  We study the extinction risk of a fragmented population residing on a network
of patches coupled by migration, where the local patch dynamics include the
Allee effect. We show that mixing between patches dramatically influences the
population's viability. Slow migration is shown to always increase the
population's global extinction risk compared to the isolated case. At fast
migration, we demonstrate that synchrony between patches minimizes the
population's extinction risk. Moreover, we discover a critical migration rate
that maximizes the extinction risk of the population, and identify an
early-warning signal when approaching this state. Our theoretical results are
confirmed via the highly-efficient weighted ensemble method. Notably, our
analysis can also be applied to studying switching in gene regulatory networks
with multiple transcriptional states.
