Global temperatures are expected to rise between 1.1 and 6.4°C over the next 100 years, although the exact rate will depend on future greenhouse emissions, and will vary spatially. Temperature can alter an individual's metabolic rate, and consequently birth and death rates. In declining populations, these alterations may manifest as changes in the rate of that population's decline, and subsequently the timing of extinction events. Predicting such events could therefore be of considerable use. We use a small-scale experimental system to investigate how the rate of temperature change can alter a population's time to extinction, and whether it is possible to predict this event using a simple phenomenological model that incorporates information about population dynamics at a constant temperature, published scaling of metabolic rates, and temperature. In addition, we examine 1) the relative importance of the direct effects of temperature on metabolic rate, and the indirect effects (via temperature driven changes in body size), on predictive accuracy (defined as the proximity of the predicted date of extinction to the mean observed date of extinction), 2) the combinations of model parameters that maximise accuracy of predictions, and 3) whether substituting temperature change through time with mean temperature produces accurate predictions. We find that extinction occurs earlier in environments that warm faster, and this can be accurately predicted (R2 > 0.84). Increasing the number of parameters that were temperature-dependent increased the model's accuracy, as did scaling these temperature-dependent parameters with either the direct effects of temperature alone, or with the direct and indirect effects. Using mean temperature through time instead of actual temperature produces less accurate predictions of extinction. These results suggest that simple phenomenological models, incorporating metabolic theory, may be useful in understanding how environmental change can alter a population's rate of extinction.
Understanding how populations will respond to future climatic change is a key goal in ecology, however the exact rate of future warming will vary both spatially and temporally. Consequently, mathematical models must be used to understand the potential range of future population dynamics under various warming scenarios. We use a combination of experimentation and modelling to show that the effects of varying rates of environmental change on population dynamics can be predicted by a simple model. However, the accuracy of these predictions depends upon, amongst other things, a detailed knowledge of how temperature will change over time, rather than approximating this change to mean temperature.