Evolutionary game dynamics in a Wright-Fisher process

Journal of Mathematical Biology
Lorens A Imhof, Martin A Nowak

Abstract

Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.

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Citations

Jan 26, 2007·Journal of Mathematical Biology·Sabin Lessard, Véronique Ladret
Apr 7, 2010·Journal of Mathematical Biology·Mats Gyllenberg, Robert Service
Jun 1, 2011·Journal of Mathematical Biology·Bin WuArne Traulsen
Nov 28, 2012·Journal of Mathematical Biology·Tomas VelozAlejandro Fajardo
Apr 4, 2008·Bulletin of Mathematical Biology·Arne TraulsenMartin A Nowak
Oct 22, 2013·Journal of Theoretical Biology·Maria Abou Chakra, Arne Traulsen
May 13, 2009·Proceedings of the National Academy of Sciences of the United States of America·Corina E TarnitaMartin A Nowak
Aug 12, 2006·Proceedings. Biological Sciences·Hisashi Ohtsuki, Martin A Nowak
Jan 15, 2009·Proceedings. Biological Sciences·Shun Kurokawa, Yasuo Ihara
Oct 23, 2009·Proceedings. Biological Sciences·Lorens A Imhof, Martin A Nowak
Aug 29, 2012·PLoS Computational Biology·Maria Abou Chakra, Arne Traulsen
Jun 27, 2013·PloS One·Christian HilbeArne Traulsen
Mar 19, 2013·Journal of Mathematical Biology·Fabio A C C Chalub, Max O Souza
Nov 28, 2012·Journal of Mathematical Biology·Benjamin Allen, Corina E Tarnita
Mar 7, 2014·Journal of the Royal Society, Interface·Jinming DuLong Wang
Nov 12, 2013·Journal of Theoretical Biology·Oliver P HauserMartin A Nowak
Jul 16, 2013·Journal of Statistical Physics·Feng Fu, Martin A Nowaks
May 15, 2013·The American Naturalist·Benjamin AllenUlf Dieckmann
Jan 21, 2016·Scientific Reports·Kristin HagelArne Traulsen
Jan 16, 2016·Scientific Reports·Yi-Shin ChenWei Pan
May 5, 2012·Journal of Theoretical Biology·Changbing TangJingyuan Zhan
Nov 29, 2011·Theoretical Population Biology·Krishnendu ChatterjeeMartin A Nowak
Mar 17, 2010·Theoretical Population Biology·Shun KurokawaYasuo Ihara
Jan 26, 2010·Journal of Theoretical Biology·Hisashi Ohtsuki
Aug 4, 2009·Journal of Theoretical Biology·Corina E TarnitaMartin A Nowak
Apr 11, 2009·Journal of Theoretical Biology·Corina E TarnitaMartin A Nowak
Mar 3, 2009·Theoretical Population Biology·Sabin Lessard, Philippe Lahaie
Feb 24, 2009·Journal of Theoretical Biology·Koh Hashimoto, Kazuyuki Aihara
Mar 3, 2009·Journal of Theoretical Biology·Tibor AntalMartin A Nowak
Dec 30, 2008·Journal of Theoretical Biology·Tibor AntalArne Traulsen
Oct 22, 2008·Journal of Theoretical Biology·David G RandMartin A Nowak
Aug 13, 2008·Journal of Theoretical Biology·Véronique Ladret, Sabin Lessard
Dec 14, 2007·Journal of Theoretical Biology·Jorge M PachecoMartin A Nowak
Oct 2, 2007·Journal of Theoretical Biology·Christina Pawlowitsch
Sep 11, 2007·Journal of Theoretical Biology·Hisashi OhtsukiMartin A Nowak
Apr 28, 2007·Journal of Theoretical Biology·Geoff Wild, Arne Traulsen
May 1, 2007·Journal of Theoretical Biology·Hisashi Ohtsuki, Martin A Nowak
May 8, 2007·Journal of Theoretical Biology·Lorens A ImhofMartin A Nowak
Mar 14, 2007·Journal of Theoretical Biology·Hisashi OhtsukiMartin A Nowak
Feb 13, 2007·Journal of Theoretical Biology·Arne TraulsenMartin A Nowak
Sep 22, 2006·Theoretical Population Biology·Drew FudenbergLorens A Imhof
Aug 12, 2006·Journal of Theoretical Biology·Jorge M PachecoMartin A Nowak
Oct 2, 2015·Journal of the Royal Society, Interface·Alex McAvoy, Christoph Hauert
Jul 6, 2014·Journal of Theoretical Biology·Whan Ghang, Martin A Nowak
May 2, 2014·Journal of Theoretical Biology·Hyeong-Chai JeongMartin A Nowak
Jul 17, 2015·Proceedings. Biological Sciences·Johannes G ReiterKrishnendu Chatterjee

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