  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 an earlier paper, we gave biologically plausible
conditions under which the quasi-stationary distribution is unique, and can be
closely approximated by distributions that are simple to compute. In this
paper, we consider conditions under which the quasi-stationary distribution, if
it exists, need not be unique, but an apparent stochastic equilibrium can
nonetheless be identified and computed; we call such a distribution a
quasi-equilibrium distribution.
