Evolutionary dynamics in the Bak-Sneppen model on small-world networks

We study the dynamics of the Bak-Sneppen model on small-world networks. For each site in the network, we define a ``connectance,'' which measures the distance to all other sites. We find radically different patterns of activity for different sites, depending on their connectance and also on the topology of the network. For a given network, the site with the minimal connectance shows long periods of stasis interrupted by much smaller periods of activity. In contrast, the activity pattern for the maximally connected site appears uniform on the same time scale. We discuss the significance of these results for speciation events.