@article{bansaye_past_2013,
Author = {Bansaye, Vincent and Lambert, Amaury},
Title = {Past, growth and persistence of source-sink
metapopulations},
Journal = {Theoretical Population Biology},
Volume = {88},
Pages = {31--46},
abstract = {Source-sink systems are metapopulations of patches
that can be of variable habitat quality. They can be
seen as graphs, where vertices represent the patches,
and the weighted oriented edges give the probability of
dispersal from one patch to another. We consider either
finite or source-transitive graphs, i.e., graphs that
are identical when viewed from a(ny) source. We assume
stochastic, individual-based, density-independent
reproduction and dispersal. By studying the path of a
single random disperser, we are able to display simple
criteria for persistence, either necessary and
sufficient, or just sufficient. In case of persistence,
we characterize the growth rate of the population as
well as the asymptotic occupancy frequencies of the
line of ascent of a random survivor. Our method allows
to decouple the roles of reproduction and dispersal.
Finally, we extend our results to the case of periodic
or random environments, where some habitats can have
variable growth rates, autocorrelated in space and
possibly in time. In the whole manuscript, special
attention is given to the example of regular graphs
where each pair of adjacent sources is separated by the
same number of identical sinks. In the case of a
periodic and random environment, we also display
examples where all patches are sinks when forbidding
dispersal but the metapopulation survives with positive
probability in the presence of dispersal, as previously
known for a two-patch mean-field model with
parent-independent dispersal.},
year = 2013
}