A fundamental problem in ecology is to understand when it is possible for one species to invade the range of another, established species.
There is widespread empirical evidence that invasions can occur when there is significant heterogeneity in space and time in the range of the resident species.
We propose a model for the invasion process with a view to understanding what factors make invasion possible. The model reduces to studying a coupled system of two stochastic differential equations. By introducing the concept of invasion rate we are able to fully characterize the conditions on the coefficients of the SDEs under which invasion is possible or impossible. This is based on joint work with Steve Evans from
UC Berkeley and Sebastian Schreiber from UC Davis.