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Climate-mediated changes in thermal stress can destabilize animal populations and promote extinction risk. However, risk assessments often focus on changes in mean temperatures and thus ignore the role of temporal variability or structure. Using Earth System Model projections, we show that significant regional differences in the statistical distribution of temperature will emerge over time and give rise to shifts in the mean, variability and persistence of thermal stress. Integrating these trends into mathematical models that simulate the dynamical and cumulative effects of thermal stress on the performance of 38 globally distributed ectotherm species revealed complex regional changes in population stability over the twenty-first century, with temperate species facing higher risk. Yet despite their idiosyncratic effects on stability, projected temperatures universally increased extinction risk. Overall, these results show that the effects of climate change may be more extensive than previously predicted on the basis of the statistical relationship between biological performance and average temperature.

Understanding the effects of climate-mediated environmental variation on the distribution of organisms is critically important in an era of global change. We used wavelet analysis to quantify the spatiotemporal (co)variation in daily water temperature for predicting the distribution of cryptic refugia across 16 intertidal sites that were characterized as ‘no’, ‘weak’ or ‘strong’ upwelling and spanned 2000 km of the European Atlantic Coast. Sites experiencing weak upwelling exhibited high synchrony in temperature but low levels of co-variability at monthly to weekly timescales, whereas the opposite was true for sites experiencing strong upwelling. This suggests upwelling generates temporal thermal refugia that can promote organismal performance by both supplying colder water that mitigates thermal stress during hot Summer months and ensuring high levels of fine-scale variation in temperature that reduce the duration of thermal extremes. Additionally, pairwise correlograms based on the Pearson-product moment correlation coefficient and wavelet coherence revealed scale dependent trends in temperature fluctuations across space, with a rapid decay in strong upwelling sites at monthly and weekly timescales. This suggests upwelling also generates spatial thermal refugia that can ‘rescue’ populations from unfavorable conditions at local and regional scales. Overall, this study highlights the importance of identifying cryptic spatiotemporal refugia that emerge from fine-scale environmental variation to map potential patterns of organismal performance in a rapidly changing world.