Effect of network topology in consumer-resource systems with species' dispersal and evolution

This paper considers consumer-resource systems, where the consumer moves on a fully- connected patch network and behaves like an agent. Using graph-theoretical method and dynamical systems theory, we show global equilibrium stability in the system. Analysis on the equilibrium demonstrates that when the dispersal rate is small, the effect of network topology is the result of the effect of each path in isolation. It is shown that varying network topology could lead to persistence and/or increase of the consumer. Moreover, agent-based selection on a network would make the network evolve to an evolutionary stable topology, where any small deviation to it will not lead to the increase of species. Our results have potential application in constructing ecological corridors and planning network topology under evolution.