Coexistence and extinction for stochastic difference equations
Thursday, June 7, 2018 - 11:00am - 11:50am
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 discuss mathematical results about persistence, coexistence, and extinction for stochastic difference equations that account for these environmental fluctuations. The mathematical theorems will be illustrated with models of Bay checkerspot butterflies, spatially structured acorn woodpecker populations, rock-paper-scissor dynamics, and competition among Kansas prairie grass species. Much of this work is in collaboration with Michel Benaim.