Modelling the long-term behaviour of evanescent ecological systems

We shall present conditions for the existence of quasistationary distributions for a large class of processes which arise in ecological modelling. These conditions are usually easy to check, because they are expressed solely in terms of the transition rates which define the model. Our results will be illustrated with reference to birth-death processes and the birth-death and catastrophe process. We also address computational issues connected with modelling large-scale systems.