The Two Regimes of Neutral Evolution: Localization on Hubs and Delocalized Diffusion

It has been argued that much of evolution takes place in the absence of fitness gradients. Such periods of evolution can be analysed by examining the mutational network formed by sequences of equal fitness, that is the neutral network. It has been demonstrated that, in large populations under a high mutation rate, the population distribution over the neutral network and average mutational robustness are given by the principle eigenvector and eigenvalue, respectively, of the network’s adjacency matrix. However, little progress has been made towards understanding the manner in which the topology of the neutral network influences the resulting population distribution and robustness. In this work, we build on recent results from spectral graph theory and utilize numerical methods to demonstrate that there exist two regimes of behaviour: convergence on hubs and diffusion over the network. We also derive approximations for the population’s behaviour under these regimes. This challenges the widespread assumption that neutral evolution always leads to exploration of the neutral network and elucidates the conditions which result in the evolution of robust organisms