Abstract
A system of replicators evolving on a surface is analysed. Population dynamics together with environmental constraints determine the network of interactions among species. We show that the mobility of individual elements, implemented as different values of the diffusion coefficient, plays a major role in shaping the topology of the emerging network by selecting simple network motifs during its evolution. This effect is fully quantified through the relative abundance of 3-node motifs and the clustering coefficient distribution. For large enough diffusion the behaviour crosses over to that of a well-stirred reactor, and parasites are able to disrupt the otherwise dynamically stable coexistence of species.