Dynamic models for insect mortality due to exposure to insecticides

Models of population dynamics play a central role in our understanding of the effects of disturbance in both natural and managed ecosystems. One of the most persistent and pervasive anthropogenic disturbances continues to be the widespread use of chemical pesticides [6]. Because they are ubiquitous and are easy to manipulate in the laboratory and in the field, pesticides are ideally suited for exploring how altering vital rates of organisms affects population dynamics of in these settings. Furthermore, pesticide effects, like other anthropogenic and natural factors, are characterized by demographic parameters that change through time, and as such represent an ideal model system for exploring the relationship between vital rates and population processes. Reproductive and mortality rates, for instance, often vary temporally in both managed and natural systems and are easily manipulated via pesticide exposure. In such cases, simple constant-parameter models often are inadequate for capturing important population dynamics. In particular, time-varying parameters may provide a much better fit to population data that are subject to changes in vital rates that may increase or decrease through time. Differential equations models, which can represent vital rates in continuous time, are especially amenable to modeling population dynamics with time-varying parameters [4]. We present here an analysis of insect-pesticide population dynamics that explores the utility of employing differential equation models with time-varying vital rates as a means of predicting population outcomes.