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

TL;DR

This paper investigates how the Bak-Sneppen model's dynamics vary on small-world networks, revealing that activity patterns depend heavily on site connectance and network topology, with implications for understanding speciation.

Contribution

It introduces the analysis of Bak-Sneppen model dynamics on small-world networks, highlighting the influence of connectance and topology on activity patterns.

Findings

Sites with minimal connectance exhibit long periods of inactivity and brief activity bursts.

Maximally connected sites show more uniform activity over time.

Network topology significantly affects the evolutionary dynamics observed.

Abstract

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.