How do stochastic environmental fluctuations influence the equilibrium of a dynamical system?
I will explain how one can analyze ecological systems governed by discrete-time dynamics (stochastic difference equations) and how, under natural assumptions, one can completely determine the long-term behavior of the system. If the system converges to a stationary distribution it is important to figure out how the average population sizes at stationarity differ from their equilibria in the absence of noise. Using the general theory, I will showcase some interesting examples and explain how environmental fluctuations can sometimes lead to population sizes increasing.