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Despite growing awareness of the need for better estimates of population responses to toxicological insults, most models rely on static estimates of life history traits. Using life history data from a series of lab experiments in which aphids were exposed to the Neem-based pesticide Margosan-O, we develop an ordinary differential equation model wth time-varying mortality rates. In particular, we tailor the time-varying mortality rates to reflect different effects of the pesticide (e.g., smothering, molt inhibition) at different life stage of the aphid. The ODE model allows us to solve an inverse problem in order to generate the optimal estimates of the mortality rates. We present this population dynamics approach to the problem of estimating population responses to chemical exposure, and discuss the potential for more general use of this methodology.

Keywords: Ordinary differential equation, least squares, inverse problem, Margosan-O, mortality rate, parameter estimate