  Source-sink systems are metapopulations of habitat patches with different,
and possibly temporally varying, habitat qualities, which are commonly used in
ecology to study the fate of spatially extended natural populations. We propose
new techniques that allow to disentangle the respective contributions of
demography and dispersal to the dynamics and fate of a single species in a
source-sink metapopulation. Our approach is valid for a general class of
stochastic, individual-based, stepping-stone models, with density-independent
demography and dispersal, provided the metapopulation is finite or else enjoys
some transitivity property. We provide 1) a simple criterion of persistence, by
studying the motion of a single random disperser until it returns to its
initial position; 2) a joint characterization of the long-term growth rate and
of the asymptotic occupancy frequencies of the ancestral lineage of a random
survivor, by using large deviations theory. Both techniques yield formulae
decoupling demography and dispersal, and can be adapted to the case of periodic
or random environments, where habitat qualities are autocorrelated in space and
possibly in time. In this last case, we display examples of coupled
time-averaged sinks allowing survival, as was previously known in the absence
of demographic stochasticity for fully mixing (Jansen and Yoshimura, 1998) and
even partially mixing (Evans et al., 2012; Schreiber, 2010) metapopulations.
