Stability of stochastic systems
Working with José Ponciano at the University of Florida, this project will integrate new mathematical ideas and models with empirical field observations to study the properties of populations that experience large fluctuations. This will allow us to test fundamental assumptions about how populations are structured. We will focus on populations that experience regular cycles, a common phenomenon arising through factors such as competition for resources or predator-prey interactions. The mathematical ideas and models developed in this project will use techniques similar to those that economists use to project stock market fluctuations or meteorologists use to predict paths of hurricanes.
Optimal survey design
This work with Laura Jiménez and John Fieberg is focused on designing survey strategies inspired by the strategies that predators use to look for prey. Our work shows that the search for prey by predators can be used as a model for understanding animal abundance survey techniques. However, there also can be important differences as well because past results from foraging theory that have not accounted for uncertainty in the detection of prey, a critical component of many survey techniques. More information on this work is at https://zebramusselsurveys.netlify.com/.