### Abstract

As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, σ, of the distribution of the mutant effect. If 4Nσ is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4Nσ is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4Nσ is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4Nσ is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.

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

Pages (from-to) | 183-192 |

Number of pages | 10 |

Journal | Genetics |

Volume | 128 |

Issue number | 1 |

Publication status | Published - 1991 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Genetics
- Genetics(clinical)

### Cite this

*Genetics*,

*128*(1), 183-192.

**A study on a nearly neutral mutation model in finite populations.** / Tachida, Hidenori.

Research output: Contribution to journal › Article

*Genetics*, vol. 128, no. 1, pp. 183-192.

}

TY - JOUR

T1 - A study on a nearly neutral mutation model in finite populations

AU - Tachida, Hidenori

PY - 1991

Y1 - 1991

N2 - As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, σ, of the distribution of the mutant effect. If 4Nσ is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4Nσ is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4Nσ is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4Nσ is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.

AB - As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, σ, of the distribution of the mutant effect. If 4Nσ is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4Nσ is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4Nσ is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4Nσ is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.

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UR - http://www.scopus.com/inward/citedby.url?scp=0025862963&partnerID=8YFLogxK

M3 - Article

C2 - 2060776

AN - SCOPUS:0025862963

VL - 128

SP - 183

EP - 192

JO - Genetics

JF - Genetics

SN - 0016-6731

IS - 1

ER -