The effect of hubs and shortcuts on fixation time in evolutionary graphs

How can a new species (like a gene, an idea, or a strategy) take over the whole of a population? This process, which is called fixation , is considerably affected by the structure of the population. There are two key quantities to quantify the fixation process, namely fixation probability and fixation time. Fixation probability has been vastly studied in recent years, but fixation time has not been completely explored, yet. This is because the discovery of a relationship between fixation time and network structure is quite challenging. In this paper we investigate this relationship for a number of well-known complex networks. We show that the existence of a few high-degree nodes (hubs) in the network results in a longer fixation time, while the existence of a few short-cuts decreases the fixation time. Furthermore we investigate the effect of network parameters, such as connection probability, on fixation time. We show that by increasing the density of edges, fixation time decreases for all types of studied networks. Finally, we survey the effect of rewiring probability in a Watts–Strogatz network on fixation time. (paper: biological modelling and information)