Lewis This is a National Science Foundation Young Investigator grant. Under its auspices, the investigator studies mechanisms that give rise to spatial patterns of self-organization in biological populations. These include territories, herds and swarms, and also spatial invasion/extinction processes. Models are expressed as nonlinear partial differential equations. Analysis entails methods from bifurcation theory, singular and regular perturbation theory, and computation. This project focuses on three main environmental applications: (1) the process of swarm formation in insects such as locusts, (2) the movement, spread and fate of genetically engineered microbes applied in agricultural systems, and (3) the process of territorial pattern formation in animals such as wolves and badgers. An understanding of these processes of population aggregation, invasion and extinction, and territorial pattern formation is key in evaluating the ecological impact that a population has in the environment. Such processes depend not only on individual movements but also on complex spatial behavioral interactions between individuals. While developing new biological models, this research employs a blend of applied mathematical analysis and large-scale numerical computation to analyse them. The models are evaluated by their ability to predict and explain data observed in the field.
