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