To persist or not to persist?
Seminar | October 10 | 4-5 p.m. | 1011 Evans Hall
Sebastian Schreiber, UC Davis
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 will be illustrated with models of Bay checkerspot butterflies, spatially structured acorn woodpecker populations, competition among Kansas prairie grass species, and the evolutionary game of rock, paper, and scissors. This work is in collaboration with Michel Benaim.