  Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have
been used in biology to describe the steady state behaviour of population
models which, while eventually certain to become extinct, nevertheless maintain
an apparent stochastic equilibrium for long periods. These distributions have
some drawbacks: they need not exist, nor be unique, and their calculation can
present problems. In this paper, we give biologically plausible conditions
under which the quasi-stationary distribution is unique, and can be closely
approximated by distributions that are simple to compute.
