  Understanding the dynamics of metapopulations close to extinction is of vital
importance for management. Levins-like models, in which local patches are
treated as either occupied or empty, have been used extensively for this
purpose, but they ignore the important role of local population dynamics. In
this paper, we consider a stochastic metapopulation model where local
populations follow a Ricker dynamics, and use this framework to investigate the
behaviour of the metapopulation at the brink of extinction. As long as
dispersal rates are not too large, the system is shown to have a time evolution
consistent with Levins' dynamics. We derive analytical expressions for the
colonisation and extinction rates (c and e) in Levins-type models in terms of
reproduction, survival, and dispersal parameters of the local populations,
providing an avenue to parameterising Levins-like models from the type of
information on local demography that is available for a number of species. To
facilitate applying our results, we provide a numerical implementation for
computing c and e.
