  On a global level, ecological communities are being perturbed at an
unprecedented rate by human activities and environmental instabilities. Yet, we
understand little about what factors facilitate or impede long-term persistence
of these communities. While observational studies indicate that increased
biodiversity must, somehow, be driving stability, theoretical studies have
argued the exact opposite viewpoint instead. This encouraged many researchers
to participate in the ongoing diversity-stability debate. Within this context,
however, there has been a severe lack of studies that consider spatial features
explicitly, even though nearly all habitats are spatially embedded. To this
end, we study here the linear stability of meta-ecosystems on networks that
describe how discrete patches are connected by dispersal between them. By
combining results from random matrix theory and network theory, we are able to
show that there are three distinct features that underlie stability: edge
density, tendency to triadic closure, and isolation or fragmentation. Our
results appear to further indicate that network sparsity does not necessarily
reduce stability, and that connections between patches are just as, if not
more, important to consider when studying the stability of large ecological
systems.
