Abstract
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 Erdös-Renyi and regular graphs, while networks with scale-free degree distribution, as those observed in real social, biological and technological systems, guarantee the coexistence of different species and therefore help enhancing species diversity.