### Abstract

Original language | English |
---|---|

Pages (from-to) | 993-1006 |

Number of pages | 14 |

Journal | Genetics |

Volume | 195 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Nov 2013 |

### Fingerprint

### Keywords

- allele fixation
- random genetic drift
- diffusion analysis
- genetic disease progression
- population genetics theory
- stochastic population dynamics

### Cite this

*Genetics*,

*195*(3), 993-1006. https://doi.org/10.1534/genetics.113.156059

}

*Genetics*, vol. 195, no. 3, pp. 993-1006. https://doi.org/10.1534/genetics.113.156059

**The characteristic trajectory of a fixing allele: a consequence of fictitious selection that arises from conditioning.** / Zhao, L.; Lascoux, M.; Overall, Andrew; Waxman, D.

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

TY - JOUR

T1 - The characteristic trajectory of a fixing allele: a consequence of fictitious selection that arises from conditioning

AU - Zhao, L.

AU - Lascoux, M.

AU - Overall, Andrew

AU - Waxman, D.

PY - 2013/11/1

Y1 - 2013/11/1

N2 - This work is concerned with the historical progression, to fixation, of an allele in a finite population. This progression is characterized by the average frequency trajectory of alleles that achieve fixation before a given time, T. Under a diffusion analysis, the average trajectory, conditional on fixation by time T, is shown to be equivalent to the average trajectory in an unconditioned problem involving additional selection. We call this additional selection "fictitious selection"; it plays the role of a selective force in the unconditioned problem but does not exist in reality. It is a consequence of conditioning on fixation. The fictitious selection is frequency dependent and can be very large compared with any real selection that is acting. We derive an approximation for the characteristic trajectory of a fixing allele, when subject to real additive selection, from an unconditioned problem, where the total selection is a combination of real and fictitious selection. Trying to reproduce the characteristic trajectory from the action of additive selection, in an infinite population, can lead to estimates of the strength of the selection that deviate from the real selection by >1000% or have the opposite sign. Strong evolutionary forces may be invoked in problems where conditioning has been carried out, but these forces may largely be an outcome of the conditioning and hence may not have a real existence. The work presented here clarifies these issues and provides two useful tools for future analyses: the characteristic trajectory of a fixing allele and the force that primarily drives this, namely fictitious selection. These should prove useful in a number of areas of interest including coalescence with selection, experimental evolution, time series analyses of ancient DNA, game theory in finite populations, and the historical dynamics of selected alleles in wild populations.

AB - This work is concerned with the historical progression, to fixation, of an allele in a finite population. This progression is characterized by the average frequency trajectory of alleles that achieve fixation before a given time, T. Under a diffusion analysis, the average trajectory, conditional on fixation by time T, is shown to be equivalent to the average trajectory in an unconditioned problem involving additional selection. We call this additional selection "fictitious selection"; it plays the role of a selective force in the unconditioned problem but does not exist in reality. It is a consequence of conditioning on fixation. The fictitious selection is frequency dependent and can be very large compared with any real selection that is acting. We derive an approximation for the characteristic trajectory of a fixing allele, when subject to real additive selection, from an unconditioned problem, where the total selection is a combination of real and fictitious selection. Trying to reproduce the characteristic trajectory from the action of additive selection, in an infinite population, can lead to estimates of the strength of the selection that deviate from the real selection by >1000% or have the opposite sign. Strong evolutionary forces may be invoked in problems where conditioning has been carried out, but these forces may largely be an outcome of the conditioning and hence may not have a real existence. The work presented here clarifies these issues and provides two useful tools for future analyses: the characteristic trajectory of a fixing allele and the force that primarily drives this, namely fictitious selection. These should prove useful in a number of areas of interest including coalescence with selection, experimental evolution, time series analyses of ancient DNA, game theory in finite populations, and the historical dynamics of selected alleles in wild populations.

KW - allele fixation

KW - random genetic drift

KW - diffusion analysis

KW - genetic disease progression

KW - population genetics theory

KW - stochastic population dynamics

U2 - 10.1534/genetics.113.156059

DO - 10.1534/genetics.113.156059

M3 - Article

VL - 195

SP - 993

EP - 1006

JO - Genetics

JF - Genetics

SN - 0016-6731

IS - 3

ER -