# CAM Colloquium: Alex Hening (Tufts) - Stochastic coexistence theory and the competitive exclusion principle

## Location

Frank H. T. Rhodes Hall 655

## Description

Abstract:

The competitive exclusion principle states in its simplest form that a number of species competing for a smaller number of resources cannot coexist. Nevertheless, in nature there are many cases where this is not true. Both experimental and theoretical studies have shown that in some instances temporal fluctuations of the environment can facilitate coexistence. Hutchinson conjectured that one can get coexistence because nonequilibrium conditions can make it possible for different species to be favored by the environment at different times. In this talk I will look at how random environmental fluctuations influence competitive exclusion. I will first discuss the theory of stochastic coexistence. After general conditions for coexistence, I will focus on ecological systems modeled by stochastic differential equations and piecewise deterministic Markov processes. In particular, I will show that, contrary to Hutchinson's explanation, one can switch between two environments in which the same species is favored and still get coexistence.

Bio:

I am an Assistant Professor in the Department of Mathematics at Tufts University. Previously I was a Chapman Fellow at Imperial College London and a postdoctoral researcher at Oxford University. I received my Ph.D. in May 2013 from UC Berkeley. My advisor was Steve Evans. I am interested in stochastic processes, mathematical biology, and dynamical systems. You can find more information in my CV.

My research is in part supported by the National Science Foundation under the grant DMS 1853463.