A unifying model to estimate thermal tolerance limits in ectotherms across static, dynamic and fluctuating exposures to thermal stress

Temperature tolerance is critical for defining the fundamental niche of ectotherms and researchers classically use either static (exposure to a constant temperature) or dynamic (ramping temperature) assays to assess tolerance. The use of different methods complicates comparison between studies and here we present a mathematical model (and R-scripts) to reconcile thermal tolerance measures obtained from static and dynamic assays. Our model uses input data from several static or dynamic experiments and is based on the well-supported assumption that thermal injury accumulation rate increases exponentially with temperature (known as a thermal death time curve). The model also assumes thermal stress at different temperatures to be additive and using experiments with Drosophila melanogaster, we validate these central assumptions by demonstrating that heat injury attained at different heat stress intensities and durations is additive. In a separate experiment we demonstrate that our model can accurately describe injury accumulation during fluctuating temperature stress and further we validate the model by successfully converting literature data of ectotherm heat tolerance (both static and dynamic assays) to a single, comparable metric (the temperature tolerated for 1 h). The model presented here has many promising applications for the analysis of ectotherm thermal tolerance and we also discuss potential pitfalls that should be considered and avoided using this model.