However, extinction can occur even when the average thermal environment appears closely matched to a population's TPC because population dynamics can be very sensitive to thermal stress. Here, we develop a new metric for assessing extinction risk using a stochastic model of logistic growth as a foundation. We show that boundaries delimiting persistence and extinction regions of parameter space can be derived for the simple case where the intrinsic (Malthusian) growth rate r varies stochastically and that these boundaries continue to make reliable predictions when temperature T varies stochastically and the Malthusian growth rate is given by a thermal performance curve r(T). We accomplish this by combining theory with stochastic simulations of population dynamics and a laboratory experiment where populations of the single-celled protist Paramecium caudatum were cultured across different temporal means and variances of temperature. The measure of risk that we develop and validate is straightforward and easily applicable to any population for which the thermal performance of Malthusian fitness is known, allowing more rigorous identification of the risks imposed by warmer and more variable temperatures across the globe.