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What and Who
Title:Graphs on which evolution is more effective
Speaker:John Lapinskas
coming from:University of Oxford
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, D3, MMCI
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Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 28 June 2016
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
The Moran process is a randomised algorithm modelling the spread of genetic mutations in populations. The algorithm runs on an underlying graph where individuals correspond to vertices, starting with a single mutant placed uniformly at random with some fixed fitness. If the underlying graph is strongly connected then the algorithm will eventually reach either fixation, in which all individuals are mutants, or extinction, in which no individuals are mutants. An infinite family of directed graphs is said to be "strongly amplifying" if for any fixed (beneficial) fitness, the extinction probability tends to 0 as the number of vertices increases. Strong amplification is a rather surprising property — it means that beneficial mutations propagate to the entire population with probability tending to 1 even though the initial mutant only has a fixed selective advantage. We give the first rigorous proof that there is a strongly amplifying family of directed graphs ("megastars"), with fixation probability roughly 1 - n^{-1/2}. We also prove that the other candidates extant in the literature give substantially lower fixation probabilities.
Contact
Name(s):Holger Dell
Video Broadcast
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Created by:Holger Dell, 06/21/2016 04:37 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Holger Dell, 06/21/2016 04:37 PM -- Created document.