  Relations among species in ecosystems can be represented by complex networks
where both negative (competition) and positive (mutualism) interactions are
concurrently present. Recently, it has been shown that many ecosystems can be
cast into mutualistic networks, and that nestedness reduces effective
inter-species competition, thus facilitating mutually beneficial interactions
and increasing the number of coexisting species or the biodiversity. However,
current approaches neglect the structure of inter-species competition by
adopting a mean-field perspective that does not deal with competitive
interactions properly. Here, we introduce a framework based on the concept of
multilayer networks, which naturally accounts for both mutualism and
competition. Hence, we abandon the mean field hypothesis and show, through a
dynamical population model and numerical simulations, that there is an
intricate relation between competition and mutualism. Specifically, we show
that when all interactions are taken into account, mutualism does not have the
same consequences on the evolution of specialist and generalist species. This
leads to a non-trivial profile of biodiversity in the parameter space of
competition and mutualism. Our findings emphasize how the simultaneous
consideration of positive and negative interactions can contribute to our
understanding of the delicate trade-offs between topology and biodiversity in
ecosystems and call for a reconsideration of previous findings in theoretical
ecology, as they may affect the structural and dynamical stability of
mutualistic systems.
