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Source-sink systems are metapopulations of habitat patches with different,and possibly temporally varying, habitat qualities, which are commonly used inecology to study the fate of spatially extended natural populations. We proposenew techniques that allow to disentangle the respective contributions ofdemography and dispersal to the dynamics and fate of a single species in asource-sink metapopulation. Our approach is valid for a general class ofstochastic, individual-based, stepping-stone models, with density-independentdemography and dispersal, provided the metapopulation is finite or else enjoyssome transitivity property. We provide 1) a simple criterion of persistence, bystudying the motion of a single random disperser until it returns to itsinitial position; 2) a joint characterization of the long-term growth rate andof the asymptotic occupancy frequencies of the ancestral lineage of a randomsurvivor, by using large deviations theory. Both techniques yield formulaedecoupling demography and dispersal, and can be adapted to the case of periodicor random environments, where habitat qualities are autocorrelated in space andpossibly in time. In this last case, we display examples of coupledtime-averaged sinks allowing survival, as was previously known in the absenceof demographic stochasticity for fully mixing (Jansen and Yoshimura, 1998) andeven partially mixing (Evans et al., 2012; Schreiber, 2010) metapopulations.

New approaches of source-sink metapopulations decoupling the roles of demography and dispersal