Figure 4. Single parameter changes in the Briere and flexTPC models.

In each panel, we show the effects on the thermal performance curve when a single parameter of the corresponding TPC model is changed while keeping all other parameters constant. For parameters other than m in the Briere model, a fixed value of $m=2$ is used (corresponding to the Briere1 model). We show the parameter values for both parametrizations of flexTPC (Equations 3 and 6), which differ on whether the optimal temperature and approximate upper thermal breadth are in unitless ($\alpha ,\beta$) or dimensional ($T_{opt},B$) form, but are otherwise identical and describe the same set of curves. Since flexTPC has biologically interpretable parameters, changing a single parameter (e.g., $T_{min}$) will change the thermal performance curve in a predictable way (as the rest of the parameters that are kept constant correspond to known curve properties). In contrast, in a model where some parameters are mathematical constants without a direct biological interpretation, changing a parameter can lead to unintuitive and possibly unintended changes in the thermal performance curve (e.g., changing $T_{min}$ also leads to changes on the height of the curve for the Briere model). This has important consequences when modeling changes in TPCs due to evolutionary or environmental factors, and when interpreting sensitivity analyses of derived quantities from TPC models (see Box 1). Note that decreasing parameter $T_{min}$ to negative values in the Briere model does not lead to models with positive performance below 0°C (see Methods).