Data from: The analysis and interpretation of critical temperatures

Critical temperatures are widely used to quantify the upper and lower thermal limits of organisms. But measured critical temperatures often vary with methodological details, leading to spirited discussions about the potential consequences of stress and acclimation during the experiments. We review a model based on the simple assumption that failure rate increases with increasing temperature, independent of previous temperature exposure, water loss or metabolism during the experiment. The model predicts that mean critical thermal maximal temperatures (CTmax) increases nonlinearly with starting temperature and ramping rate, a pattern frequently observed in empirical studies. We then develop a statistical model that estimates a failure rate function (the relationship between failure rate and current temperature) using maximum likelihood; the best model accounts for 58% of the variation in CTmax in an exemplary dataset for tsetse flies. We then extend the model to incorporate potential effects of stress and acclimation on the failure rate function; the results show how stress accumulation at low ramping rate may increase the failure rate and reduce observed values of CTmax. We also applied the model to an acclimation experiment with hornworm larvae that used a single starting temperature and ramping rate; the analyses show that increasing acclimation temperature significantly reduced the slope of the failure rate function, increasing the temperature at which failure occurred. The model directly applies to critical thermal minima, and can utilize data from both ramping and constant temperature assays. Our model provides a new approach to analyzing and interpreting critical temperatures.

临界温度（critical temperatures）被广泛用于量化生物体的上下热极限。但实测临界温度常随实验方法细节而异，由此引发了关于实验过程中胁迫与驯化潜在影响的激烈讨论。我们综述了一项基于简单假设的模型：实验过程中，失败率随温度升高而上升，且不受此前温度暴露、水分流失或代谢的影响。该模型预测，平均临界最高热温度（critical thermal maximal temperatures, CTmax）会随起始温度与升温速率（ramping rate）呈非线性增长，这一规律在实证研究中屡见不鲜。随后我们开发了一种统计模型，可通过极大似然（maximum likelihood）估计失败率函数（失败率与当前温度的关系）；最优模型在一个采采蝇（tsetse flies）的典型数据集中共解释了58%的CTmax变异。我们进一步将模型拓展，以纳入胁迫与驯化对失败率函数的潜在影响；结果显示，低升温速率下的胁迫积累如何提升失败率并降低观测到的CTmax数值。我们还将该模型应用于一项以单一起始温度与升温速率开展的烟草天蛾幼虫（hornworm larvae）驯化实验；分析结果表明，提升驯化温度可显著降低失败率函数的斜率，提高失败发生时的温度。该模型可直接适用于临界最低热温度（critical thermal minima），并可利用升温测定与恒温测定法（constant temperature assays）所得的数据。我们的模型为临界温度的分析与解读提供了全新的研究路径。