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Strong bounds for evolution in networks

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

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Authors

P.G. Spirakis



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 Mar 28, 2024
Journal Journal of Computer and System Sciences
Print ISSN 0022-0000
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.

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