Strong bounds for evolution in networks

Mertzios, G.B.; Spirakis, P.G.

Abstract

This work studies the generalized Moran process, as introduced by Lieberman et al. [Nature, 433:312-316, 2005]. We introduce the parameterized notions of selective amplifiers and selective suppressors of evolution, i.e. of networks (graphs) with many “strong starts” and many “weak starts” for the mutant, respectively. We first prove the existence of strong selective amplifiers and of (quite) strong selective suppressors. Furthermore we provide strong upper bounds and almost tight lower bounds (by proving the “Thermal Theorem”) for the traditional notion of fixation probability of Lieberman et al., i.e. assuming a random initial placement of the mutant.

Citation

Mertzios, G., & Spirakis, P. (2018). Strong bounds for evolution in networks. Journal of Computer and System Sciences, 97, 60-82. https://doi.org/10.1016/j.jcss.2018.04.004

• Journal Article Type: Article
• Acceptance Date: Apr 27, 2018
• Online Publication Date: May 8, 2018
• Publication Date: Nov 1, 2018
• Deposit Date: Apr 27, 2018
• Publicly Available Date: May 8, 2019
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Electronic ISSN: 1090-2724
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 97
• Pages: 60-82
• DOI: https://doi.org/10.1016/j.jcss.2018.04.004
• Keywords: Evolutionary dynamics, Undirected graphs, Fixation probability, Lower bound, Markov chain.
• Public URL: https://durham-repository.worktribe.com/output/1327990