ABSTRACT

We study a general class of birth-and-death processes that describe the size of populations going to extinction with probability one. The scale of the population is measured in terms of a ‘carrying capacity’ K. When K is large, the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct. Our aim is to quantify the time for the process to reach the quasi-stationary regime and the mean time to extinction in the quasi-stationary distribution as a function of K, for large K. In dimension one, we also give a quantitative description of this quasistationary distribution.