Despite growing awareness of the shortcomings of static toxicological metrics such as the LC₅₀ or LD₅₀ for predicting the effects of chemical toxicants on non-target organisms, few reliable alternatives exist. Leslie matrix models allow the incorporation of age or stage class structure, and have been widely embraced as a more sophisticated means of modeling population endpoints. However, these models also are constrained by tradeoffs between realism and tractability, and in practice they are most often used with constant life history parameter values. Using a partial differential equation (pde) model, we present here a population dynamics approach to modeling toxicological risk that allows for the incorporation of stage structure as well as time-varying life history parameter values. The pde model does a better job of predicting aphid population responses to a Neem-based pesticide than the Leslie matrix model, particularly at higher concentrations (e.g. 60, 80 ppm). We discuss the potential for more general uses of this methodology.