Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics

Population dynamics models are useful predictive tools in applied ecology, and especially toxicological risk assessment. Many models that are useful for capturing deterministic constant-parameter dynamics are inadequate for dealing with temporally variable life history parameter values typical of many anthropogenic disturbances, including those associated with toxicological insults. Using aphid-insecticide population data as an example, here we show that constant-parameter versions of commonly used population dynamics models (a matrix model and a simple differential equation model) do not adequately capture the population dynamics of aphids subjected to a selective pesticide. However, a simple modification of the differential equation model with time-varying mortality rates provides a highly accurate fit to aphid population data. Our results suggest that variable coefficient differential equation models with time-dependent parameters provide an accurate and simple means of assessing the effects of disturbances on populations in cases where the effects of disturbance vary significantly through time. We suggest that this approach has potential for a wide range of ecological applications.