Interplay between pesticide use and natural predator behaviors

We are interested in the combination of natural predators and conventional pesticides which contribute to the control of aphids, an agricultural pest. Although aphids are prey to many insects, the unique landscape for large-scale farming can reduce migration to and mobility within agricultural fields. In contrast, some small-scale and natural practices can foster an efficient natural predator community. Alongside these landscape choices, insecticide use can cause predator disorientation and sluggishness, further impacting mobility. To investigate how these different effects come together to determine pest control, we develop a partial differential equation model for predator-prey interactions within an agricultural field for a single season. We describe realistic use of pesticide sprays, which occur in pulses after pests pass a threshold abundance. The model also describes predator prey-taxis, or movement towards food sources, and how this behavior is impacted by pesticides. We consider these effects for a variety of migration and hunting behaviors and discuss the implications of our results for different agricultural practices.