### Abstract

We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.

Original language | English |
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Pages (from-to) | 381-388 |

Number of pages | 8 |

Journal | Genetics |

Volume | 161 |

Issue number | 1 |

Publication status | Published - Jan 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Genetics

### Cite this

*Genetics*,

*161*(1), 381-388.

**A neutral model with fluctuating population size and its effective size.** / Iizuka, Masaru; Tachida, Hidenori; Matsuda, Hirotsugu.

Research output: Contribution to journal › Article

*Genetics*, vol. 161, no. 1, pp. 381-388.

}

TY - JOUR

T1 - A neutral model with fluctuating population size and its effective size

AU - Iizuka, Masaru

AU - Tachida, Hidenori

AU - Matsuda, Hirotsugu

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.

AB - We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.

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M3 - Article

C2 - 12019252

AN - SCOPUS:0036262931

VL - 161

SP - 381

EP - 388

JO - Genetics

JF - Genetics

SN - 0016-6731

IS - 1

ER -