On testing the tolerance-plasticity trade-off hypothesis as the change of thermal tolerance across two environments

The world is warming rapidly, threatening the extinction of much of the world's biota. Thermal tolerance plasticity has been touted as an important buffer against global warming. The temperature tolerance-plasticity trade-off hypothesis (TOH) posits that ectotherms who have adapted to high temperatures have done so at the expense of having limited plasticity to further improve their heat tolerance. Empirical evidence is mixed and inconsistencies may arise due to statistical artefacts caused by spurious correlations. This lack of consensus is problematic because an accurate evaluation of the TOH is crucial for estimating the buffering capacity of thermal plasticity in ectotherms that already live close to their upper physiological thermal limits. In this study, we demonstrate that the manner in which the statistical bias has been addressed when evaluating the TOH, as measured at the intraspecific level by the change in thermal tolerance across two environments, is erroneous. This is because there has never been a statistically robust prediction for either a trade-off or a lack of trade-off in two-environment experiments, which is surprising given the importance of such predictions in this field. Here, we derive a statistical framework to correctly test the hypothesis that the observed change in thermal tolerance is consistent with TOH predictions. To demonstrate how our approach can alter the conclusions and interpretations of the TOH, we apply it to two existing datasets. We show that the TOH may indeed be valid, despite previous claims to the contrary, highlighting the critical importance of a sound statistical approach to avoid spurious conclusions that can have significant implications for our understanding of climate change responses.