### Abstract

Language | English |
---|---|

Pages | 147-158 |

Number of pages | 12 |

Journal | Biometrics |

Volume | 24 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1968 |

Externally published | Yes |

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### Cite this

*Biometrics*,

*24*(1), 147-158. https://doi.org/10.2307/2528466

}

*Biometrics*, vol. 24, no. 1, pp. 147-158. https://doi.org/10.2307/2528466

**The multi-type Galton-Watson process in a genetical context.** / Pollard, J. H.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The multi-type Galton-Watson process in a genetical context

AU - Pollard, J. H.

PY - 1968/3

Y1 - 1968/3

N2 - In 1966 Ewens noted that the probability of fixation of a favourable new mutant linked to another gene is practically independent of the population size for a large random-mating population, and that what normally determines the fate of a new mutant gene is the behaviour of its frequency while it is rare. Because the relative frequency of the new mutant is small initially, he was able to obtain a linear recurrence relation over time for the expected relative frequencies of the two gametes which contain the mutant. This is a very interesting result, and immediately suggests a two-type Galton-Watson process as a suitable discrete-time stochastic model. In the present paper, some techniques associated with the multi-type Galton-Watson process and developed in the field of population mathematics are used to study the frequency of occurrence of a rare mutant gene. The use of these techniques in practice is demonstrated by the solution of a numerical example.

AB - In 1966 Ewens noted that the probability of fixation of a favourable new mutant linked to another gene is practically independent of the population size for a large random-mating population, and that what normally determines the fate of a new mutant gene is the behaviour of its frequency while it is rare. Because the relative frequency of the new mutant is small initially, he was able to obtain a linear recurrence relation over time for the expected relative frequencies of the two gametes which contain the mutant. This is a very interesting result, and immediately suggests a two-type Galton-Watson process as a suitable discrete-time stochastic model. In the present paper, some techniques associated with the multi-type Galton-Watson process and developed in the field of population mathematics are used to study the frequency of occurrence of a rare mutant gene. The use of these techniques in practice is demonstrated by the solution of a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=0014266161&partnerID=8YFLogxK

U2 - 10.2307/2528466

DO - 10.2307/2528466

M3 - Article

VL - 24

SP - 147

EP - 158

JO - Biometrics

T2 - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -