Temporal Autocorrelation Increases Temperature‐Driven Extinction Risk by Clustering Stressful Conditions

Climate change affects the thermal environment in complex ways, including changing its temporal autocorrelation structure and intensifying heatwave regimes. While theory shows that higher temporal autocorrelation may exacerbate extinction risks, little work has been done to incorporate autocorrelation into thermal performance-based forecasting. Here, we pair stochastic simulation models of population dynamics with systematically generated temperature time series to determine when increasing the temporal autocorrelation of variable thermal environments generates greater extinction risks. We show that by clustering stressful conditions, increasing autocorrelation reduces the extent of warming and variability which populations with unimodal thermal tolerance can survive. We validate our predictions with a factorial experiment in protist microcosms, where we find that higher autocorrelation significantly elevates extinction risk across mean temperature treatments when environments include stressful temperatures. Taken together, these results provide the foundation for predicting which species and environments face the greatest thermal risks under increasing autocorrelation.