Incorporating variation in death times improves predictions of ectotherm responses to stressful temperatures

Predicting survival of ectotherms in stressful and variable thermal environments is an essential challenge in this era of heat waves and climate change. Recent thermal death time (TDT) models, based on an exponential relationship between average time to death (or failure) tf and temperature, enable accounting for average survival responses to both the magnitude and duration of stressful temperatures. However, extending these deterministic and probabilistic models to predict patterns of survival in fluctuating temperatures currently requires additional assumptions: e.g., that injury accumulation due to heat stress is additive across temperatures, and that the shape of the cumulative survival curve does not change with temperature. We evaluate these assumptions and their consequences by using a parametric survival model and available data on failure (knockdown) times of adult Drosophila. We find that the variance in log(tf) increases with increasing constant temperatures in most Drosophila species, resulting in changes in the shape of the failure density and survival curves across temperatures. We compare predictions of three deterministic and probabilistic models that differ in their TDT assumptions using D. melanogaster data in fluctuating (but stressful) temperatures. All three models consistently underestimate observed median failure times except at extremely high temperatures, suggesting non-additivity of heat injury accumulation. Our parametric model, incorporating temperature-dependent variance, provides more accurate predictions of cumulative survival curves in fluctuating temperatures. Our findings highlight the importance of understanding both mean and variation in failure times, and how these change across temperatures, for modeling survival in fluctuating thermal environments.