  We consider populations with time-varying growth rates living in sinks. Each
population, when isolated, would become extinct. Dispersal-induced growth (DIG)
occurs when the populations are able to persist and grow exponentially when
dispersal among the populations is present. We provide a mathematical analysis
of this surprising phenomenon, in the context of a deterministic model with
periodic variation of growth rates and non-symmetric migration which are
assumed to be piecewise continuous. We also consider a stochastic model with
random variation of growth rates and migration. This work extends existing
results of the literature on the DIG effects obtained for periodic continuous
growth rates and time independent symmetric migration.
