### Abstract

We present a revision of Maynard Smith's evolutionary stability criteria for populations which are very large (though technically finite) and of unknown size. We call this the large population ESS, as distinct from Maynard Smith's infinite population ESS and Schaffer's finite population ESS. Building on Schaffer's finite population model, we define the large population ESS as a strategy which cannot be invaded by any finite number of mutants, as long as the population size is sufficiently large. The large population ESS is not equivalent to the infinite population ESS: we give examples of games in which a large population ESS exists but an infinite population ESS does not, and vice versa. Our main contribution is a simple set of two criteria for a large population ESS, which are similar (but not identical) to those originally proposed by Maynard Smith for infinite populations.

Original language | English (US) |
---|---|

Pages (from-to) | 397-401 |

Number of pages | 5 |

Journal | Journal of Theoretical Biology |

Volume | 227 |

Issue number | 3 |

DOIs | |

State | Published - Apr 7 2004 |

### Fingerprint

### Keywords

- ESS
- Evolutionary stability
- Large populations

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)

### Cite this

**Evolutionary stability for large populations.** / Neill, Daniel.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 227, no. 3, pp. 397-401. https://doi.org/10.1016/j.jtbi.2003.11.017

}

TY - JOUR

T1 - Evolutionary stability for large populations

AU - Neill, Daniel

PY - 2004/4/7

Y1 - 2004/4/7

N2 - We present a revision of Maynard Smith's evolutionary stability criteria for populations which are very large (though technically finite) and of unknown size. We call this the large population ESS, as distinct from Maynard Smith's infinite population ESS and Schaffer's finite population ESS. Building on Schaffer's finite population model, we define the large population ESS as a strategy which cannot be invaded by any finite number of mutants, as long as the population size is sufficiently large. The large population ESS is not equivalent to the infinite population ESS: we give examples of games in which a large population ESS exists but an infinite population ESS does not, and vice versa. Our main contribution is a simple set of two criteria for a large population ESS, which are similar (but not identical) to those originally proposed by Maynard Smith for infinite populations.

AB - We present a revision of Maynard Smith's evolutionary stability criteria for populations which are very large (though technically finite) and of unknown size. We call this the large population ESS, as distinct from Maynard Smith's infinite population ESS and Schaffer's finite population ESS. Building on Schaffer's finite population model, we define the large population ESS as a strategy which cannot be invaded by any finite number of mutants, as long as the population size is sufficiently large. The large population ESS is not equivalent to the infinite population ESS: we give examples of games in which a large population ESS exists but an infinite population ESS does not, and vice versa. Our main contribution is a simple set of two criteria for a large population ESS, which are similar (but not identical) to those originally proposed by Maynard Smith for infinite populations.

KW - ESS

KW - Evolutionary stability

KW - Large populations

UR - http://www.scopus.com/inward/record.url?scp=1542268956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542268956&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2003.11.017

DO - 10.1016/j.jtbi.2003.11.017

M3 - Article

VL - 227

SP - 397

EP - 401

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 3

ER -