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Here you can find a sampling of talks that I have given.

Stochastic persistence and extinction: Two long standing, fundamental questions in biology are “Under what conditions do populations persist or go extinct? When do interacting species coexist?” The answers to these questions are essential for guiding conservation efforts and identifying mechanisms that maintain biodiversity. Mathematical models play an important role in identifying these mechanisms and, when coupled with empirical work, can determine whether or not a given mechanism is operating in a specific population or community. For over a century, nonlinear difference and differential equations have been used to identify these mechanisms. These models, however, fail to account for stochastic fluctuations in environmental conditions such as temperature and precipitation. In this talk, I present theorems about persistence, coexistence, and extinction for stochastic difference equations that account for species interactions, population structure, and environmental fluctuations. The theorems are illustrated with models of Bay checkerspot butterflies, spatially structured acorn woodpecker populations, competition among annual plants, evolutionary games of and rock-paper-scissor. These slides are from a talk that I gave at Shanghai Normal University, Fudan University, Harbin Engineering University, an Renmin University during a 2019 trip to China . I have given variants of this talk at at the Neyman Seminar in UC/Berkeley, CIRM in France, IMA at University of Minnesota, University of Alberta, the BAMM conference in Richmond, VA, and the University of Pennsylvania.