  We consider a model in which agents of different species move over a complex
network, are subject to reproduction and compete for resources. The
complementary roles of competition and diffusion produce a variety of fixed
points, whose stability depends on the structure of the underlying complex
network. The survival and death of species is influenced by the network degree
distribution, clustering, degree-degree correlations and community structures.
We found that the invasion of all the nodes by just one species is possible
only in Erdos-Renyi and regular graphs, while networks with scale--free degree
distribution, as those observed in real social, biological and technological
systems, guarantee the co-existence of different species and therefore help
enhancing species diversity.
