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Strong bounds for evolution in networks.

Mertzios, G.B. and Spirakis, P.G. (2018) 'Strong bounds for evolution in networks.', Journal of computer and system sciences., 97 . pp. 60-82.

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.

Item Type:Article
Keywords:Evolutionary dynamics, Undirected graphs, Fixation probability, Lower bound, Markov chain.
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.jcss.2018.04.004
Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:27 April 2018
Date deposited:30 April 2018
Date of first online publication:08 May 2018
Date first made open access:08 May 2019

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