  We study the phenomenon of multistability in mutualistic networks of plants
and pollinators, where one desired state in which all species coexist competes
with multiple states in which some species are gone extinct. In this setting,
we examine the relation between the endangerment of pollinator species and
their position within the mutualistic network. To this end, we compare
endangerment rankings which are derived from the species' probabilities of
going extinct due to random shock perturbations with rankings obtained from
different network theoretic centrality metrics. We find that a pollinator's
endangerment is strongly linked to its degree of mutualistic specialization and
its position within the core-periphery structure of its mutualistic network,
with the most endangered species being specialists in the outer periphery.
Since particularly well established instances of such peripheral areas are
tree-shaped structures which stem from links between nodes/species in the
outermost shell of the network, we summarized our findings in the admittedly
ambiguous slogan 'keep the bees off the trees'. Finally, we challenge the
generality of our findings by testing whether the title of this work still
applies when being located in the outer periphery allows pollinators to avoid
competitive pressure.
