Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher model

Journal of Mathematical Biology
Timothy ChumleyAlexander Roitershtein

Abstract

We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type Markov chain with a frequency dependent fitness. In a strong selection regime that favors one of the two groups, we obtain qualitatively matching lower and upper bounds for the fixation probability of the advantageous population. In the infinite population limit we obtain an exact result showing that a single advantageous mutant can invade an infinite population with a positive probability. We also give asymptotically sharp bounds for the fixation time distribution.

References

Feb 19, 1998·Theoretical Population Biology·B Rannala
Apr 9, 2004·Nature·Martin A NowakDrew Fudenberg
Nov 4, 2004·Bulletin of Mathematical Biology·Christine TaylorMartin A Nowak
Feb 8, 2006·Journal of Mathematical Biology·Lorens A Imhof, Martin A Nowak
Mar 17, 2006·Artificial Life·Seth Bullock, Mark A Bedau
Sep 22, 2006·Theoretical Population Biology·Drew FudenbergLorens A Imhof
Nov 7, 2006·Bulletin of Mathematical Biology·Tibor Antal, István Scheuring
Jan 26, 2007·Journal of Mathematical Biology·Sabin Lessard, Véronique Ladret
Jul 31, 2008·Journal of the Royal Society, Interface·Z Patwa, L M Wahl
Jan 7, 2009·Proceedings of the National Academy of Sciences of the United States of America·Arne TraulsenKarl Sigmund
Dec 17, 2009·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Martin A NowakTibor Antal
Feb 10, 2010·Proceedings of the National Academy of Sciences of the United States of America·Arne TraulsenManfred Milinski
Nov 28, 2012·Journal of Mathematical Biology·Benjamin Allen, Corina E Tarnita
Mar 19, 2013·Journal of Mathematical Biology·Fabio A C C Chalub, Max O Souza
Sep 10, 2014·The Quarterly Review of Biology·David M McCandlish, Arlin Stoltzfus
Oct 28, 2014·Scientific Reports·Ben Adlam, Martin A Nowak
Dec 3, 2014·Theoretical Population Biology·David M McCandlishJoshua B Plotkin

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Citations

May 27, 2020·PLoS Computational Biology·Paul LemarreSuzanne S Sindi
Jul 18, 2018·Physical Review. E·Daniel B WilsonMaria Bruna
Jul 25, 2020·Journal of Mathematical Biology·Gorgui GackouArnaud Personne

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