A General Theory of Coexistence for Stochastic Populations

Dr. Alexandru Hening
Assistant Professor of Mathematics
Texas A&M University

One of the longstanding, fundamental problems in population biology is understanding the coexistence of multiple interacting species. In order to accurately model real ecosystems one needs a theory that takes into account the interplay between species interactions (predation, competition, mutualism, etc) and environmental stochasticity. Modern coexistence theory (MCT) is the most successful theory which incorporates all these factors. However, MCT has some significant drawbacks and rigorous mathematical results are only available in special settings. I will present a general theory of coexistence and extinction for populations modelled by stochastic differential equations, explain how the theory resolves an important conjecture by Pallis, and showcase with an illuminating example that environmental fluctuations can facilitate coexistence.