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J Math Biol. 2018 Jan;76(1-2):1-35. doi: 10.1007/s00285-017-1137-2. Epub 2017 May 16.

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

Author information

1
Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, MA, 01075, USA.
2
Department of Economics, Social Sciences University of Ankara, Hükümet Meydani No:2 Ulus, Ankara, Turkey.
3
Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA. matzavinos@brown.edu.
4
Computational Science and Engineering Laboratory, ETH Zürich, 8092, Zurich, Switzerland. matzavinos@brown.edu.
5
Department of Mathematics, Iowa State University, Ames, IA, 50011, USA.

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.

KEYWORDS:

Evolutionary game dynamics; Finite populations; Stochastic dynamics; Strong selection

PMID:
28509259
DOI:
10.1007/s00285-017-1137-2

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