  How high should be the rate of immigration into a stochastic population in
order to significantly reduce the probability of observing the population
extinct? Is there any relation between the population size distributions with
and without immigration? Under what conditions can one justify the simple patch
occupancy models which ignore the population distribution and its dynamics in a
patch, and treat a patch simply as either occupied or empty? We address these
questions by exactly solving a simple stochastic model obtained by adding a
steady immigration to a variant of the Verhulst model: a prototypical model of
an isolated stochastic population.
