Divergence of discrete- versus continuous-time calculations of the temperature dependence of maximum population growth rate

The temperature dependence of population fitness $\left(r_{\text{m}}\right)$ is key to predicting ectotherm responses to climatic change. Discrete-time matrix projection models (MPMs) are used to calculate $r_{\text{m}}$ because they capture variation in its underlying life-history trait values and time delays inherent in those traits. However, MPM calculations can be laborious and do not capture time's continuous nature. More complex approaches for calculating temperature-dependent $r_{\text{m}}$ may be more accurate but they are notoriously difficult to parameterise. Ordinary differential equation-based models (ODEMs) offer a relatively tractable alternative of intermediate complexity, but it is unknown whether they broadly agree with MPM calculations when environmental variation is introduced. Here we investigate differences in the predicted temperature dependence of $r_{\text{m}}$ obtained from an ODEM with those calculated from MPMs using temperature- and resource dependent life-history trait data for the disease vector, Aedes aegypti. We show that the level of agreement between discrete- and continuous-time representations of temperature-dependent $r_{\text{m}}$ can vary with resource availability and is extremely sensitive to juvenile survival characterisations. This finding suggests that ODEMs can only provide comparable $r_{\text{m}}$ predictions to standard methods when resources are not limiting, questioning the ability of existing mathematical models to reliably predict arthropod responses to environmental variation.