Divergence of discrete- versus continuous-time calculations of the temperature dependence of maximum population growth rate in a disease vector

Abstract

The temperature dependence of maximal population growth rate (r_m) is key to predicting how organisms respond and adapt to natural and anthropogenic changes in climate. For organisms with complex life histories, discrete-time matrix projection models (MPMs) can be used to calculate temperature-dependent r_m because they directly capture variation in empirically-observed life-history trait values as well as the time delays inherent in those traits. However, MPM calculations can be laborious and do not capture the continuous nature of time. Temperature-dependent r_m calculated from more complex approaches based on delay-differential equation and integral projection models are more accurate but are notoriously difficult to parameterise. Ordinary differential equation-based models (ODEMs) offer a relatively tractable alternative of intermediate complexity but it is largely unknown whether ODEM-based calculations and MPMs broadly agree when the effects of time delays and altered juvenile survival trajectories on temperature-dependent r_m are introduced by environmental variation. Here we investigate differences in the predicted temperature dependence of r_m obtained from an ODE-based model with those calculated from MPMs using high-resolution temperature- and resource dependent life-history trait data for the globally-distributed disease vector, Aedes aegypti. We show that the level of agreement between discrete- and continuous-time representations of temperature-dependent r_m can vary with resource availability, and is extremely sensitive to how juvenile survival is characterised. This finding suggests that analytic r_m models can consistently provide comparable r_m predictions to standard methods except for under severe resource constraints. Our study also suggests that all formulations of the intrinsic growth rate of a population may not be equally accurate for all types of organisms in all situations. Furthermore, this study's findings raise questions relating to whether existing mathematical models can be used to predict and understand population-level effects of environmental change.