  Mutualistic networks have attracted increasing attention in the ecological
literature in the last decades as they play a key role in the maintenance of
biodiversity. Here, we develop an analytical framework to study the structural
stability of these networks including both mutualistic and competitive
interactions. Analytical and numerical analyses show that the structure of the
competitive network fundamentally alters the necessary conditions for species
coexistence in communities. Using 50 real mutualistic networks, we show that
when the relative importance of shared partners is incorporated via weighted
competition, the feasibility area in the parameter space is highly correlated
with May's stability criteria and can be predicted by a functional relationship
between the number of species, the network connectance and the average
interaction strength in the community. Our work reopens a decade-long debate
about the complexity-stability relationship in ecological communities, and
highlights the role of the relative structures of different interaction types.
